Comparison of DFT solvers

We compare four different approaches for solving the DFT minimisation problem, namely a density-based SCF, a potential-based SCF, direct minimisation and Newton.

First we setup our problem

In [1]:
using DFTK
using LinearAlgebra

a = 10.26  # Silicon lattice constant in Bohr
lattice = a / 2 * [[0 1 1.];
                   [1 0 1.];
                   [1 1 0.]]
Si = ElementPsp(:Si, psp=load_psp("hgh/lda/Si-q4"))
atoms     = [Si, Si]
positions = [ones(3)/8, -ones(3)/8]

model = model_LDA(lattice, atoms, positions)
basis = PlaneWaveBasis(model; Ecut=5, kgrid=[3, 3, 3])

# Convergence we desire
tol = 1e-12
is_converged = DFTK.ScfConvergenceDensity(tol)
Out[1]:
#512 (generic function with 1 method)

Density-based self-consistent field

In [2]:
scfres_scf = self_consistent_field(basis; is_converged)
n     Energy            log10(ΔE)   log10(Δρ)   Diag
---   ---------------   ---------   ---------   ----
  1   -7.846842727876                   -0.70    4.2
  2   -7.852322843061       -2.26       -1.53    1.0
  3   -7.852646088990       -3.49       -2.52    3.2
  4   -7.852646678900       -6.23       -3.36    2.5
  5   -7.852646686053       -8.15       -4.82    1.0
  6   -7.852646686726       -9.17       -5.24    3.8
  7   -7.852646686730      -11.39       -6.09    1.0
  8   -7.852646686730      -12.60       -7.25    2.8
  9   -7.852646686730   +    -Inf       -7.59    2.2
 10   -7.852646686730      -14.75       -8.40    2.0
 11   -7.852646686730   +  -14.57       -9.56    2.0
 12   -7.852646686730      -15.05       -9.37    1.2
 13   -7.852646686730   +    -Inf      -10.56    1.8
 14   -7.852646686730   +    -Inf      -10.68    2.0
 15   -7.852646686730   +    -Inf      -11.47    1.0
 16   -7.852646686730   +  -14.57      -11.63    1.8
 17   -7.852646686730      -14.57      -11.90    1.0
 18   -7.852646686730      -14.75      -12.22    1.2
Out[2]:
(ham = Hamiltonian(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), HamiltonianBlock[DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [0.0, 0.5625437115174675, 2.25017484606987, 2.25017484606987, 0.5625437115174675, 0.5625437115174675, 0.7500582820232901, 2.0626602755640477, 4.50034969213974, 3.5627768396106276  …  3.7502914101164504, 3.7502914101164504, 2.0626602755640477, 1.5001165640465801, 0.7500582820232901, 2.0626602755640477, 4.50034969213974, 3.5627768396106276, 1.5001165640465801, 0.5625437115174675]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [-0.30116136598756804 -0.36869760795125184 … -0.5702190219244254 -0.36869760795125195; -0.3686976079512516 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456163; … ; -0.5702190219244256 -0.264614164394795 … -2.291992881132685 -1.1751172086054253; -0.3686976079512515 -0.2539389812456162 … -1.1751172086054256 -0.6560706269776425;;; -0.3686976079512517 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456166; -0.6560706269776425 -1.3741022038947448 … -0.1651225671881503 -0.31565743774427135; … ; -0.2646141643947949 -0.16512256718815066 … -0.8632000905877295 -0.4898593856167607; -0.25393898124561615 -0.31565743774427135 … -0.48985938561676046 -0.31565743774427124;;; -0.5702190219244254 -1.1751172086054258 … -0.1242245197168452 -0.264614164394795; -1.1751172086054256 -2.8292222589777416 … -0.1750685951638031 -0.48985938561676046; … ; -0.1242245197168452 -0.1750685951638037 … -0.30112950922681153 -0.17506859516380358; -0.2646141643947948 -0.48985938561676046 … -0.17506859516380294 -0.1651225671881503;;; … ;;; -0.8720732197039092 -0.36117451106748844 … -3.5504427268225025 -1.881971917366274; -0.3611745110674882 -0.13192205269891222 … -1.3219289313234115 -0.747481991474731; … ; -3.5504427268225025 -1.3219289313234115 … -11.011681230319526 -8.06878895093237; -1.8819719173662737 -0.747481991474731 … -8.06878895093237 -4.5798976647669045;;; -0.5702190219244254 -0.2646141643947948 … -2.2919928811326855 -1.1751172086054256; -0.2646141643947947 -0.16512256718815055 … -0.8632000905877295 -0.48985938561676046; … ; -2.2919928811326855 -0.8632000905877297 … -11.026309596728632 -6.029372075563462; -1.1751172086054253 -0.4898593856167603 … -6.029372075563462 -2.8292222589777416;;; -0.3686976079512518 -0.2539389812456165 … -1.1751172086054256 -0.6560706269776427; -0.25393898124561626 -0.3156574377442714 … -0.4898593856167604 -0.31565743774427135; … ; -1.1751172086054256 -0.48985938561676057 … -6.029372075563461 -2.829222258977741; -0.6560706269776424 -0.3156574377442712 … -2.829222258977741 -1.3741022038947448]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), ComplexF64[0.11164094023604486 + 0.0im 0.1729534009156557 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.07139183057793365 - 0.07139183057793365im 0.10318729458139622 - 0.10318729458139622im … -0.035578676822652595 + 0.035578676822652595im 0.035578676822652595 - 0.035578676822652595im; … ; -0.08538801146445177 + 0.0im -0.10864081623630145 + 0.0im … 0.0 + 0.08076812854291712im 0.0 - 0.0im; -0.07139183057793365 + 0.07139183057793365im -0.10318729458139622 + 0.10318729458139622im … -0.035578676822652595 + 0.035578676822652595im -0.035578676822652595 + 0.035578676822652595im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [0.39155563703350926 0.37851742089980084 … 0.3446996002702456 0.3785174208998008; 0.37851742089980067 0.36645844064796645 … 0.32735728172229467 0.3636495426205898; … ; 0.3446996002702455 0.32735728172229467 … 0.30751926941856966 0.33438053198661; 0.37851742089980067 0.3636495426205898 … 0.33438053198661005 0.36645844064796645;;; 0.3785174208998008 0.3664584406479666 … 0.32735728172229484 0.3636495426205899; 0.3664584406479665 0.35102886341776024 … 0.311194013460622 0.3519170663492357; … ; 0.3273572817222947 0.311194013460622 … 0.2982412284122674 0.32142600281512734; 0.3636495426205898 0.35191706634923564 … 0.3214260028151274 0.35191706634923564;;; 0.34469960027024554 0.3343805319866101 … 0.2865351537639698 0.3273572817222948; 0.33438053198661 0.3186160477630048 … 0.27805891882351624 0.3214260028151274; … ; 0.2865351537639697 0.27805891882351624 … 0.25590185772314566 0.27805891882351624; 0.3273572817222946 0.32142600281512734 … 0.27805891882351624 0.311194013460622;;; … ;;; 0.304874749289073 0.2830366689624084 … 0.28556433231756906 0.3009573705184396; 0.28303666896240826 0.25898431622276247 … 0.2726330012865946 0.28541419662665096; … ; 0.285564332317569 0.2726330012865946 … 0.27716038913773156 0.2812108737838244; 0.30095737051843946 0.28541419662665096 … 0.2812108737838245 0.2930827262717236;;; 0.34469960027024554 0.3273572817222948 … 0.30751926941856983 0.3343805319866101; 0.32735728172229467 0.3111940134606219 … 0.2982412284122674 0.32142600281512734; … ; 0.3075192694185697 0.2982412284122674 … 0.27716038913773156 0.2931311914702573; 0.33438053198661 0.32142600281512734 … 0.2931311914702573 0.3186160477630048;;; 0.3785174208998008 0.3636495426205899 … 0.33438053198661016 0.3664584406479666; 0.36364954262058974 0.3519170663492356 … 0.3214260028151273 0.3519170663492357; … ; 0.33438053198661005 0.3214260028151273 … 0.29313119147025735 0.31861604776300484; 0.3664584406479665 0.3519170663492357 … 0.3186160477630049 0.3510288634177603]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [-0.5033081923122255 -0.49665655722571456 … -0.4771919009649006 -0.49665655722571456; -0.49665655722571456 -0.4848182087107497 … -0.47638044576679117 -0.4920413111694392; … ; -0.47719190096490055 -0.47638044576679117 … -0.4122880708739224 -0.4550700815561307; -0.49665655722571456 -0.4920413111694392 … -0.4550700815561307 -0.4848182087107497;;; -0.49665655722571456 -0.4848182087107497 … -0.47638044576679117 -0.4920413111694392; -0.4848182087107497 -0.45837440791486983 … -0.4706560157057298 -0.48617902517563427; … ; -0.47638044576679117 -0.4706560157057298 … -0.4463984364362234 -0.4688943963915335; -0.4920413111694392 -0.48617902517563427 … -0.4688943963915335 -0.48617902517563427;;; -0.4771919009649006 -0.4550700815561307 … -0.4605141234226784 -0.47638044576679117; -0.4550700815561307 -0.40906618243913573 … -0.45671990832114834 -0.4688943963915336; … ; -0.46051412342267833 -0.45671990832114834 … -0.4451449566034985 -0.45671990832114834; -0.47638044576679117 -0.4688943963915335 … -0.45671990832114834 -0.4706560157057298;;; … ;;; -0.4494759508409202 -0.4551499722014993 … -0.3712598626179138 -0.4177457152027701; -0.4551499722014992 -0.4488035109977225 … -0.4174380107134267 -0.4441260992987871; … ; -0.3712598626179138 -0.4174380107134267 … -0.25365698328408465 -0.29979809105961114; -0.41774571520277004 -0.4441260992987871 … -0.29979809105961114 -0.36106343264803265;;; -0.4771919009649006 -0.47638044576679117 … -0.41228807087392244 -0.4550700815561307; -0.47638044576679117 -0.4706560157057298 … -0.4463984364362234 -0.4688943963915336; … ; -0.4122880708739224 -0.4463984364362234 … -0.25365698328408465 -0.34106330230084914; -0.4550700815561307 -0.4688943963915335 … -0.34106330230084914 -0.40906618243913573;;; -0.49665655722571456 -0.4920413111694392 … -0.4550700815561307 -0.4848182087107497; -0.4920413111694392 -0.48617902517563427 … -0.4688943963915335 -0.48617902517563427; … ; -0.4550700815561307 -0.4688943963915335 … -0.3410633023008492 -0.40906618243913573; -0.4848182087107497 -0.48617902517563427 … -0.40906618243913573 -0.45837440791486983])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [0.0, 0.5625437115174675, 2.25017484606987, 2.25017484606987, 0.5625437115174675, 0.5625437115174675, 0.7500582820232901, 2.0626602755640477, 4.50034969213974, 3.5627768396106276  …  3.7502914101164504, 3.7502914101164504, 2.0626602755640477, 1.5001165640465801, 0.7500582820232901, 2.0626602755640477, 4.50034969213974, 3.5627768396106276, 1.5001165640465801, 0.5625437115174675]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [-0.41291392126628423 -0.48683674427716556 … -0.7027113226190804 -0.4868367442771657; -0.4868367442771655 -0.774430395040426 … -0.4136373284392913 -0.38233074979446574; … ; -0.7027113226190806 -0.4136373284392915 … -2.396761682588038 -1.2958067581749462; -0.4868367442771654 -0.38233074979446563 … -1.2958067581749462 -0.7744303950404258;;; -0.4868367442771655 -0.7744303950404259 … -0.41363732843929113 -0.3823307497944659; -0.7744303950404257 -1.4814477483918544 … -0.3245845694332581 -0.4499193965706699; … ; -0.41363732843929135 -0.3245845694332585 … -1.0113572986116854 -0.6373277791931669; -0.3823307497944656 -0.44991939657067 … -0.6373277791931666 -0.44991939657066987;;; -0.7027113226190804 -1.2958067581749464 … -0.29820348937555374 -0.4136373284392914; -1.2958067581749462 -2.9196723936538724 … -0.3537295846614352 -0.6373277791931666; … ; -0.29820348937555385 -0.3537295846614358 … -0.4903726081071644 -0.35372958466143567; -0.41363732843929135 -0.6373277791931666 … -0.353729584661435 -0.3245845694332581;;; … ;;; -1.0166744212557564 -0.5332878143065793 … -3.6361382571228473 -1.9987602620506044; -0.5332878143065791 -0.3217412474738722 … -1.4667339407502435 -0.9061938941468672; … ; -3.6361382571228473 -1.4667339407502435 … -10.988177824465879 -8.087376168208158; -1.9987602620506042 -0.9061938941468672 … -8.087376168208158 -4.6478783711432134;;; -0.7027113226190804 -0.4136373284392912 … -2.3967616825880382 -1.2958067581749462; -0.4136373284392912 -0.3245845694332584 … -1.0113572986116854 -0.6373277791931666; … ; -2.3967616825880382 -1.0113572986116857 … -11.002806190874985 -6.077304186394054; -1.2958067581749462 -0.6373277791931664 … -6.077304186394054 -2.9196723936538724;;; -0.48683674427716556 -0.3823307497944658 … -1.2958067581749462 -0.7744303950404259; -0.38233074979446574 -0.4499193965706701 … -0.6373277791931666 -0.4499193965706699; … ; -1.2958067581749462 -0.6373277791931669 … -6.077304186394053 -2.9196723936538724; -0.7744303950404257 -0.44991939657066976 … -2.9196723936538724 -1.4814477483918544]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), ComplexF64[0.11164094023604486 + 0.0im 0.1729534009156557 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.07139183057793365 - 0.07139183057793365im 0.10318729458139622 - 0.10318729458139622im … -0.035578676822652595 + 0.035578676822652595im 0.035578676822652595 - 0.035578676822652595im; … ; -0.08538801146445177 + 0.0im -0.10864081623630145 + 0.0im … 0.0 + 0.08076812854291712im 0.0 - 0.0im; -0.07139183057793365 + 0.07139183057793365im -0.10318729458139622 + 0.10318729458139622im … -0.035578676822652595 + 0.035578676822652595im -0.035578676822652595 + 0.035578676822652595im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, (ψ_reals = Array{ComplexF64, 3}[[0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; … ;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im]],)), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [0.06250485683527418, 1.000077709364387, 3.062737984928434, 4.000310837457548, 1.562621420881854, 0.2500194273410967, 0.5000388546821934, 1.0625825661996608, 2.750213700752063, 2.7502137007520635  …  2.5001942734109663, 4.5628545489750145, 3.062737984928434, 1.7501359913876768, 1.5626214208818543, 1.062582566199661, 2.750213700752063, 2.750213700752064, 1.0625825661996608, 0.5000388546821934]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [-0.30116136598756804 -0.36869760795125184 … -0.5702190219244254 -0.36869760795125195; -0.3686976079512516 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456163; … ; -0.5702190219244256 -0.264614164394795 … -2.291992881132685 -1.1751172086054253; -0.3686976079512515 -0.2539389812456162 … -1.1751172086054256 -0.6560706269776425;;; -0.3686976079512517 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456166; -0.6560706269776425 -1.3741022038947448 … -0.1651225671881503 -0.31565743774427135; … ; -0.2646141643947949 -0.16512256718815066 … -0.8632000905877295 -0.4898593856167607; -0.25393898124561615 -0.31565743774427135 … -0.48985938561676046 -0.31565743774427124;;; -0.5702190219244254 -1.1751172086054258 … -0.1242245197168452 -0.264614164394795; -1.1751172086054256 -2.8292222589777416 … -0.1750685951638031 -0.48985938561676046; … ; -0.1242245197168452 -0.1750685951638037 … -0.30112950922681153 -0.17506859516380358; -0.2646141643947948 -0.48985938561676046 … -0.17506859516380294 -0.1651225671881503;;; … ;;; -0.8720732197039092 -0.36117451106748844 … -3.5504427268225025 -1.881971917366274; -0.3611745110674882 -0.13192205269891222 … -1.3219289313234115 -0.747481991474731; … ; -3.5504427268225025 -1.3219289313234115 … -11.011681230319526 -8.06878895093237; -1.8819719173662737 -0.747481991474731 … -8.06878895093237 -4.5798976647669045;;; -0.5702190219244254 -0.2646141643947948 … -2.2919928811326855 -1.1751172086054256; -0.2646141643947947 -0.16512256718815055 … -0.8632000905877295 -0.48985938561676046; … ; -2.2919928811326855 -0.8632000905877297 … -11.026309596728632 -6.029372075563462; -1.1751172086054253 -0.4898593856167603 … -6.029372075563462 -2.8292222589777416;;; -0.3686976079512518 -0.2539389812456165 … -1.1751172086054256 -0.6560706269776427; -0.25393898124561626 -0.3156574377442714 … -0.4898593856167604 -0.31565743774427135; … ; -1.1751172086054256 -0.48985938561676057 … -6.029372075563461 -2.829222258977741; -0.6560706269776424 -0.3156574377442712 … -2.829222258977741 -1.3741022038947448]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), ComplexF64[0.10663902257822168 - 0.028573839981478756im 0.16397423109777803 - 0.0439367628021639im … -0.0048810168633526265 + 0.01821620292663248im 0.0048810168633526265 - 0.01821620292663248im; 0.04668482831007231 - 0.08086049457567514im 0.06370661418591363 - 0.11034309254819058im … -0.05243363114037364 + 0.030272571053484264im 0.05243363114037364 - 0.030272571053484264im; … ; -0.08918635851135279 + 0.023897412738989543im -0.12067576411442682 + 0.03233497354046929im … -0.019302751901532963 + 0.07203885082241784im -0.0038605503803065926 + 0.014407770164483566im; -0.051048693065027635 + 0.08841893004861681im -0.0743729428832569 + 0.128817715782219im … -0.02947884616601673 + 0.017019619769349337im -0.05895769233203346 + 0.034039239538698675im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [0.39155563703350926 0.37851742089980084 … 0.3446996002702456 0.3785174208998008; 0.37851742089980067 0.36645844064796645 … 0.32735728172229467 0.3636495426205898; … ; 0.3446996002702455 0.32735728172229467 … 0.30751926941856966 0.33438053198661; 0.37851742089980067 0.3636495426205898 … 0.33438053198661005 0.36645844064796645;;; 0.3785174208998008 0.3664584406479666 … 0.32735728172229484 0.3636495426205899; 0.3664584406479665 0.35102886341776024 … 0.311194013460622 0.3519170663492357; … ; 0.3273572817222947 0.311194013460622 … 0.2982412284122674 0.32142600281512734; 0.3636495426205898 0.35191706634923564 … 0.3214260028151274 0.35191706634923564;;; 0.34469960027024554 0.3343805319866101 … 0.2865351537639698 0.3273572817222948; 0.33438053198661 0.3186160477630048 … 0.27805891882351624 0.3214260028151274; … ; 0.2865351537639697 0.27805891882351624 … 0.25590185772314566 0.27805891882351624; 0.3273572817222946 0.32142600281512734 … 0.27805891882351624 0.311194013460622;;; … ;;; 0.304874749289073 0.2830366689624084 … 0.28556433231756906 0.3009573705184396; 0.28303666896240826 0.25898431622276247 … 0.2726330012865946 0.28541419662665096; … ; 0.285564332317569 0.2726330012865946 … 0.27716038913773156 0.2812108737838244; 0.30095737051843946 0.28541419662665096 … 0.2812108737838245 0.2930827262717236;;; 0.34469960027024554 0.3273572817222948 … 0.30751926941856983 0.3343805319866101; 0.32735728172229467 0.3111940134606219 … 0.2982412284122674 0.32142600281512734; … ; 0.3075192694185697 0.2982412284122674 … 0.27716038913773156 0.2931311914702573; 0.33438053198661 0.32142600281512734 … 0.2931311914702573 0.3186160477630048;;; 0.3785174208998008 0.3636495426205899 … 0.33438053198661016 0.3664584406479666; 0.36364954262058974 0.3519170663492356 … 0.3214260028151273 0.3519170663492357; … ; 0.33438053198661005 0.3214260028151273 … 0.29313119147025735 0.31861604776300484; 0.3664584406479665 0.3519170663492357 … 0.3186160477630049 0.3510288634177603]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [-0.5033081923122255 -0.49665655722571456 … -0.4771919009649006 -0.49665655722571456; -0.49665655722571456 -0.4848182087107497 … -0.47638044576679117 -0.4920413111694392; … ; -0.47719190096490055 -0.47638044576679117 … -0.4122880708739224 -0.4550700815561307; -0.49665655722571456 -0.4920413111694392 … -0.4550700815561307 -0.4848182087107497;;; -0.49665655722571456 -0.4848182087107497 … -0.47638044576679117 -0.4920413111694392; -0.4848182087107497 -0.45837440791486983 … -0.4706560157057298 -0.48617902517563427; … ; -0.47638044576679117 -0.4706560157057298 … -0.4463984364362234 -0.4688943963915335; -0.4920413111694392 -0.48617902517563427 … -0.4688943963915335 -0.48617902517563427;;; -0.4771919009649006 -0.4550700815561307 … -0.4605141234226784 -0.47638044576679117; -0.4550700815561307 -0.40906618243913573 … -0.45671990832114834 -0.4688943963915336; … ; -0.46051412342267833 -0.45671990832114834 … -0.4451449566034985 -0.45671990832114834; -0.47638044576679117 -0.4688943963915335 … -0.45671990832114834 -0.4706560157057298;;; … ;;; -0.4494759508409202 -0.4551499722014993 … -0.3712598626179138 -0.4177457152027701; -0.4551499722014992 -0.4488035109977225 … -0.4174380107134267 -0.4441260992987871; … ; -0.3712598626179138 -0.4174380107134267 … -0.25365698328408465 -0.29979809105961114; -0.41774571520277004 -0.4441260992987871 … -0.29979809105961114 -0.36106343264803265;;; -0.4771919009649006 -0.47638044576679117 … -0.41228807087392244 -0.4550700815561307; -0.47638044576679117 -0.4706560157057298 … -0.4463984364362234 -0.4688943963915336; … ; -0.4122880708739224 -0.4463984364362234 … -0.25365698328408465 -0.34106330230084914; -0.4550700815561307 -0.4688943963915335 … -0.34106330230084914 -0.40906618243913573;;; -0.49665655722571456 -0.4920413111694392 … -0.4550700815561307 -0.4848182087107497; -0.4920413111694392 -0.48617902517563427 … -0.4688943963915335 -0.48617902517563427; … ; -0.4550700815561307 -0.4688943963915335 … -0.3410633023008492 -0.40906618243913573; -0.4848182087107497 -0.48617902517563427 … -0.40906618243913573 -0.45837440791486983])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [0.06250485683527418, 1.000077709364387, 3.062737984928434, 4.000310837457548, 1.562621420881854, 0.2500194273410967, 0.5000388546821934, 1.0625825661996608, 2.750213700752063, 2.7502137007520635  …  2.5001942734109663, 4.5628545489750145, 3.062737984928434, 1.7501359913876768, 1.5626214208818543, 1.062582566199661, 2.750213700752063, 2.750213700752064, 1.0625825661996608, 0.5000388546821934]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [-0.41291392126628423 -0.48683674427716556 … -0.7027113226190804 -0.4868367442771657; -0.4868367442771655 -0.774430395040426 … -0.4136373284392913 -0.38233074979446574; … ; -0.7027113226190806 -0.4136373284392915 … -2.396761682588038 -1.2958067581749462; -0.4868367442771654 -0.38233074979446563 … -1.2958067581749462 -0.7744303950404258;;; -0.4868367442771655 -0.7744303950404259 … -0.41363732843929113 -0.3823307497944659; -0.7744303950404257 -1.4814477483918544 … -0.3245845694332581 -0.4499193965706699; … ; -0.41363732843929135 -0.3245845694332585 … -1.0113572986116854 -0.6373277791931669; -0.3823307497944656 -0.44991939657067 … -0.6373277791931666 -0.44991939657066987;;; -0.7027113226190804 -1.2958067581749464 … -0.29820348937555374 -0.4136373284392914; -1.2958067581749462 -2.9196723936538724 … -0.3537295846614352 -0.6373277791931666; … ; -0.29820348937555385 -0.3537295846614358 … -0.4903726081071644 -0.35372958466143567; -0.41363732843929135 -0.6373277791931666 … -0.353729584661435 -0.3245845694332581;;; … ;;; -1.0166744212557564 -0.5332878143065793 … -3.6361382571228473 -1.9987602620506044; -0.5332878143065791 -0.3217412474738722 … -1.4667339407502435 -0.9061938941468672; … ; -3.6361382571228473 -1.4667339407502435 … -10.988177824465879 -8.087376168208158; -1.9987602620506042 -0.9061938941468672 … -8.087376168208158 -4.6478783711432134;;; -0.7027113226190804 -0.4136373284392912 … -2.3967616825880382 -1.2958067581749462; -0.4136373284392912 -0.3245845694332584 … -1.0113572986116854 -0.6373277791931666; … ; -2.3967616825880382 -1.0113572986116857 … -11.002806190874985 -6.077304186394054; -1.2958067581749462 -0.6373277791931664 … -6.077304186394054 -2.9196723936538724;;; -0.48683674427716556 -0.3823307497944658 … -1.2958067581749462 -0.7744303950404259; -0.38233074979446574 -0.4499193965706701 … -0.6373277791931666 -0.4499193965706699; … ; -1.2958067581749462 -0.6373277791931669 … -6.077304186394053 -2.9196723936538724; -0.7744303950404257 -0.44991939657066976 … -2.9196723936538724 -1.4814477483918544]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), ComplexF64[0.10663902257822168 - 0.028573839981478756im 0.16397423109777803 - 0.0439367628021639im … -0.0048810168633526265 + 0.01821620292663248im 0.0048810168633526265 - 0.01821620292663248im; 0.04668482831007231 - 0.08086049457567514im 0.06370661418591363 - 0.11034309254819058im … -0.05243363114037364 + 0.030272571053484264im 0.05243363114037364 - 0.030272571053484264im; … ; -0.08918635851135279 + 0.023897412738989543im -0.12067576411442682 + 0.03233497354046929im … -0.019302751901532963 + 0.07203885082241784im -0.0038605503803065926 + 0.014407770164483566im; -0.051048693065027635 + 0.08841893004861681im -0.0743729428832569 + 0.128817715782219im … -0.02947884616601673 + 0.017019619769349337im -0.05895769233203346 + 0.034039239538698675im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, (ψ_reals = Array{ComplexF64, 3}[[0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; … ;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im]],)), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [0.0833398091136989, 0.8959029479722631, 2.8335535098657623, 4.396174930747617, 1.8334758005013758, 0.3958640932900698, 0.8959029479722631, 1.3334369458191824, 2.8960583667010367, 3.39609722138323  …  1.89598065733665, 3.833631219230149, 2.8335535098657623, 1.3959418026544566, 1.0834175184780857, 0.8333980911369889, 2.3960195120188432, 2.8960583667010367, 1.0834175184780857, 0.3958640932900698]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [-0.30116136598756804 -0.36869760795125184 … -0.5702190219244254 -0.36869760795125195; -0.3686976079512516 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456163; … ; -0.5702190219244256 -0.264614164394795 … -2.291992881132685 -1.1751172086054253; -0.3686976079512515 -0.2539389812456162 … -1.1751172086054256 -0.6560706269776425;;; -0.3686976079512517 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456166; -0.6560706269776425 -1.3741022038947448 … -0.1651225671881503 -0.31565743774427135; … ; -0.2646141643947949 -0.16512256718815066 … -0.8632000905877295 -0.4898593856167607; -0.25393898124561615 -0.31565743774427135 … -0.48985938561676046 -0.31565743774427124;;; -0.5702190219244254 -1.1751172086054258 … -0.1242245197168452 -0.264614164394795; -1.1751172086054256 -2.8292222589777416 … -0.1750685951638031 -0.48985938561676046; … ; -0.1242245197168452 -0.1750685951638037 … -0.30112950922681153 -0.17506859516380358; -0.2646141643947948 -0.48985938561676046 … -0.17506859516380294 -0.1651225671881503;;; … ;;; -0.8720732197039092 -0.36117451106748844 … -3.5504427268225025 -1.881971917366274; -0.3611745110674882 -0.13192205269891222 … -1.3219289313234115 -0.747481991474731; … ; -3.5504427268225025 -1.3219289313234115 … -11.011681230319526 -8.06878895093237; -1.8819719173662737 -0.747481991474731 … -8.06878895093237 -4.5798976647669045;;; -0.5702190219244254 -0.2646141643947948 … -2.2919928811326855 -1.1751172086054256; -0.2646141643947947 -0.16512256718815055 … -0.8632000905877295 -0.48985938561676046; … ; -2.2919928811326855 -0.8632000905877297 … -11.026309596728632 -6.029372075563462; -1.1751172086054253 -0.4898593856167603 … -6.029372075563462 -2.8292222589777416;;; -0.3686976079512518 -0.2539389812456165 … -1.1751172086054256 -0.6560706269776427; -0.25393898124561626 -0.3156574377442714 … -0.4898593856167604 -0.31565743774427135; … ; -1.1751172086054256 -0.48985938561676057 … -6.029372075563461 -2.829222258977741; -0.6560706269776424 -0.3156574377442712 … -2.829222258977741 -1.3741022038947448]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), ComplexF64[0.09525460347564817 - 0.05499527095821653im 0.14610260131202302 - 0.08435237619680104im … -0.018766875445216862 + 0.032505181770432406im 5.2088543048880615e-19 - 9.022000305289992e-19im; 0.024619950292842606 - 0.09188290537270884im 0.03407002323540016 - 0.12715105772956556im … -0.07491066001757686 + 0.02007225085619212im 0.04494639601054611 - 0.012043350513715271im; … ; -0.07966512642409461 + 0.045994682185976576im -0.10748648020277889 + 0.06205734827931975im … -0.02968662889946843 + 0.05141874955932189im 0.0 - 0.0im; -0.026921300372532365 + 0.10047166079611371im -0.039739321889381986 + 0.14830916834950758im … -0.016846285674482424 + 0.0045139486419415575im -0.05053885702344723 + 0.013541845925824664im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [0.39155563703350926 0.37851742089980084 … 0.3446996002702456 0.3785174208998008; 0.37851742089980067 0.36645844064796645 … 0.32735728172229467 0.3636495426205898; … ; 0.3446996002702455 0.32735728172229467 … 0.30751926941856966 0.33438053198661; 0.37851742089980067 0.3636495426205898 … 0.33438053198661005 0.36645844064796645;;; 0.3785174208998008 0.3664584406479666 … 0.32735728172229484 0.3636495426205899; 0.3664584406479665 0.35102886341776024 … 0.311194013460622 0.3519170663492357; … ; 0.3273572817222947 0.311194013460622 … 0.2982412284122674 0.32142600281512734; 0.3636495426205898 0.35191706634923564 … 0.3214260028151274 0.35191706634923564;;; 0.34469960027024554 0.3343805319866101 … 0.2865351537639698 0.3273572817222948; 0.33438053198661 0.3186160477630048 … 0.27805891882351624 0.3214260028151274; … ; 0.2865351537639697 0.27805891882351624 … 0.25590185772314566 0.27805891882351624; 0.3273572817222946 0.32142600281512734 … 0.27805891882351624 0.311194013460622;;; … ;;; 0.304874749289073 0.2830366689624084 … 0.28556433231756906 0.3009573705184396; 0.28303666896240826 0.25898431622276247 … 0.2726330012865946 0.28541419662665096; … ; 0.285564332317569 0.2726330012865946 … 0.27716038913773156 0.2812108737838244; 0.30095737051843946 0.28541419662665096 … 0.2812108737838245 0.2930827262717236;;; 0.34469960027024554 0.3273572817222948 … 0.30751926941856983 0.3343805319866101; 0.32735728172229467 0.3111940134606219 … 0.2982412284122674 0.32142600281512734; … ; 0.3075192694185697 0.2982412284122674 … 0.27716038913773156 0.2931311914702573; 0.33438053198661 0.32142600281512734 … 0.2931311914702573 0.3186160477630048;;; 0.3785174208998008 0.3636495426205899 … 0.33438053198661016 0.3664584406479666; 0.36364954262058974 0.3519170663492356 … 0.3214260028151273 0.3519170663492357; … ; 0.33438053198661005 0.3214260028151273 … 0.29313119147025735 0.31861604776300484; 0.3664584406479665 0.3519170663492357 … 0.3186160477630049 0.3510288634177603]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [-0.5033081923122255 -0.49665655722571456 … -0.4771919009649006 -0.49665655722571456; -0.49665655722571456 -0.4848182087107497 … -0.47638044576679117 -0.4920413111694392; … ; -0.47719190096490055 -0.47638044576679117 … -0.4122880708739224 -0.4550700815561307; -0.49665655722571456 -0.4920413111694392 … -0.4550700815561307 -0.4848182087107497;;; -0.49665655722571456 -0.4848182087107497 … -0.47638044576679117 -0.4920413111694392; -0.4848182087107497 -0.45837440791486983 … -0.4706560157057298 -0.48617902517563427; … ; -0.47638044576679117 -0.4706560157057298 … -0.4463984364362234 -0.4688943963915335; -0.4920413111694392 -0.48617902517563427 … -0.4688943963915335 -0.48617902517563427;;; -0.4771919009649006 -0.4550700815561307 … -0.4605141234226784 -0.47638044576679117; -0.4550700815561307 -0.40906618243913573 … -0.45671990832114834 -0.4688943963915336; … ; -0.46051412342267833 -0.45671990832114834 … -0.4451449566034985 -0.45671990832114834; -0.47638044576679117 -0.4688943963915335 … -0.45671990832114834 -0.4706560157057298;;; … ;;; -0.4494759508409202 -0.4551499722014993 … -0.3712598626179138 -0.4177457152027701; -0.4551499722014992 -0.4488035109977225 … -0.4174380107134267 -0.4441260992987871; … ; -0.3712598626179138 -0.4174380107134267 … -0.25365698328408465 -0.29979809105961114; -0.41774571520277004 -0.4441260992987871 … -0.29979809105961114 -0.36106343264803265;;; -0.4771919009649006 -0.47638044576679117 … -0.41228807087392244 -0.4550700815561307; -0.47638044576679117 -0.4706560157057298 … -0.4463984364362234 -0.4688943963915336; … ; -0.4122880708739224 -0.4463984364362234 … -0.25365698328408465 -0.34106330230084914; -0.4550700815561307 -0.4688943963915335 … -0.34106330230084914 -0.40906618243913573;;; -0.49665655722571456 -0.4920413111694392 … -0.4550700815561307 -0.4848182087107497; -0.4920413111694392 -0.48617902517563427 … -0.4688943963915335 -0.48617902517563427; … ; -0.4550700815561307 -0.4688943963915335 … -0.3410633023008492 -0.40906618243913573; -0.4848182087107497 -0.48617902517563427 … -0.40906618243913573 -0.45837440791486983])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [0.0833398091136989, 0.8959029479722631, 2.8335535098657623, 4.396174930747617, 1.8334758005013758, 0.3958640932900698, 0.8959029479722631, 1.3334369458191824, 2.8960583667010367, 3.39609722138323  …  1.89598065733665, 3.833631219230149, 2.8335535098657623, 1.3959418026544566, 1.0834175184780857, 0.8333980911369889, 2.3960195120188432, 2.8960583667010367, 1.0834175184780857, 0.3958640932900698]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [-0.41291392126628423 -0.48683674427716556 … -0.7027113226190804 -0.4868367442771657; -0.4868367442771655 -0.774430395040426 … -0.4136373284392913 -0.38233074979446574; … ; -0.7027113226190806 -0.4136373284392915 … -2.396761682588038 -1.2958067581749462; -0.4868367442771654 -0.38233074979446563 … -1.2958067581749462 -0.7744303950404258;;; -0.4868367442771655 -0.7744303950404259 … -0.41363732843929113 -0.3823307497944659; -0.7744303950404257 -1.4814477483918544 … -0.3245845694332581 -0.4499193965706699; … ; -0.41363732843929135 -0.3245845694332585 … -1.0113572986116854 -0.6373277791931669; -0.3823307497944656 -0.44991939657067 … -0.6373277791931666 -0.44991939657066987;;; -0.7027113226190804 -1.2958067581749464 … -0.29820348937555374 -0.4136373284392914; -1.2958067581749462 -2.9196723936538724 … -0.3537295846614352 -0.6373277791931666; … ; -0.29820348937555385 -0.3537295846614358 … -0.4903726081071644 -0.35372958466143567; -0.41363732843929135 -0.6373277791931666 … -0.353729584661435 -0.3245845694332581;;; … ;;; -1.0166744212557564 -0.5332878143065793 … -3.6361382571228473 -1.9987602620506044; -0.5332878143065791 -0.3217412474738722 … -1.4667339407502435 -0.9061938941468672; … ; -3.6361382571228473 -1.4667339407502435 … -10.988177824465879 -8.087376168208158; -1.9987602620506042 -0.9061938941468672 … -8.087376168208158 -4.6478783711432134;;; -0.7027113226190804 -0.4136373284392912 … -2.3967616825880382 -1.2958067581749462; -0.4136373284392912 -0.3245845694332584 … -1.0113572986116854 -0.6373277791931666; … ; -2.3967616825880382 -1.0113572986116857 … -11.002806190874985 -6.077304186394054; -1.2958067581749462 -0.6373277791931664 … -6.077304186394054 -2.9196723936538724;;; -0.48683674427716556 -0.3823307497944658 … -1.2958067581749462 -0.7744303950404259; -0.38233074979446574 -0.4499193965706701 … -0.6373277791931666 -0.4499193965706699; … ; -1.2958067581749462 -0.6373277791931669 … -6.077304186394053 -2.9196723936538724; -0.7744303950404257 -0.44991939657066976 … -2.9196723936538724 -1.4814477483918544]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), ComplexF64[0.09525460347564817 - 0.05499527095821653im 0.14610260131202302 - 0.08435237619680104im … -0.018766875445216862 + 0.032505181770432406im 5.2088543048880615e-19 - 9.022000305289992e-19im; 0.024619950292842606 - 0.09188290537270884im 0.03407002323540016 - 0.12715105772956556im … -0.07491066001757686 + 0.02007225085619212im 0.04494639601054611 - 0.012043350513715271im; … ; -0.07966512642409461 + 0.045994682185976576im -0.10748648020277889 + 0.06205734827931975im … -0.02968662889946843 + 0.05141874955932189im 0.0 - 0.0im; -0.026921300372532365 + 0.10047166079611371im -0.039739321889381986 + 0.14830916834950758im … -0.016846285674482424 + 0.0045139486419415575im -0.05053885702344723 + 0.013541845925824664im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, (ψ_reals = Array{ComplexF64, 3}[[0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; … ;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im]],)), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [0.1666796182273978, 0.22918447506267198, 1.4167767549328811, 3.7294564578380256, 3.416932173661655, 1.2292621844270586, 1.2292621844270586, 0.9167379002506877, 1.729301039109252, 3.6669516010027516  …  4.729534167202412, 4.417009883026042, 2.2293398937914453, 1.1667573275917844, 0.41669904556849446, 1.2292621844270588, 3.1669127463205577, 4.729534167202412, 2.1668350369561713, 0.7292233297448653]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [-0.30116136598756804 -0.36869760795125184 … -0.5702190219244254 -0.36869760795125195; -0.3686976079512516 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456163; … ; -0.5702190219244256 -0.264614164394795 … -2.291992881132685 -1.1751172086054253; -0.3686976079512515 -0.2539389812456162 … -1.1751172086054256 -0.6560706269776425;;; -0.3686976079512517 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456166; -0.6560706269776425 -1.3741022038947448 … -0.1651225671881503 -0.31565743774427135; … ; -0.2646141643947949 -0.16512256718815066 … -0.8632000905877295 -0.4898593856167607; -0.25393898124561615 -0.31565743774427135 … -0.48985938561676046 -0.31565743774427124;;; -0.5702190219244254 -1.1751172086054258 … -0.1242245197168452 -0.264614164394795; -1.1751172086054256 -2.8292222589777416 … -0.1750685951638031 -0.48985938561676046; … ; -0.1242245197168452 -0.1750685951638037 … -0.30112950922681153 -0.17506859516380358; -0.2646141643947948 -0.48985938561676046 … -0.17506859516380294 -0.1651225671881503;;; … ;;; -0.8720732197039092 -0.36117451106748844 … -3.5504427268225025 -1.881971917366274; -0.3611745110674882 -0.13192205269891222 … -1.3219289313234115 -0.747481991474731; … ; -3.5504427268225025 -1.3219289313234115 … -11.011681230319526 -8.06878895093237; -1.8819719173662737 -0.747481991474731 … -8.06878895093237 -4.5798976647669045;;; -0.5702190219244254 -0.2646141643947948 … -2.2919928811326855 -1.1751172086054256; -0.2646141643947947 -0.16512256718815055 … -0.8632000905877295 -0.48985938561676046; … ; -2.2919928811326855 -0.8632000905877297 … -11.026309596728632 -6.029372075563462; -1.1751172086054253 -0.4898593856167603 … -6.029372075563462 -2.8292222589777416;;; -0.3686976079512518 -0.2539389812456165 … -1.1751172086054256 -0.6560706269776427; -0.25393898124561626 -0.3156574377442714 … -0.4898593856167604 -0.31565743774427135; … ; -1.1751172086054256 -0.48985938561676057 … -6.029372075563461 -2.829222258977741; -0.6560706269776424 -0.3156574377442712 … -2.829222258977741 -1.3741022038947448]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), ComplexF64[0.10836454158744746 + 0.0im 0.16454392299317003 + 0.0im … -0.0 - 1.0216068167279948e-18im 0.0 + 0.03680726463308285im; 0.0757741533540503 - 0.0757741533540503im 0.1141835519100639 - 0.1141835519100639im … -0.03847188688271061 + 0.03847188688271061im 0.012823962294236874 - 0.012823962294236874im; … ; -0.07579695351601741 + 0.0im -0.08711072462387971 + 0.0im … 0.0 + 0.06907686686237845im 0.0 - 0.02302562228745948im; -0.0692966484992815 + 0.0692966484992815im -0.09802716364420207 + 0.09802716364420207im … -0.03421471645670587 + 0.03421471645670587im -0.011404905485568627 + 0.011404905485568627im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [0.39155563703350926 0.37851742089980084 … 0.3446996002702456 0.3785174208998008; 0.37851742089980067 0.36645844064796645 … 0.32735728172229467 0.3636495426205898; … ; 0.3446996002702455 0.32735728172229467 … 0.30751926941856966 0.33438053198661; 0.37851742089980067 0.3636495426205898 … 0.33438053198661005 0.36645844064796645;;; 0.3785174208998008 0.3664584406479666 … 0.32735728172229484 0.3636495426205899; 0.3664584406479665 0.35102886341776024 … 0.311194013460622 0.3519170663492357; … ; 0.3273572817222947 0.311194013460622 … 0.2982412284122674 0.32142600281512734; 0.3636495426205898 0.35191706634923564 … 0.3214260028151274 0.35191706634923564;;; 0.34469960027024554 0.3343805319866101 … 0.2865351537639698 0.3273572817222948; 0.33438053198661 0.3186160477630048 … 0.27805891882351624 0.3214260028151274; … ; 0.2865351537639697 0.27805891882351624 … 0.25590185772314566 0.27805891882351624; 0.3273572817222946 0.32142600281512734 … 0.27805891882351624 0.311194013460622;;; … ;;; 0.304874749289073 0.2830366689624084 … 0.28556433231756906 0.3009573705184396; 0.28303666896240826 0.25898431622276247 … 0.2726330012865946 0.28541419662665096; … ; 0.285564332317569 0.2726330012865946 … 0.27716038913773156 0.2812108737838244; 0.30095737051843946 0.28541419662665096 … 0.2812108737838245 0.2930827262717236;;; 0.34469960027024554 0.3273572817222948 … 0.30751926941856983 0.3343805319866101; 0.32735728172229467 0.3111940134606219 … 0.2982412284122674 0.32142600281512734; … ; 0.3075192694185697 0.2982412284122674 … 0.27716038913773156 0.2931311914702573; 0.33438053198661 0.32142600281512734 … 0.2931311914702573 0.3186160477630048;;; 0.3785174208998008 0.3636495426205899 … 0.33438053198661016 0.3664584406479666; 0.36364954262058974 0.3519170663492356 … 0.3214260028151273 0.3519170663492357; … ; 0.33438053198661005 0.3214260028151273 … 0.29313119147025735 0.31861604776300484; 0.3664584406479665 0.3519170663492357 … 0.3186160477630049 0.3510288634177603]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [-0.5033081923122255 -0.49665655722571456 … -0.4771919009649006 -0.49665655722571456; -0.49665655722571456 -0.4848182087107497 … -0.47638044576679117 -0.4920413111694392; … ; -0.47719190096490055 -0.47638044576679117 … -0.4122880708739224 -0.4550700815561307; -0.49665655722571456 -0.4920413111694392 … -0.4550700815561307 -0.4848182087107497;;; -0.49665655722571456 -0.4848182087107497 … -0.47638044576679117 -0.4920413111694392; -0.4848182087107497 -0.45837440791486983 … -0.4706560157057298 -0.48617902517563427; … ; -0.47638044576679117 -0.4706560157057298 … -0.4463984364362234 -0.4688943963915335; -0.4920413111694392 -0.48617902517563427 … -0.4688943963915335 -0.48617902517563427;;; -0.4771919009649006 -0.4550700815561307 … -0.4605141234226784 -0.47638044576679117; -0.4550700815561307 -0.40906618243913573 … -0.45671990832114834 -0.4688943963915336; … ; -0.46051412342267833 -0.45671990832114834 … -0.4451449566034985 -0.45671990832114834; -0.47638044576679117 -0.4688943963915335 … -0.45671990832114834 -0.4706560157057298;;; … ;;; -0.4494759508409202 -0.4551499722014993 … -0.3712598626179138 -0.4177457152027701; -0.4551499722014992 -0.4488035109977225 … -0.4174380107134267 -0.4441260992987871; … ; -0.3712598626179138 -0.4174380107134267 … -0.25365698328408465 -0.29979809105961114; -0.41774571520277004 -0.4441260992987871 … -0.29979809105961114 -0.36106343264803265;;; -0.4771919009649006 -0.47638044576679117 … -0.41228807087392244 -0.4550700815561307; -0.47638044576679117 -0.4706560157057298 … -0.4463984364362234 -0.4688943963915336; … ; -0.4122880708739224 -0.4463984364362234 … -0.25365698328408465 -0.34106330230084914; -0.4550700815561307 -0.4688943963915335 … -0.34106330230084914 -0.40906618243913573;;; -0.49665655722571456 -0.4920413111694392 … -0.4550700815561307 -0.4848182087107497; -0.4920413111694392 -0.48617902517563427 … -0.4688943963915335 -0.48617902517563427; … ; -0.4550700815561307 -0.4688943963915335 … -0.3410633023008492 -0.40906618243913573; -0.4848182087107497 -0.48617902517563427 … -0.40906618243913573 -0.45837440791486983])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [0.1666796182273978, 0.22918447506267198, 1.4167767549328811, 3.7294564578380256, 3.416932173661655, 1.2292621844270586, 1.2292621844270586, 0.9167379002506877, 1.729301039109252, 3.6669516010027516  …  4.729534167202412, 4.417009883026042, 2.2293398937914453, 1.1667573275917844, 0.41669904556849446, 1.2292621844270588, 3.1669127463205577, 4.729534167202412, 2.1668350369561713, 0.7292233297448653]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [-0.41291392126628423 -0.48683674427716556 … -0.7027113226190804 -0.4868367442771657; -0.4868367442771655 -0.774430395040426 … -0.4136373284392913 -0.38233074979446574; … ; -0.7027113226190806 -0.4136373284392915 … -2.396761682588038 -1.2958067581749462; -0.4868367442771654 -0.38233074979446563 … -1.2958067581749462 -0.7744303950404258;;; -0.4868367442771655 -0.7744303950404259 … -0.41363732843929113 -0.3823307497944659; -0.7744303950404257 -1.4814477483918544 … -0.3245845694332581 -0.4499193965706699; … ; -0.41363732843929135 -0.3245845694332585 … -1.0113572986116854 -0.6373277791931669; -0.3823307497944656 -0.44991939657067 … -0.6373277791931666 -0.44991939657066987;;; -0.7027113226190804 -1.2958067581749464 … -0.29820348937555374 -0.4136373284392914; -1.2958067581749462 -2.9196723936538724 … -0.3537295846614352 -0.6373277791931666; … ; -0.29820348937555385 -0.3537295846614358 … -0.4903726081071644 -0.35372958466143567; -0.41363732843929135 -0.6373277791931666 … -0.353729584661435 -0.3245845694332581;;; … ;;; -1.0166744212557564 -0.5332878143065793 … -3.6361382571228473 -1.9987602620506044; -0.5332878143065791 -0.3217412474738722 … -1.4667339407502435 -0.9061938941468672; … ; -3.6361382571228473 -1.4667339407502435 … -10.988177824465879 -8.087376168208158; -1.9987602620506042 -0.9061938941468672 … -8.087376168208158 -4.6478783711432134;;; -0.7027113226190804 -0.4136373284392912 … -2.3967616825880382 -1.2958067581749462; -0.4136373284392912 -0.3245845694332584 … -1.0113572986116854 -0.6373277791931666; … ; -2.3967616825880382 -1.0113572986116857 … -11.002806190874985 -6.077304186394054; -1.2958067581749462 -0.6373277791931664 … -6.077304186394054 -2.9196723936538724;;; -0.48683674427716556 -0.3823307497944658 … -1.2958067581749462 -0.7744303950404259; -0.38233074979446574 -0.4499193965706701 … -0.6373277791931666 -0.4499193965706699; … ; -1.2958067581749462 -0.6373277791931669 … -6.077304186394053 -2.9196723936538724; -0.7744303950404257 -0.44991939657066976 … -2.9196723936538724 -1.4814477483918544]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), ComplexF64[0.10836454158744746 + 0.0im 0.16454392299317003 + 0.0im … -0.0 - 1.0216068167279948e-18im 0.0 + 0.03680726463308285im; 0.0757741533540503 - 0.0757741533540503im 0.1141835519100639 - 0.1141835519100639im … -0.03847188688271061 + 0.03847188688271061im 0.012823962294236874 - 0.012823962294236874im; … ; -0.07579695351601741 + 0.0im -0.08711072462387971 + 0.0im … 0.0 + 0.06907686686237845im 0.0 - 0.02302562228745948im; -0.0692966484992815 + 0.0692966484992815im -0.09802716364420207 + 0.09802716364420207im … -0.03421471645670587 + 0.03421471645670587im -0.011404905485568627 + 0.011404905485568627im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, (ψ_reals = Array{ComplexF64, 3}[[0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; … ;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im]],))]), basis = PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), energies = Energies(total = -7.852646686729848), converged = true, occupation_threshold = 1.0e-6, ρ = [0.09132316917748033 0.08747419134080957 … 0.07684754935963678 0.08747419134080957; 0.0874741913408096 0.0808996687216456 … 0.07642471016972087 0.08486944834427292; … ; 0.07684754935963677 0.07642471016972087 … 0.047784666671022005 0.06587895342303804; 0.0874741913408096 0.08486944834427292 … 0.06587895342303804 0.0808996687216456;;; 0.08747419134080958 0.08089966872164558 … 0.07642471016972088 0.08486944834427292; 0.08089966872164561 0.06744471469775161 … 0.07348669934704843 0.08163768629015303; … ; 0.07642471016972088 0.07348669934704843 … 0.06188804119996931 0.07259829028447433; 0.08486944834427292 0.08163768629015303 … 0.07259829028447433 0.08163768629015303;;; 0.07684754935963678 0.06587895342303804 … 0.0684720369897418 0.07642471016972086; 0.06587895342303805 0.04657864264981153 … 0.06665759371632352 0.07259829028447434; … ; 0.06847203698974179 0.0666575937163235 … 0.06132515314381332 0.06665759371632352; 0.07642471016972088 0.07259829028447433 … 0.06665759371632352 0.07348669934704843;;; … ;;; 0.06328495229886298 0.06591651445953084 … 0.03394064888051984 0.04987593485999227; 0.06591651445953085 0.06297790960105917 … 0.049756397885279254 0.06087020457146679; … ; 0.033940648880519834 0.049756397885279254 … 0.009696353214074025 0.016831338792591972; 0.04987593485999228 0.06087020457146679 … 0.016831338792591972 0.030985721885051342;;; 0.07684754935963678 0.07642471016972086 … 0.04778466667102201 0.06587895342303804; 0.07642471016972088 0.07348669934704842 … 0.06188804119996931 0.07259829028447434; … ; 0.047784666671022005 0.06188804119996931 … 0.009696353214074025 0.025710010675306254; 0.06587895342303805 0.07259829028447431 … 0.025710010675306254 0.04657864264981153;;; 0.08747419134080958 0.0848694483442729 … 0.06587895342303805 0.08089966872164558; 0.0848694483442729 0.08163768629015303 … 0.07259829028447431 0.08163768629015301; … ; 0.06587895342303804 0.07259829028447431 … 0.02571001067530626 0.04657864264981153; 0.0808996687216456 0.08163768629015301 … 0.04657864264981153 0.0674447146977516;;;;], α = 0.8, eigenvalues = [[-0.16677707596310404, 0.2642777178298737, 0.26427771782987397, 0.26427771782987414, 0.3573203719044865, 0.35732037190448673, 0.35732037190448707], [-0.11613218761086685, 0.07040532320001006, 0.22624813603018493, 0.22624813603018498, 0.3361178489460035, 0.3934379776179747, 0.39343797761797517], [-0.09588938143643551, 0.08764319967954286, 0.17312704142738622, 0.17312704142738625, 0.2919724892213011, 0.33773212507289924, 0.5327646516179261], [-0.045051463485982254, 0.022269526239775718, 0.09831189251532126, 0.1844640932211336, 0.32292701516246924, 0.48024696021464475, 0.502442233546123]], occupation = [[2.0, 2.0, 2.0, 2.0, 0.0, 0.0, 0.0], [2.0, 2.0, 2.0, 2.0, 0.0, 0.0, 0.0], [2.0, 2.0, 2.0, 2.0, 0.0, 0.0, 0.0], [2.0, 2.0, 2.0, 2.0, 0.0, 0.0, 0.0]], εF = 0.2897120818381747, n_iter = 18, n_ep_extra = 3, ψ = Matrix{ComplexF64}[[0.8935738975999168 - 0.3383967421809045im -2.3627306464634787e-16 - 3.5069545150511287e-16im … -6.288673466839176e-12 - 1.9769752873785596e-12im -5.1576055077341546e-12 - 1.6215450507101661e-12im; 0.09004919439996942 - 0.034101660873052816im -0.23079222043286052 - 0.0427725179974698im … 0.2996199828370816 + 0.07505075743665005im -0.3670376286563709 + 0.04548103789718368im; … ; 0.011029834102342964 - 0.004177001965985621im 0.044447311754531156 + 0.02946526062295925im … 0.051673298112657 - 0.02903379727430788im -0.036368458931177974 + 0.004721366597978744im; -0.09004919439996924 + 0.034101660873052456im 0.2043568150962331 + 0.24569891560695617im … 0.12613224899178604 - 0.3142691631906129im 0.06738668399898129 - 0.006580242959402325im], [0.8434791477847202 - 0.38871361689346223im 0.175563166933907 + 0.08964231094727132im … -7.72205368883425e-14 - 6.146299534183135e-14im 1.084759008302518e-13 - 1.9591587056847658e-14im; 0.057501599123646135 - 0.026499356422996074im -0.007813821656572977 - 0.003989726563141169im … 1.6887230780948004e-12 - 1.558384165052831e-13im -2.296813621468681e-12 + 1.3451569231290343e-12im; … ; 0.007039235476122653 - 0.0032440003872936116im 0.0768236264541385 + 0.0392260377331393im … -0.03118768061056975 + 0.05502584238526645im -0.0629566125947793 - 0.06412615230792992im; -0.10256476043147825 + 0.047266514054128544im -0.08078592636343332 - 0.04124918260309519im … -0.1323779502979612 + 0.23356043430121884im -0.26722305633363885 - 0.2721872366508748im], [0.25537338965881984 + 0.8981509812141548im 2.7984207870887357e-16 - 4.137850898582896e-16im … -2.3026589278117973e-15 + 3.027768860095337e-15im -6.060436387646611e-11 + 4.1824887107545785e-11im; 0.01880218654534007 + 0.06612749400879284im -0.05673901514732578 - 0.007170440041628914im … -0.01985510318803593 + 0.015488696223609603im -0.0028470447768683617 - 0.014633304167052592im; … ; 0.0037934112574907666 + 0.013341468535998182im -4.914500192252989e-18 + 1.6987533146277813e-16im … 6.632056296893111e-13 - 3.563823632954095e-13im -0.059812455777970154 + 0.0247807280320454im; -0.04190136973383673 - 0.147367571816865im -0.28486149145844436 - 0.03599960696124572im … 0.3010731057211354 - 0.2348630390512623im -0.13941750521962418 + 0.06306742107509283im], [-0.7769791631918391 - 0.22539933058742487im 2.94085597363339e-16 + 5.449120515590654e-16im … 0.17250627190570944 - 0.07328016921985134im -2.6638121967144338e-6 - 9.316277116851189e-7im; -0.3721314541352527 - 0.10795422145947679im -0.6150189617084744 - 0.11984374549881113im … -0.16402854841406414 + 0.06967876175084375im -1.4007670910719967e-6 + 1.7877484289935976e-6im; … ; -0.010942544393057802 - 0.0031743993892786294im -0.0016132972581194935 - 0.00031437012198599044im … 0.014887458133949916 - 0.006324053369782337im -0.029482743595282006 - 0.0330471157025554im; 0.06259889812214887 + 0.018159753054740452im -0.012254629710204903 - 0.00238796007214497im … 0.12455978357106713 - 0.05291252593865455im -0.3133233011994311 - 0.3511964251859512im]], diagonalization = NamedTuple{(:λ, :X, :residual_norms, :iterations, :converged, :n_matvec), Tuple{Vector{Vector{Float64}}, Vector{Matrix{ComplexF64}}, Vector{Vector{Float64}}, Vector{Int64}, Bool, Int64}}[(λ = [[-0.16677707596310404, 0.2642777178298737, 0.26427771782987397, 0.26427771782987414, 0.3573203719044865, 0.35732037190448673, 0.35732037190448707], [-0.11613218761086685, 0.07040532320001006, 0.22624813603018493, 0.22624813603018498, 0.3361178489460035, 0.3934379776179747, 0.39343797761797517], [-0.09588938143643551, 0.08764319967954286, 0.17312704142738622, 0.17312704142738625, 0.2919724892213011, 0.33773212507289924, 0.5327646516179261], [-0.045051463485982254, 0.022269526239775718, 0.09831189251532126, 0.1844640932211336, 0.32292701516246924, 0.48024696021464475, 0.502442233546123]], X = [[0.8935738975999168 - 0.3383967421809045im -2.3627306464634787e-16 - 3.5069545150511287e-16im … -6.288673466839176e-12 - 1.9769752873785596e-12im -5.1576055077341546e-12 - 1.6215450507101661e-12im; 0.09004919439996942 - 0.034101660873052816im -0.23079222043286052 - 0.0427725179974698im … 0.2996199828370816 + 0.07505075743665005im -0.3670376286563709 + 0.04548103789718368im; … ; 0.011029834102342964 - 0.004177001965985621im 0.044447311754531156 + 0.02946526062295925im … 0.051673298112657 - 0.02903379727430788im -0.036368458931177974 + 0.004721366597978744im; -0.09004919439996924 + 0.034101660873052456im 0.2043568150962331 + 0.24569891560695617im … 0.12613224899178604 - 0.3142691631906129im 0.06738668399898129 - 0.006580242959402325im], [0.8434791477847202 - 0.38871361689346223im 0.175563166933907 + 0.08964231094727132im … -7.72205368883425e-14 - 6.146299534183135e-14im 1.084759008302518e-13 - 1.9591587056847658e-14im; 0.057501599123646135 - 0.026499356422996074im -0.007813821656572977 - 0.003989726563141169im … 1.6887230780948004e-12 - 1.558384165052831e-13im -2.296813621468681e-12 + 1.3451569231290343e-12im; … ; 0.007039235476122653 - 0.0032440003872936116im 0.0768236264541385 + 0.0392260377331393im … -0.03118768061056975 + 0.05502584238526645im -0.0629566125947793 - 0.06412615230792992im; -0.10256476043147825 + 0.047266514054128544im -0.08078592636343332 - 0.04124918260309519im … -0.1323779502979612 + 0.23356043430121884im -0.26722305633363885 - 0.2721872366508748im], [0.25537338965881984 + 0.8981509812141548im 2.7984207870887357e-16 - 4.137850898582896e-16im … -2.3026589278117973e-15 + 3.027768860095337e-15im -6.060436387646611e-11 + 4.1824887107545785e-11im; 0.01880218654534007 + 0.06612749400879284im -0.05673901514732578 - 0.007170440041628914im … -0.01985510318803593 + 0.015488696223609603im -0.0028470447768683617 - 0.014633304167052592im; … ; 0.0037934112574907666 + 0.013341468535998182im -4.914500192252989e-18 + 1.6987533146277813e-16im … 6.632056296893111e-13 - 3.563823632954095e-13im -0.059812455777970154 + 0.0247807280320454im; -0.04190136973383673 - 0.147367571816865im -0.28486149145844436 - 0.03599960696124572im … 0.3010731057211354 - 0.2348630390512623im -0.13941750521962418 + 0.06306742107509283im], [-0.7769791631918391 - 0.22539933058742487im 2.94085597363339e-16 + 5.449120515590654e-16im … 0.17250627190570944 - 0.07328016921985134im -2.6638121967144338e-6 - 9.316277116851189e-7im; -0.3721314541352527 - 0.10795422145947679im -0.6150189617084744 - 0.11984374549881113im … -0.16402854841406414 + 0.06967876175084375im -1.4007670910719967e-6 + 1.7877484289935976e-6im; … ; -0.010942544393057802 - 0.0031743993892786294im -0.0016132972581194935 - 0.00031437012198599044im … 0.014887458133949916 - 0.006324053369782337im -0.029482743595282006 - 0.0330471157025554im; 0.06259889812214887 + 0.018159753054740452im -0.012254629710204903 - 0.00238796007214497im … 0.12455978357106713 - 0.05291252593865455im -0.3133233011994311 - 0.3511964251859512im]], residual_norms = [[3.701728347825846e-14, 3.7850602989413616e-14, 3.824150591168035e-14, 3.166265968332941e-14, 1.2071238937968939e-10, 7.224360224675579e-10, 5.925711443981016e-10], [1.5647059324492598e-14, 3.0602017836042165e-14, 3.156287072833983e-14, 2.014208609852224e-14, 4.028686284310488e-14, 2.605114320970584e-12, 3.731252071819073e-12], [1.0805624161880544e-14, 8.58157365310204e-15, 6.937007202532757e-14, 3.9681220033684294e-14, 3.2755528310531764e-14, 3.5496902808294113e-12, 4.031860437172869e-8], [7.032185499756424e-15, 8.704858617829625e-15, 2.587707858557109e-14, 2.440156486442369e-14, 3.0336318254307362e-12, 1.8320826483365852e-6, 2.8298805051824137e-6]], iterations = [2, 1, 1, 1], converged = 1, n_matvec = 62)], stage = :finalize, algorithm = "SCF", norm_Δρ = 3.4935902352412584e-13)

Potential-based SCF

In [3]:
scfres_scfv = DFTK.scf_potential_mixing(basis; is_converged)
n     Energy            log10(ΔE)   log10(Δρ)   α      Diag
---   ---------------   ---------   ---------   ----   ----
  1   -7.846819379907                   -0.70           4.2
  2   -7.852528003848       -2.24       -1.62   0.80    5.0
  3   -7.852609688719       -4.09       -2.78   0.80    5.0
  4   -7.852646571415       -4.43       -3.57   0.80    7.2
  5   -7.852646683368       -6.95       -4.55   0.80    8.8
  6   -7.852646686679       -8.48       -5.09   0.80   10.5
  7   -7.852646686724      -10.34       -6.12   0.80   11.2
  8   -7.852646686730      -11.27       -7.13   0.80   13.5
  9   -7.852646686730      -13.32       -7.77   0.80   15.0
 10   -7.852646686730      -15.05       -9.38   0.80   16.8
 11   -7.852646686730      -15.05       -9.29   0.80   19.0
 12   -7.852646686730   +  -14.45      -10.19   0.80   19.8
 13   -7.852646686730      -14.27      -11.67   0.80   21.0
 14   -7.852646686730   +  -14.45      -12.33   0.80   23.5
Out[3]:
(ham = Hamiltonian(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), HamiltonianBlock[DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [0.0, 0.5625437115174675, 2.25017484606987, 2.25017484606987, 0.5625437115174675, 0.5625437115174675, 0.7500582820232901, 2.0626602755640477, 4.50034969213974, 3.5627768396106276  …  3.7502914101164504, 3.7502914101164504, 2.0626602755640477, 1.5001165640465801, 0.7500582820232901, 2.0626602755640477, 4.50034969213974, 3.5627768396106276, 1.5001165640465801, 0.5625437115174675]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), ComplexF64[0.11164094023604486 + 0.0im 0.1729534009156557 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.07139183057793365 - 0.07139183057793365im 0.10318729458139622 - 0.10318729458139622im … -0.035578676822652595 + 0.035578676822652595im 0.035578676822652595 - 0.035578676822652595im; … ; -0.08538801146445177 + 0.0im -0.10864081623630145 + 0.0im … 0.0 + 0.08076812854291712im 0.0 - 0.0im; -0.07139183057793365 + 0.07139183057793365im -0.10318729458139622 + 0.10318729458139622im … -0.035578676822652595 + 0.035578676822652595im -0.035578676822652595 + 0.035578676822652595im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [-0.41291392126632637 -0.48683674427720564 … -0.702711322619116 -0.4868367442772059; -0.4868367442772055 -0.7744303950404638 … -0.4136373284393247 -0.3823307497945041; … ; -0.7027113226191162 -0.4136373284393249 … -2.396761682588072 -1.2958067581749806; -0.4868367442772054 -0.38233074979450404 … -1.2958067581749808 -0.7744303950404636;;; -0.48683674427720564 -0.7744303950404638 … -0.41363732843932477 -0.38233074979450443; -0.7744303950404636 -1.4814477483918906 … -0.3245845694332897 -0.44991939657070656; … ; -0.4136373284393248 -0.32458456943329006 … -1.0113572986117156 -0.6373277791931993; -0.38233074979450393 -0.4499193965707065 … -0.637327779193199 -0.4499193965707064;;; -0.702711322619116 -1.295806758174981 … -0.2982034893755826 -0.413637328439325; -1.2958067581749808 -2.9196723936539075 … -0.35372958466146276 -0.637327779193199; … ; -0.2982034893755826 -0.3537295846614633 … -0.49037260810718925 -0.35372958466146315; -0.4136373284393247 -0.637327779193199 … -0.35372958466146254 -0.32458456943328984;;; … ;;; -1.0166744212557877 -0.5332878143066075 … -3.6361382571228837 -1.9987602620506377; -0.5332878143066073 -0.32174124747389765 … -1.466733940750274 -0.9061938941468961; … ; -3.6361382571228837 -1.466733940750274 … -10.988177824465925 -8.0873761682082; -1.9987602620506375 -0.9061938941468961 … -8.0873761682082 -4.647878371143251;;; -0.702711322619116 -0.41363732843932477 … -2.3967616825880724 -1.2958067581749808; -0.4136373284393246 -0.32458456943328995 … -1.0113572986117159 -0.637327779193199; … ; -2.3967616825880724 -1.011357298611716 … -11.002806190875031 -6.077304186394092; -1.2958067581749806 -0.6373277791931988 … -6.077304186394092 -2.9196723936539075;;; -0.4868367442772057 -0.38233074979450427 … -1.2958067581749808 -0.7744303950404638; -0.38233074979450404 -0.4499193965707065 … -0.637327779193199 -0.44991939657070656; … ; -1.2958067581749808 -0.637327779193199 … -6.07730418639409 -2.919672393653907; -0.7744303950404635 -0.4499193965707064 … -2.919672393653907 -1.4814477483918906])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [0.0, 0.5625437115174675, 2.25017484606987, 2.25017484606987, 0.5625437115174675, 0.5625437115174675, 0.7500582820232901, 2.0626602755640477, 4.50034969213974, 3.5627768396106276  …  3.7502914101164504, 3.7502914101164504, 2.0626602755640477, 1.5001165640465801, 0.7500582820232901, 2.0626602755640477, 4.50034969213974, 3.5627768396106276, 1.5001165640465801, 0.5625437115174675]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [-0.41291392126632637 -0.48683674427720564 … -0.702711322619116 -0.4868367442772059; -0.4868367442772055 -0.7744303950404638 … -0.4136373284393247 -0.3823307497945041; … ; -0.7027113226191162 -0.4136373284393249 … -2.396761682588072 -1.2958067581749806; -0.4868367442772054 -0.38233074979450404 … -1.2958067581749808 -0.7744303950404636;;; -0.48683674427720564 -0.7744303950404638 … -0.41363732843932477 -0.38233074979450443; -0.7744303950404636 -1.4814477483918906 … -0.3245845694332897 -0.44991939657070656; … ; -0.4136373284393248 -0.32458456943329006 … -1.0113572986117156 -0.6373277791931993; -0.38233074979450393 -0.4499193965707065 … -0.637327779193199 -0.4499193965707064;;; -0.702711322619116 -1.295806758174981 … -0.2982034893755826 -0.413637328439325; -1.2958067581749808 -2.9196723936539075 … -0.35372958466146276 -0.637327779193199; … ; -0.2982034893755826 -0.3537295846614633 … -0.49037260810718925 -0.35372958466146315; -0.4136373284393247 -0.637327779193199 … -0.35372958466146254 -0.32458456943328984;;; … ;;; -1.0166744212557877 -0.5332878143066075 … -3.6361382571228837 -1.9987602620506377; -0.5332878143066073 -0.32174124747389765 … -1.466733940750274 -0.9061938941468961; … ; -3.6361382571228837 -1.466733940750274 … -10.988177824465925 -8.0873761682082; -1.9987602620506375 -0.9061938941468961 … -8.0873761682082 -4.647878371143251;;; -0.702711322619116 -0.41363732843932477 … -2.3967616825880724 -1.2958067581749808; -0.4136373284393246 -0.32458456943328995 … -1.0113572986117159 -0.637327779193199; … ; -2.3967616825880724 -1.011357298611716 … -11.002806190875031 -6.077304186394092; -1.2958067581749806 -0.6373277791931988 … -6.077304186394092 -2.9196723936539075;;; -0.4868367442772057 -0.38233074979450427 … -1.2958067581749808 -0.7744303950404638; -0.38233074979450404 -0.4499193965707065 … -0.637327779193199 -0.44991939657070656; … ; -1.2958067581749808 -0.637327779193199 … -6.07730418639409 -2.919672393653907; -0.7744303950404635 -0.4499193965707064 … -2.919672393653907 -1.4814477483918906]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), ComplexF64[0.11164094023604486 + 0.0im 0.1729534009156557 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.07139183057793365 - 0.07139183057793365im 0.10318729458139622 - 0.10318729458139622im … -0.035578676822652595 + 0.035578676822652595im 0.035578676822652595 - 0.035578676822652595im; … ; -0.08538801146445177 + 0.0im -0.10864081623630145 + 0.0im … 0.0 + 0.08076812854291712im 0.0 - 0.0im; -0.07139183057793365 + 0.07139183057793365im -0.10318729458139622 + 0.10318729458139622im … -0.035578676822652595 + 0.035578676822652595im -0.035578676822652595 + 0.035578676822652595im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, (ψ_reals = Array{ComplexF64, 3}[[-0.015411189761215765 + 0.05004085466742328im -0.06864138320050574 - 0.07990060144342327im … 0.08275995554035344 + 0.035685601649827606im 0.06332950045313805 + 0.1253071097762007im; -0.10831746141456731 - 0.0024308496143408964im -0.08518239672048056 - 0.07353819627003749im … 0.05120749756372342 + 0.06132837509147145im -0.027541496515851 + 0.07576290346669554im; … ; 0.08850269216321582 + 0.0836731653251854im 0.06135377967453766 + 0.031229182102079155im … -0.01669179618957107 - 0.09518698668555245im 0.07207542154236045 + 0.019571122782447763im; 0.09453478190268902 + 0.08124211898708104im 0.04387288100795807 - 0.00928534329125408im … 0.04172479993003492 - 0.050929635423281314im 0.11874644556805566 + 0.07194631914350347im;;; -0.12078620043359352 + 0.022051122647759505im -0.19497215785446287 - 0.05899739342217958im … 0.06324702251020886 + 0.11632441540387115im 0.016972313042426187 + 0.12962528880482088im; -0.06098135899818548 - 0.03952078134559228im -0.07369694669735719 - 0.0196909184213478im … 0.018637389570043496 + 0.07283176079760607im -0.04594793226899214 + 0.05171264610877194im; … ; 0.07276089705789852 + 0.039011833495671375im 0.004549264008697668 - 0.026889916288504068im … 0.03697604131055187 - 0.020991593107906548im 0.10392534723939029 + 0.044887903416834976im; -0.0037006733951600638 + 0.0529104182661555im -0.1286317180835799 - 0.050257298052359456im … 0.06452036370349695 + 0.04589961100212147im 0.08370190117169726 + 0.13467007245563611im;;; -0.14899888182093698 - 0.0278588543992637im -0.16066918110291936 - 0.01954489705564709im … 0.012923216315620874 + 0.07725368146346764im -0.05104235567509694 + 0.06533594352342013im; -0.04841948016284105 - 0.07854651350211865im 0.019894370132515455 - 0.000714051049874067im … -0.006078616635881498 + 0.027414646831021076im -0.03699273161792986 - 0.01603964545430523im; … ; -0.021707050488370676 + 0.023659410242153994im -0.06542905333556631 - 0.02361051615163339im … 0.038893741695574024 + 0.02242786980354699im 0.042734557350040475 + 0.0583252978667829im; -0.11191565325149791 + 0.022191876739912134im -0.16944384953089206 - 0.010098951314458246im … 0.04031126024212027 + 0.07509698620322101im 0.0006956063590300224 + 0.10069886121612914im;;; … ;;; -0.026804747920456985 - 0.011693699730970734im -0.007069655543666995 + 0.020425092278724105im … -0.06373991586796646 - 0.028811435695798297im -0.024860196318960824 - 0.03322651775829241im; 0.012997958745374589 + 0.005800273660348734im 0.015793463243834287 + 0.01426788944552836im … -0.006114584180926155 - 0.015393557138614653im 0.01631467357676094 - 0.009488806366304729im; … ; -0.03565047072650708 - 0.048900723467431836im -0.02586953354966093 - 0.011795601350800688im … -0.0310820870663721 - 0.016480693518113335im -0.028560924682575053 - 0.0576713994244366im; -0.0336274531678089 - 0.038534893441224766im -0.017837287018735794 + 0.0015863894638605308im … -0.07580575032683509 - 0.037221789300448574im -0.04966246058792777 - 0.056612355510088516im;;; 0.017484635514522562 + 0.037336852165032935im 0.028226604904775694 + 0.045721315017720046im … -0.014448099444867683 - 0.05463903824869835im 0.03749968588407996 - 0.025727677107217607im; 0.042831583825330005 + 0.0288388968971472im 0.02138102847942567 + 0.004453280496141791im … 0.058397200167432245 - 0.01793981969375795im 0.08284662537734616 + 0.006744819168942569im; … ; -0.062111302627884654 - 0.02309463174883834im -0.0413438604645288 + 0.04465139157854721im … -0.11752641211646642 - 0.08819700562795296im -0.06752998608995305 - 0.1014090211045373im; -0.05064514000767936 + 0.022816791186773128im -0.0066064129736317905 + 0.06629674412534611im … -0.10971434950646469 - 0.10850998283783309im -0.04233391173960335 - 0.06205723102838844im;;; 0.07261511332671697 + 0.09071466120967249im 0.030209495807726992 + 0.014882585762286711im … 0.10801800634069636 - 0.019039671198406983im 0.14271066365405607 + 0.049191178431258364im; 0.019652607511379608 + 0.014328021048188484im -0.016977145663741335 - 0.04140196521005714im … 0.11334017947149616 + 0.0119565388058872im 0.08212253150990671 + 0.05207011129960051im; … ; -0.02213534889050324 + 0.09728018498866137im -0.0029656296964601985 + 0.10430371072791084im … -0.07491617190210312 - 0.10307047062784441im -0.019660329462347297 - 0.04535978388733683im; 0.05366963933634697 + 0.10966474653748137im 0.04606972095781878 + 0.08095167999725822im … 0.002987686753435625 - 0.09293227957603331im 0.05533655669285957 + 0.01728746584304787im]],)), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [0.06250485683527418, 1.000077709364387, 3.062737984928434, 4.000310837457548, 1.562621420881854, 0.2500194273410967, 0.5000388546821934, 1.0625825661996608, 2.750213700752063, 2.7502137007520635  …  2.5001942734109663, 4.5628545489750145, 3.062737984928434, 1.7501359913876768, 1.5626214208818543, 1.062582566199661, 2.750213700752063, 2.750213700752064, 1.0625825661996608, 0.5000388546821934]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), ComplexF64[0.10663902257822168 - 0.028573839981478756im 0.16397423109777803 - 0.0439367628021639im … -0.0048810168633526265 + 0.01821620292663248im 0.0048810168633526265 - 0.01821620292663248im; 0.04668482831007231 - 0.08086049457567514im 0.06370661418591363 - 0.11034309254819058im … -0.05243363114037364 + 0.030272571053484264im 0.05243363114037364 - 0.030272571053484264im; … ; -0.08918635851135279 + 0.023897412738989543im -0.12067576411442682 + 0.03233497354046929im … -0.019302751901532963 + 0.07203885082241784im -0.0038605503803065926 + 0.014407770164483566im; -0.051048693065027635 + 0.08841893004861681im -0.0743729428832569 + 0.128817715782219im … -0.02947884616601673 + 0.017019619769349337im -0.05895769233203346 + 0.034039239538698675im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [-0.41291392126632637 -0.48683674427720564 … -0.702711322619116 -0.4868367442772059; -0.4868367442772055 -0.7744303950404638 … -0.4136373284393247 -0.3823307497945041; … ; -0.7027113226191162 -0.4136373284393249 … -2.396761682588072 -1.2958067581749806; -0.4868367442772054 -0.38233074979450404 … -1.2958067581749808 -0.7744303950404636;;; -0.48683674427720564 -0.7744303950404638 … -0.41363732843932477 -0.38233074979450443; -0.7744303950404636 -1.4814477483918906 … -0.3245845694332897 -0.44991939657070656; … ; -0.4136373284393248 -0.32458456943329006 … -1.0113572986117156 -0.6373277791931993; -0.38233074979450393 -0.4499193965707065 … -0.637327779193199 -0.4499193965707064;;; -0.702711322619116 -1.295806758174981 … -0.2982034893755826 -0.413637328439325; -1.2958067581749808 -2.9196723936539075 … -0.35372958466146276 -0.637327779193199; … ; -0.2982034893755826 -0.3537295846614633 … -0.49037260810718925 -0.35372958466146315; -0.4136373284393247 -0.637327779193199 … -0.35372958466146254 -0.32458456943328984;;; … ;;; -1.0166744212557877 -0.5332878143066075 … -3.6361382571228837 -1.9987602620506377; -0.5332878143066073 -0.32174124747389765 … -1.466733940750274 -0.9061938941468961; … ; -3.6361382571228837 -1.466733940750274 … -10.988177824465925 -8.0873761682082; -1.9987602620506375 -0.9061938941468961 … -8.0873761682082 -4.647878371143251;;; -0.702711322619116 -0.41363732843932477 … -2.3967616825880724 -1.2958067581749808; -0.4136373284393246 -0.32458456943328995 … -1.0113572986117159 -0.637327779193199; … ; -2.3967616825880724 -1.011357298611716 … -11.002806190875031 -6.077304186394092; -1.2958067581749806 -0.6373277791931988 … -6.077304186394092 -2.9196723936539075;;; -0.4868367442772057 -0.38233074979450427 … -1.2958067581749808 -0.7744303950404638; -0.38233074979450404 -0.4499193965707065 … -0.637327779193199 -0.44991939657070656; … ; -1.2958067581749808 -0.637327779193199 … -6.07730418639409 -2.919672393653907; -0.7744303950404635 -0.4499193965707064 … -2.919672393653907 -1.4814477483918906])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [0.06250485683527418, 1.000077709364387, 3.062737984928434, 4.000310837457548, 1.562621420881854, 0.2500194273410967, 0.5000388546821934, 1.0625825661996608, 2.750213700752063, 2.7502137007520635  …  2.5001942734109663, 4.5628545489750145, 3.062737984928434, 1.7501359913876768, 1.5626214208818543, 1.062582566199661, 2.750213700752063, 2.750213700752064, 1.0625825661996608, 0.5000388546821934]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [-0.41291392126632637 -0.48683674427720564 … -0.702711322619116 -0.4868367442772059; -0.4868367442772055 -0.7744303950404638 … -0.4136373284393247 -0.3823307497945041; … ; -0.7027113226191162 -0.4136373284393249 … -2.396761682588072 -1.2958067581749806; -0.4868367442772054 -0.38233074979450404 … -1.2958067581749808 -0.7744303950404636;;; -0.48683674427720564 -0.7744303950404638 … -0.41363732843932477 -0.38233074979450443; -0.7744303950404636 -1.4814477483918906 … -0.3245845694332897 -0.44991939657070656; … ; -0.4136373284393248 -0.32458456943329006 … -1.0113572986117156 -0.6373277791931993; -0.38233074979450393 -0.4499193965707065 … -0.637327779193199 -0.4499193965707064;;; -0.702711322619116 -1.295806758174981 … -0.2982034893755826 -0.413637328439325; -1.2958067581749808 -2.9196723936539075 … -0.35372958466146276 -0.637327779193199; … ; -0.2982034893755826 -0.3537295846614633 … -0.49037260810718925 -0.35372958466146315; -0.4136373284393247 -0.637327779193199 … -0.35372958466146254 -0.32458456943328984;;; … ;;; -1.0166744212557877 -0.5332878143066075 … -3.6361382571228837 -1.9987602620506377; -0.5332878143066073 -0.32174124747389765 … -1.466733940750274 -0.9061938941468961; … ; -3.6361382571228837 -1.466733940750274 … -10.988177824465925 -8.0873761682082; -1.9987602620506375 -0.9061938941468961 … -8.0873761682082 -4.647878371143251;;; -0.702711322619116 -0.41363732843932477 … -2.3967616825880724 -1.2958067581749808; -0.4136373284393246 -0.32458456943328995 … -1.0113572986117159 -0.637327779193199; … ; -2.3967616825880724 -1.011357298611716 … -11.002806190875031 -6.077304186394092; -1.2958067581749806 -0.6373277791931988 … -6.077304186394092 -2.9196723936539075;;; -0.4868367442772057 -0.38233074979450427 … -1.2958067581749808 -0.7744303950404638; -0.38233074979450404 -0.4499193965707065 … -0.637327779193199 -0.44991939657070656; … ; -1.2958067581749808 -0.637327779193199 … -6.07730418639409 -2.919672393653907; -0.7744303950404635 -0.4499193965707064 … -2.919672393653907 -1.4814477483918906]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), ComplexF64[0.10663902257822168 - 0.028573839981478756im 0.16397423109777803 - 0.0439367628021639im … -0.0048810168633526265 + 0.01821620292663248im 0.0048810168633526265 - 0.01821620292663248im; 0.04668482831007231 - 0.08086049457567514im 0.06370661418591363 - 0.11034309254819058im … -0.05243363114037364 + 0.030272571053484264im 0.05243363114037364 - 0.030272571053484264im; … ; -0.08918635851135279 + 0.023897412738989543im -0.12067576411442682 + 0.03233497354046929im … -0.019302751901532963 + 0.07203885082241784im -0.0038605503803065926 + 0.014407770164483566im; -0.051048693065027635 + 0.08841893004861681im -0.0743729428832569 + 0.128817715782219im … -0.02947884616601673 + 0.017019619769349337im -0.05895769233203346 + 0.034039239538698675im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, (ψ_reals = Array{ComplexF64, 3}[[0.11148919387100817 - 0.06081023228980133im -0.044036188564191184 - 0.009124296292305238im … 0.0893608981370888 + 0.04153538814647461im 0.16541394436034035 - 0.046366385581716754im; -0.05883237857941452 - 0.04571454154936652im -0.14111275947650148 + 0.00872041489310499im … 0.07179072700367897 - 0.04949429480183547im 0.06624132118709863 - 0.11613916104191024im; … ; 0.04766706028202251 - 0.03724126706649765im -0.016550195164289065 + 0.007137684376678639im … -0.01250077914875447 - 0.008911595079902291im 0.05905292870809564 - 0.06174736825996005im; 0.08166384926128678 - 0.01262419445297829im -0.00859090332372467 - 0.0071519996747508524im … 0.025685736525308978 + 0.04635195596194895im 0.10131430399842292 - 0.010185257603026902im;;; -0.029867663276613235 - 0.0010952102871171422im -0.09489424550881387 + 0.00984503001640781im … 0.057693716141502545 - 0.01836414443214473im 0.06057539080221191 - 0.07100452913350053im; -0.12572987385577813 - 0.004025119502004478im -0.15849575250920495 + 0.03562734572468044im … 0.02661176586262229 - 0.05427383150257193im -0.006153702077252401 - 0.06303558866683145im; … ; -0.03396821067697421 - 0.023014868788718286im -0.030873831518804414 + 0.025887743306105424im … 0.007618679493675359 - 0.03319848983682122im 0.014031080776188956 - 0.0604779820077012im; -0.0071437506337691985 + 0.02567094932211494im -0.04978822935617194 + 0.03960651796016395im … 0.031177070034925532 - 0.0032313104745861623im 0.03511899421631645 - 0.032697953198310835im;;; -0.007039180641855623 + 0.02737305472373017im -0.011100257230504517 + 0.018468487288750213im … 0.02239554924698653 - 0.005769848808409471im 0.020103324701477486 + 0.012273683410517763im; -0.07513526844836595 + 0.020806645185705415im -0.07156972306084144 + 0.03131994793025972im … -0.0005441413124085692 - 0.015257693652728102im -0.028578984237554818 - 0.0038036574169033528im; … ; -0.01597124349665775 + 0.030856236227243157im -0.0006887278583915823 + 0.03718032351075273im … 0.0023429042044287186 - 0.022763181302581627im -0.006943926153154982 - 0.014272460178877087im; -0.009432261245431717 + 0.0481704893703655im 0.018450029982892108 + 0.04474927465529243im … 0.00997227280727842 - 0.014337322503916252im 0.007800125958610087 + 0.017145224783978508im;;; … ;;; -0.004715260407838293 - 0.019280399564992265im 0.0138173743222892 - 0.008253626853696093im … -0.06481310117782255 - 0.008176236098978891im -0.0453301316828102 - 0.007821239842740128im; 0.022788255897626487 - 0.006493018732889783im 0.019694192094050593 - 0.0020126318477650127im … -0.02411942819482821 + 0.0022907406577737034im 0.0040355384670626195 - 5.168196685985353e-5im; … ; -0.033088655728567916 - 0.013934819493142707im -0.004459816107226283 - 0.0008483036377689862im … -0.021207900932182132 - 0.01784594128089759im -0.044160840516562216 - 0.0037094535611512294im; -0.02745704634618292 - 0.005494130495937389im 0.003776838072538073 + 0.006505720916025038im … -0.05440131268259238 - 0.008183446401463394im -0.05365628892189216 + 0.012744200091847954im;;; 0.0571735584789024 - 0.04632662556403823im 0.04324382478725927 - 0.021382512430931103im … -0.0797301797820979 + 0.026842691123756007im 0.023654043538594592 + 0.009713417412145495im; 0.07718980240628234 + 0.006787902245401541im 0.02927622642047225 + 0.013564196708497539im … 0.01056423640069528 + 0.019461579502056958im 0.06454187198856784 - 0.002970907062681289im; … ; 0.0015249565607779903 - 0.006098566517654395im 0.02868826629472434 + 0.021485372837037206im … -0.07418032947114636 - 0.03089807641908923im -0.07487579844850306 - 0.027654321994212094im; 0.020536362808271605 - 0.009088136407569971im 0.036636009896538924 + 0.004056907027925965im … -0.11202036756841133 + 0.006771696698637989im -0.08637756113198695 - 1.932172101966417e-5im;;; 0.16353966881873666 - 0.031459292746278227im 0.06790065857579164 - 0.0071500093293300135im … 0.038672089354137115 + 0.0813418614832827im 0.16071887437879323 + 0.018607285785332862im; 0.0860981921408251 + 0.00517403703268122im -0.010942983346147812 + 0.017145615571282066im … 0.07142945896169117 + 0.017374423627986753im 0.14477529021482521 - 0.020470879699122875im; … ; 0.07646602994794907 - 0.016788856326900338im 0.0496042200928713 + 0.02861009362321059im … -0.07960021152082566 - 0.00892997264180358im -0.0012314602921522505 - 0.027414277150698402im; 0.108391897073994 - 0.001552533930046172im 0.055553823670923805 + 0.005007119288813322im … -0.08057896637530969 + 0.06244720341393885im 0.06542586673219336 + 0.017578112772682876im]],)), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [0.0833398091136989, 0.8959029479722631, 2.8335535098657623, 4.396174930747617, 1.8334758005013758, 0.3958640932900698, 0.8959029479722631, 1.3334369458191824, 2.8960583667010367, 3.39609722138323  …  1.89598065733665, 3.833631219230149, 2.8335535098657623, 1.3959418026544566, 1.0834175184780857, 0.8333980911369889, 2.3960195120188432, 2.8960583667010367, 1.0834175184780857, 0.3958640932900698]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), ComplexF64[0.09525460347564817 - 0.05499527095821653im 0.14610260131202302 - 0.08435237619680104im … -0.018766875445216862 + 0.032505181770432406im 5.2088543048880615e-19 - 9.022000305289992e-19im; 0.024619950292842606 - 0.09188290537270884im 0.03407002323540016 - 0.12715105772956556im … -0.07491066001757686 + 0.02007225085619212im 0.04494639601054611 - 0.012043350513715271im; … ; -0.07966512642409461 + 0.045994682185976576im -0.10748648020277889 + 0.06205734827931975im … -0.02968662889946843 + 0.05141874955932189im 0.0 - 0.0im; -0.026921300372532365 + 0.10047166079611371im -0.039739321889381986 + 0.14830916834950758im … -0.016846285674482424 + 0.0045139486419415575im -0.05053885702344723 + 0.013541845925824664im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [-0.41291392126632637 -0.48683674427720564 … -0.702711322619116 -0.4868367442772059; -0.4868367442772055 -0.7744303950404638 … -0.4136373284393247 -0.3823307497945041; … ; -0.7027113226191162 -0.4136373284393249 … -2.396761682588072 -1.2958067581749806; -0.4868367442772054 -0.38233074979450404 … -1.2958067581749808 -0.7744303950404636;;; -0.48683674427720564 -0.7744303950404638 … -0.41363732843932477 -0.38233074979450443; -0.7744303950404636 -1.4814477483918906 … -0.3245845694332897 -0.44991939657070656; … ; -0.4136373284393248 -0.32458456943329006 … -1.0113572986117156 -0.6373277791931993; -0.38233074979450393 -0.4499193965707065 … -0.637327779193199 -0.4499193965707064;;; -0.702711322619116 -1.295806758174981 … -0.2982034893755826 -0.413637328439325; -1.2958067581749808 -2.9196723936539075 … -0.35372958466146276 -0.637327779193199; … ; -0.2982034893755826 -0.3537295846614633 … -0.49037260810718925 -0.35372958466146315; -0.4136373284393247 -0.637327779193199 … -0.35372958466146254 -0.32458456943328984;;; … ;;; -1.0166744212557877 -0.5332878143066075 … -3.6361382571228837 -1.9987602620506377; -0.5332878143066073 -0.32174124747389765 … -1.466733940750274 -0.9061938941468961; … ; -3.6361382571228837 -1.466733940750274 … -10.988177824465925 -8.0873761682082; -1.9987602620506375 -0.9061938941468961 … -8.0873761682082 -4.647878371143251;;; -0.702711322619116 -0.41363732843932477 … -2.3967616825880724 -1.2958067581749808; -0.4136373284393246 -0.32458456943328995 … -1.0113572986117159 -0.637327779193199; … ; -2.3967616825880724 -1.011357298611716 … -11.002806190875031 -6.077304186394092; -1.2958067581749806 -0.6373277791931988 … -6.077304186394092 -2.9196723936539075;;; -0.4868367442772057 -0.38233074979450427 … -1.2958067581749808 -0.7744303950404638; -0.38233074979450404 -0.4499193965707065 … -0.637327779193199 -0.44991939657070656; … ; -1.2958067581749808 -0.637327779193199 … -6.07730418639409 -2.919672393653907; -0.7744303950404635 -0.4499193965707064 … -2.919672393653907 -1.4814477483918906])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [0.0833398091136989, 0.8959029479722631, 2.8335535098657623, 4.396174930747617, 1.8334758005013758, 0.3958640932900698, 0.8959029479722631, 1.3334369458191824, 2.8960583667010367, 3.39609722138323  …  1.89598065733665, 3.833631219230149, 2.8335535098657623, 1.3959418026544566, 1.0834175184780857, 0.8333980911369889, 2.3960195120188432, 2.8960583667010367, 1.0834175184780857, 0.3958640932900698]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [-0.41291392126632637 -0.48683674427720564 … -0.702711322619116 -0.4868367442772059; -0.4868367442772055 -0.7744303950404638 … -0.4136373284393247 -0.3823307497945041; … ; -0.7027113226191162 -0.4136373284393249 … -2.396761682588072 -1.2958067581749806; -0.4868367442772054 -0.38233074979450404 … -1.2958067581749808 -0.7744303950404636;;; -0.48683674427720564 -0.7744303950404638 … -0.41363732843932477 -0.38233074979450443; -0.7744303950404636 -1.4814477483918906 … -0.3245845694332897 -0.44991939657070656; … ; -0.4136373284393248 -0.32458456943329006 … -1.0113572986117156 -0.6373277791931993; -0.38233074979450393 -0.4499193965707065 … -0.637327779193199 -0.4499193965707064;;; -0.702711322619116 -1.295806758174981 … -0.2982034893755826 -0.413637328439325; -1.2958067581749808 -2.9196723936539075 … -0.35372958466146276 -0.637327779193199; … ; -0.2982034893755826 -0.3537295846614633 … -0.49037260810718925 -0.35372958466146315; -0.4136373284393247 -0.637327779193199 … -0.35372958466146254 -0.32458456943328984;;; … ;;; -1.0166744212557877 -0.5332878143066075 … -3.6361382571228837 -1.9987602620506377; -0.5332878143066073 -0.32174124747389765 … -1.466733940750274 -0.9061938941468961; … ; -3.6361382571228837 -1.466733940750274 … -10.988177824465925 -8.0873761682082; -1.9987602620506375 -0.9061938941468961 … -8.0873761682082 -4.647878371143251;;; -0.702711322619116 -0.41363732843932477 … -2.3967616825880724 -1.2958067581749808; -0.4136373284393246 -0.32458456943328995 … -1.0113572986117159 -0.637327779193199; … ; -2.3967616825880724 -1.011357298611716 … -11.002806190875031 -6.077304186394092; -1.2958067581749806 -0.6373277791931988 … -6.077304186394092 -2.9196723936539075;;; -0.4868367442772057 -0.38233074979450427 … -1.2958067581749808 -0.7744303950404638; -0.38233074979450404 -0.4499193965707065 … -0.637327779193199 -0.44991939657070656; … ; -1.2958067581749808 -0.637327779193199 … -6.07730418639409 -2.919672393653907; -0.7744303950404635 -0.4499193965707064 … -2.919672393653907 -1.4814477483918906]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), ComplexF64[0.09525460347564817 - 0.05499527095821653im 0.14610260131202302 - 0.08435237619680104im … -0.018766875445216862 + 0.032505181770432406im 5.2088543048880615e-19 - 9.022000305289992e-19im; 0.024619950292842606 - 0.09188290537270884im 0.03407002323540016 - 0.12715105772956556im … -0.07491066001757686 + 0.02007225085619212im 0.04494639601054611 - 0.012043350513715271im; … ; -0.07966512642409461 + 0.045994682185976576im -0.10748648020277889 + 0.06205734827931975im … -0.02968662889946843 + 0.05141874955932189im 0.0 - 0.0im; -0.026921300372532365 + 0.10047166079611371im -0.039739321889381986 + 0.14830916834950758im … -0.016846285674482424 + 0.0045139486419415575im -0.05053885702344723 + 0.013541845925824664im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, (ψ_reals = Array{ComplexF64, 3}[[-0.0028458277555049867 - 0.02148739845579329im -0.04004939162386152 - 0.009761915121626474im … 0.02065440542108421 + 0.010188341248654071im 0.0326033717803766 + 0.00014815575373566814im; -0.08685425646719067 - 0.03490392627014273im -0.10047382343957517 - 0.01091279229385518im … -0.023605970544913736 - 0.0029561108293566806im -0.03380805618328506 - 0.036402763383381886im; … ; 0.020096685748183143 + 0.04268789248912455im 0.01437309099878375 + 0.024698839801799877im … -0.022357158271531327 + 0.028223221955494537im -0.006813861852184655 + 0.022732654313539262im; 0.05772581556650635 + 0.03856795265278268im 0.027136594235865466 + 0.016957593787837823im … 0.04543022681266627 + 0.00400701522953056im 0.05519716858945117 + 0.015949704116584914im;;; -0.07265808035879348 - 0.06209272489044389im -0.055693506090927235 - 0.00755038827748163im … -0.009692687065056148 + 0.020514275625813726im -0.0312243001143952 - 0.024899674131665064im; -0.09747034620808002 - 0.06350125426261596im -0.06580952123035927 + 0.0272388232737957im … -0.02687093099096482 - 0.011794057450080463im -0.06789358368466883 - 0.07522632786437401im; … ; 0.03728091528023593 + 0.0019450403254489598im 0.04212017901940131 + 0.06229058202499204im … -0.00570463676734699 - 0.018059891946563357im 0.01706506280076945 - 0.033504006347387344im; 0.03455966763275415 + 0.02689675598595203im 0.025115415749737788 + 0.04900104681314458im … 0.03030462294246733 - 0.012202564952960026im 0.0370111535641543 - 0.008322195126794558im;;; -0.05076571564426481 - 0.020208242211836952im -0.03280271958245848 - 0.012734339302421897im … -0.014183120467135074 + 0.00592815423721736im -0.03823134961487765 - 0.010430936858911579im; -0.025401461596503486 - 0.026590073508297445im 0.024963703277931293 + 0.06318419132136836im … -0.021364947149256693 - 0.026319897835417085im -0.04446483137404823 - 0.05940962830122419im; … ; 0.02828065449356444 + 0.05040366381849552im 0.02362847560997684 + 0.06200171260308579im … 0.004755161711232045 - 0.008504630784155027im 0.020563730347530115 - 0.0046302758859486im; 0.0073499174261204385 + 0.059287732302164706im -0.005106459716568782 + 0.033597013605935755im … 0.01380166018694122 + 0.004652476567527305im 0.010728855441904318 + 0.030623550403843368im;;; … ;;; 0.011340415723247517 + 0.00486903812992198im 0.016741492651875536 + 0.009758054202635261im … 0.01912262250680136 + 0.004118998510469461im 0.00895435842660262 - 0.03890999279177988im; 0.004263217838926076 - 0.007605111157131465im 0.009961966803264452 - 0.0007850179857268582im … 0.004689044378874902 - 0.004608815553928032im -0.0027457295603006433 - 0.01649588411366153im; … ; 0.009242857440021474 - 0.01906641423155228im 0.0032130464712218114 + 0.02079420153359624im … -0.006066927152604951 + 0.010106237309622831im -0.005155661031129301 - 0.05841881302440268im; 0.006355378862301798 - 0.009638782356055305im 0.002980225682465952 + 0.025729216361196426im … 0.015402292926362311 + 0.02765757410264328im 0.005273282456089642 - 0.07633604192738422im;;; 0.03757560167594212 + 0.017534036680392953im 0.028667030851272826 + 0.020820851744348227im … 0.015192535628540694 - 0.023094142289999807im 0.02018218106859899 - 0.07618301359376758im; 0.018453969834849985 + 0.015540930418882649im 0.002041262095245098 - 0.0060416631803413496im … -0.0026372325773589517 - 0.03789444059793322im -0.006781162573163992 - 0.048894395795101124im; … ; 0.014644434173532284 + 0.05140413012769979im -0.004222755888070737 + 0.0487979709635989im … -0.03570159322785663 - 0.027103610312596914im -0.02056670734929842 - 0.0587836214205672im; 0.020260603206692963 + 0.0282302425541842im 0.011705424354965034 + 0.038281819342040224im … 0.005895731387857588 + 0.01750265255592958im 0.0030821616721664856 - 0.07721272444151253im;;; 0.06309907996974226 + 0.057867619637404395im 0.00644297653989228 - 0.004814598188998338im … 0.03025979627508444 - 0.03135404149991399im 0.05645718280829208 - 0.01965934544823425im; -0.0009681218201489138 + 0.005513239043199114im -0.05083309351901332 + 0.004884468527862994im … -0.015844455468257634 - 0.05495387308178608im 0.010923788061657832 - 0.03207222375686056im; … ; 0.005455164519384347 + 0.08977458449441737im -0.005423265011080041 + 0.03823683335041763im … -0.029918889812614348 + 0.021727880021872266im -0.013931781277829155 + 0.043733171779534494im; 0.05255032686747174 + 0.07038921012372978im 0.012678795083252833 + 0.020908474492585618im … 0.02237571928379552 + 0.011427533232851207im 0.04359791856676222 - 0.012130468361920534im]],)), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), DFTK.RealFourierOperator[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [0.1666796182273978, 0.22918447506267198, 1.4167767549328811, 3.7294564578380256, 3.416932173661655, 1.2292621844270586, 1.2292621844270586, 0.9167379002506877, 1.729301039109252, 3.6669516010027516  …  4.729534167202412, 4.417009883026042, 2.2293398937914453, 1.1667573275917844, 0.41669904556849446, 1.2292621844270588, 3.1669127463205577, 4.729534167202412, 2.1668350369561713, 0.7292233297448653]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), ComplexF64[0.10836454158744746 + 0.0im 0.16454392299317003 + 0.0im … -0.0 - 1.0216068167279948e-18im 0.0 + 0.03680726463308285im; 0.0757741533540503 - 0.0757741533540503im 0.1141835519100639 - 0.1141835519100639im … -0.03847188688271061 + 0.03847188688271061im 0.012823962294236874 - 0.012823962294236874im; … ; -0.07579695351601741 + 0.0im -0.08711072462387971 + 0.0im … 0.0 + 0.06907686686237845im 0.0 - 0.02302562228745948im; -0.0692966484992815 + 0.0692966484992815im -0.09802716364420207 + 0.09802716364420207im … -0.03421471645670587 + 0.03421471645670587im -0.011404905485568627 + 0.011404905485568627im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [-0.41291392126632637 -0.48683674427720564 … -0.702711322619116 -0.4868367442772059; -0.4868367442772055 -0.7744303950404638 … -0.4136373284393247 -0.3823307497945041; … ; -0.7027113226191162 -0.4136373284393249 … -2.396761682588072 -1.2958067581749806; -0.4868367442772054 -0.38233074979450404 … -1.2958067581749808 -0.7744303950404636;;; -0.48683674427720564 -0.7744303950404638 … -0.41363732843932477 -0.38233074979450443; -0.7744303950404636 -1.4814477483918906 … -0.3245845694332897 -0.44991939657070656; … ; -0.4136373284393248 -0.32458456943329006 … -1.0113572986117156 -0.6373277791931993; -0.38233074979450393 -0.4499193965707065 … -0.637327779193199 -0.4499193965707064;;; -0.702711322619116 -1.295806758174981 … -0.2982034893755826 -0.413637328439325; -1.2958067581749808 -2.9196723936539075 … -0.35372958466146276 -0.637327779193199; … ; -0.2982034893755826 -0.3537295846614633 … -0.49037260810718925 -0.35372958466146315; -0.4136373284393247 -0.637327779193199 … -0.35372958466146254 -0.32458456943328984;;; … ;;; -1.0166744212557877 -0.5332878143066075 … -3.6361382571228837 -1.9987602620506377; -0.5332878143066073 -0.32174124747389765 … -1.466733940750274 -0.9061938941468961; … ; -3.6361382571228837 -1.466733940750274 … -10.988177824465925 -8.0873761682082; -1.9987602620506375 -0.9061938941468961 … -8.0873761682082 -4.647878371143251;;; -0.702711322619116 -0.41363732843932477 … -2.3967616825880724 -1.2958067581749808; -0.4136373284393246 -0.32458456943328995 … -1.0113572986117159 -0.637327779193199; … ; -2.3967616825880724 -1.011357298611716 … -11.002806190875031 -6.077304186394092; -1.2958067581749806 -0.6373277791931988 … -6.077304186394092 -2.9196723936539075;;; -0.4868367442772057 -0.38233074979450427 … -1.2958067581749808 -0.7744303950404638; -0.38233074979450404 -0.4499193965707065 … -0.637327779193199 -0.44991939657070656; … ; -1.2958067581749808 -0.637327779193199 … -6.07730418639409 -2.919672393653907; -0.7744303950404635 -0.4499193965707064 … -2.919672393653907 -1.4814477483918906])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [0.1666796182273978, 0.22918447506267198, 1.4167767549328811, 3.7294564578380256, 3.416932173661655, 1.2292621844270586, 1.2292621844270586, 0.9167379002506877, 1.729301039109252, 3.6669516010027516  …  4.729534167202412, 4.417009883026042, 2.2293398937914453, 1.1667573275917844, 0.41669904556849446, 1.2292621844270588, 3.1669127463205577, 4.729534167202412, 2.1668350369561713, 0.7292233297448653]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [-0.41291392126632637 -0.48683674427720564 … -0.702711322619116 -0.4868367442772059; -0.4868367442772055 -0.7744303950404638 … -0.4136373284393247 -0.3823307497945041; … ; -0.7027113226191162 -0.4136373284393249 … -2.396761682588072 -1.2958067581749806; -0.4868367442772054 -0.38233074979450404 … -1.2958067581749808 -0.7744303950404636;;; -0.48683674427720564 -0.7744303950404638 … -0.41363732843932477 -0.38233074979450443; -0.7744303950404636 -1.4814477483918906 … -0.3245845694332897 -0.44991939657070656; … ; -0.4136373284393248 -0.32458456943329006 … -1.0113572986117156 -0.6373277791931993; -0.38233074979450393 -0.4499193965707065 … -0.637327779193199 -0.4499193965707064;;; -0.702711322619116 -1.295806758174981 … -0.2982034893755826 -0.413637328439325; -1.2958067581749808 -2.9196723936539075 … -0.35372958466146276 -0.637327779193199; … ; -0.2982034893755826 -0.3537295846614633 … -0.49037260810718925 -0.35372958466146315; -0.4136373284393247 -0.637327779193199 … -0.35372958466146254 -0.32458456943328984;;; … ;;; -1.0166744212557877 -0.5332878143066075 … -3.6361382571228837 -1.9987602620506377; -0.5332878143066073 -0.32174124747389765 … -1.466733940750274 -0.9061938941468961; … ; -3.6361382571228837 -1.466733940750274 … -10.988177824465925 -8.0873761682082; -1.9987602620506375 -0.9061938941468961 … -8.0873761682082 -4.647878371143251;;; -0.702711322619116 -0.41363732843932477 … -2.3967616825880724 -1.2958067581749808; -0.4136373284393246 -0.32458456943328995 … -1.0113572986117159 -0.637327779193199; … ; -2.3967616825880724 -1.011357298611716 … -11.002806190875031 -6.077304186394092; -1.2958067581749806 -0.6373277791931988 … -6.077304186394092 -2.9196723936539075;;; -0.4868367442772057 -0.38233074979450427 … -1.2958067581749808 -0.7744303950404638; -0.38233074979450404 -0.4499193965707065 … -0.637327779193199 -0.44991939657070656; … ; -1.2958067581749808 -0.637327779193199 … -6.07730418639409 -2.919672393653907; -0.7744303950404635 -0.4499193965707064 … -2.919672393653907 -1.4814477483918906]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), ComplexF64[0.10836454158744746 + 0.0im 0.16454392299317003 + 0.0im … -0.0 - 1.0216068167279948e-18im 0.0 + 0.03680726463308285im; 0.0757741533540503 - 0.0757741533540503im 0.1141835519100639 - 0.1141835519100639im … -0.03847188688271061 + 0.03847188688271061im 0.012823962294236874 - 0.012823962294236874im; … ; -0.07579695351601741 + 0.0im -0.08711072462387971 + 0.0im … 0.0 + 0.06907686686237845im 0.0 - 0.02302562228745948im; -0.0692966484992815 + 0.0692966484992815im -0.09802716364420207 + 0.09802716364420207im … -0.03421471645670587 + 0.03421471645670587im -0.011404905485568627 + 0.011404905485568627im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, (ψ_reals = Array{ComplexF64, 3}[[0.05346826369885535 - 0.011236653838933361im 0.06731523712591272 - 0.01417033268361528im … -0.06451142709786505 + 0.013534886208059909im 0.00726127390700595 - 0.0015306005741634147im; 0.06019418773799014 - 0.012634077871387657im 0.0523836672408603 - 0.01103445863412537im … -0.022431068536584397 + 0.004689068098661792im 0.03154158969145164 - 0.006641133216898495im; 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0.0874741913407971 0.08089966872163502 … 0.07642471016971135 0.08486944834426095; … ; 0.07684754935962752 0.07642471016971135 … 0.04778466667101894 0.06587895342303128; 0.0874741913407971 0.08486944834426098 … 0.06587895342303128 0.08089966872163502;;; 0.0874741913407971 0.08089966872163502 … 0.07642471016971136 0.08486944834426095; 0.08089966872163502 0.06744471469774382 … 0.07348669934703934 0.08163768629014212; … ; 0.07642471016971135 0.07348669934703934 … 0.061888041199964404 0.07259829028446634; 0.08486944834426095 0.08163768629014213 … 0.07259829028446634 0.08163768629014213;;; 0.07684754935962751 0.06587895342303128 … 0.06847203698973393 0.07642471016971135; 0.06587895342303127 0.04657864264980779 … 0.06665759371631641 0.07259829028446632; … ; 0.06847203698973393 0.06665759371631641 … 0.06132515314380829 0.06665759371631641; 0.07642471016971135 0.07259829028446634 … 0.06665759371631641 0.07348669934703934;;; … ;;; 0.06328495229885778 0.06591651445952479 … 0.03394064888051951 0.04987593485998943; 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-0.07999511926871422 - 0.05359628326257376im -0.27593092273341946 + 0.35061620927907866im … 0.028278600807847415 + 0.5687975672006864im 0.08737328906248651 - 0.0409684319865793im; … ; -0.00979834301029283 - 0.006564835108490675im 0.020672569994968918 - 0.02186948865273243im … 0.013524751923255213 + 0.09274925084343716im 0.047348973548266914 + 0.050002703557360764im; 0.07999511926871926 + 0.053596283262576976im -0.07354187961437303 + 0.13650906715725838im … 0.08315599925721358 + 0.195392102941083im 0.30274950006612134 + 0.4529561207916031im], [-0.9120335849068459 - 0.1753570321032324im 0.19694974189239234 - 0.008304737463747972im … -8.444143858652737e-12 + 5.7992568227463806e-11im -7.65626139285032e-11 - 4.467448835954515e-11im; -0.062175087225745544 - 0.01195442684030099im -0.008765677820332258 + 0.0003696204538737571im … -4.9343348212508646e-11 + 3.196935950574034e-12im -1.0925406843271659e-11 - 3.6015740621736884e-11im; … ; -0.00761135492577586 - 0.0014634380050868978im 0.08618204869292317 - 0.00363401993627666im … 0.07911893427399769 + 0.014092572416140987im -0.03463104706496708 - 0.06647177932316826im; 0.11090079273101301 + 0.02132293612103364im -0.09062702401468622 + 0.0038214502559435924im … 0.3358249842864855 + 0.05981675504388219im -0.1469935229022186 - 0.28214338864053307im], [0.8168185374154896 - 0.45243588511108274im 3.481956668782399e-15 + 2.820322993585445e-15im … 8.119694037639818e-11 + 7.066021172849558e-11im 1.2140537080509139e-8 + 5.320971184015247e-9im; 0.060139290686060144 - 0.03331116027017861im -0.04993906457998081 - 0.027871506582067423im … -0.02170236061496078 - 0.012772327506113644im -0.00614388487441812 + 0.0012820482066230458im; … ; 0.012133326182879897 - 0.006720650817087331im -7.170106125732976e-15 + 6.920718088762383e-17im … 1.6566843777110858e-10 + 2.1700964838736957e-10im 0.03361402130316107 + 0.05554721387323892im; -0.1340226387229184 + 0.07423515554309994im -0.25072194822836075 - 0.13993050308585675im … 0.3290840230760657 + 0.19367335360456767im 0.08094963813947612 + 0.12993263574474634im], [-0.7923977041334531 + 0.16311761630071706im -1.269168284225208e-15 + 4.030067299950224e-16im … -0.18351094953370092 + 0.03812792353193287im 3.724879415208084e-6 - 8.119292372390721e-7im; -0.37951611042082145 + 0.07812461211919204im -0.6135121783287809 + 0.1273328458743064im … 0.17449057376902838 - 0.03625376985032518im -1.4558384508755386e-6 + 3.2222311405162407e-7im; … ; -0.011159690587871075 + 0.002297258204876614im -0.0016093447141399624 + 0.0003340152806781025im … -0.015837384026494806 + 0.003290405671923383im 0.02369908154163019 + 0.03741428000299485im; 0.0638411240650275 - 0.013141900746458308im -0.012224606127978044 + 0.0025371849866238im … -0.13250716165978693 + 0.027534076856651584im 0.25185920284066593 + 0.3976003226158537im]], residual_norms = [[1.2766032242027678e-13, 2.0949203172543295e-13, 1.1332019335882213e-13, 3.2076376213085055e-13, 4.0604089942168814e-11, 5.861041974773755e-10, 3.5984353799721325e-11], [1.1880483244884895e-13, 1.1651291063735727e-13, 2.6939245269704877e-13, 2.3843131454342563e-13, 1.967961902952778e-10, 5.331947405466464e-10, 4.241894450300499e-10], [6.711448586172646e-14, 1.1113570239990984e-13, 2.0799321825468317e-13, 2.0620911238722632e-13, 3.5071751496414626e-11, 9.556803429832234e-10, 1.5306355528058583e-7], [1.4595549436958644e-13, 7.633421053500369e-14, 1.282619340229482e-13, 2.3981640198681086e-13, 1.453476027482004e-9, 1.289495260083182e-5, 5.723549913678774e-6]], iterations = [32, 21, 21, 20], converged = 1, n_matvec = 651)], stage = :finalize, algorithm = "SCF", occupation_threshold = 1.0e-6)

Direct minimization

In [4]:
scfres_dm = direct_minimization(basis; tol)

# Newton algorithm
Iter     Function value   Gradient norm 
     0     1.425348e+01     2.918826e+00
 * time: 0.4231750965118408
     1     1.268181e+00     1.938401e+00
 * time: 0.619391918182373
     2    -1.734181e+00     2.068951e+00
 * time: 0.6431360244750977
     3    -3.725216e+00     1.999793e+00
 * time: 0.6774039268493652
     4    -5.034507e+00     2.027656e+00
 * time: 0.7114109992980957
     5    -6.687103e+00     1.604574e+00
 * time: 0.7459530830383301
     6    -7.398493e+00     7.650012e-01
 * time: 0.7798011302947998
     7    -7.648230e+00     4.028789e-01
 * time: 0.8034560680389404
     8    -7.754205e+00     1.161407e-01
 * time: 0.8271400928497314
     9    -7.787118e+00     1.313925e-01
 * time: 0.8508830070495605
    10    -7.808108e+00     8.301570e-02
 * time: 0.8746471405029297
    11    -7.823295e+00     9.649904e-02
 * time: 0.8989090919494629
    12    -7.840840e+00     5.387239e-02
 * time: 0.9229109287261963
    13    -7.849539e+00     2.541474e-02
 * time: 0.9467740058898926
    14    -7.851483e+00     1.579025e-02
 * time: 0.9707839488983154
    15    -7.852323e+00     9.518510e-03
 * time: 0.9951310157775879
    16    -7.852553e+00     4.450574e-03
 * time: 1.0193610191345215
    17    -7.852624e+00     2.518064e-03
 * time: 1.0429821014404297
    18    -7.852640e+00     1.312737e-03
 * time: 1.066890001296997
    19    -7.852644e+00     7.808754e-04
 * time: 1.0910499095916748
    20    -7.852646e+00     6.240227e-04
 * time: 1.1149299144744873
    21    -7.852646e+00     3.516188e-04
 * time: 1.138679027557373
    22    -7.852647e+00     1.810348e-04
 * time: 1.162485122680664
    23    -7.852647e+00     1.273356e-04
 * time: 1.1862671375274658
    24    -7.852647e+00     4.383329e-05
 * time: 1.2102229595184326
    25    -7.852647e+00     2.708629e-05
 * time: 1.2340049743652344
    26    -7.852647e+00     1.590137e-05
 * time: 1.2578930854797363
    27    -7.852647e+00     7.825464e-06
 * time: 1.2818551063537598
    28    -7.852647e+00     4.868781e-06
 * time: 1.3647871017456055
    29    -7.852647e+00     2.381251e-06
 * time: 1.388627052307129
    30    -7.852647e+00     1.508672e-06
 * time: 1.4124560356140137
    31    -7.852647e+00     1.050220e-06
 * time: 1.4364879131317139
    32    -7.852647e+00     5.320034e-07
 * time: 1.4605069160461426
    33    -7.852647e+00     2.588588e-07
 * time: 1.4842960834503174
    34    -7.852647e+00     1.560996e-07
 * time: 1.508044958114624
    35    -7.852647e+00     1.002919e-07
 * time: 1.5317420959472656
    36    -7.852647e+00     5.817649e-08
 * time: 1.555577039718628
    37    -7.852647e+00     2.987254e-08
 * time: 1.5792760848999023
    38    -7.852647e+00     1.747276e-08
 * time: 1.6030540466308594
    39    -7.852647e+00     9.591149e-09
 * time: 1.6268839836120605
    40    -7.852647e+00     6.680819e-09
 * time: 1.650813102722168
    41    -7.852647e+00     3.815612e-09
 * time: 1.67494797706604
    42    -7.852647e+00     3.796757e-09
 * time: 1.7197070121765137
    43    -7.852647e+00     3.796687e-09
 * time: 1.7961111068725586
Out[4]:
(ham = Hamiltonian(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), HamiltonianBlock[DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [0.0, 0.5625437115174675, 2.25017484606987, 2.25017484606987, 0.5625437115174675, 0.5625437115174675, 0.7500582820232901, 2.0626602755640477, 4.50034969213974, 3.5627768396106276  …  3.7502914101164504, 3.7502914101164504, 2.0626602755640477, 1.5001165640465801, 0.7500582820232901, 2.0626602755640477, 4.50034969213974, 3.5627768396106276, 1.5001165640465801, 0.5625437115174675]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [-0.30116136598756804 -0.36869760795125184 … -0.5702190219244254 -0.36869760795125195; -0.3686976079512516 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456163; … ; -0.5702190219244256 -0.264614164394795 … -2.291992881132685 -1.1751172086054253; -0.3686976079512515 -0.2539389812456162 … -1.1751172086054256 -0.6560706269776425;;; -0.3686976079512517 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456166; -0.6560706269776425 -1.3741022038947448 … -0.1651225671881503 -0.31565743774427135; … ; -0.2646141643947949 -0.16512256718815066 … -0.8632000905877295 -0.4898593856167607; -0.25393898124561615 -0.31565743774427135 … -0.48985938561676046 -0.31565743774427124;;; -0.5702190219244254 -1.1751172086054258 … -0.1242245197168452 -0.264614164394795; -1.1751172086054256 -2.8292222589777416 … -0.1750685951638031 -0.48985938561676046; … ; -0.1242245197168452 -0.1750685951638037 … -0.30112950922681153 -0.17506859516380358; -0.2646141643947948 -0.48985938561676046 … -0.17506859516380294 -0.1651225671881503;;; … ;;; -0.8720732197039092 -0.36117451106748844 … -3.5504427268225025 -1.881971917366274; -0.3611745110674882 -0.13192205269891222 … -1.3219289313234115 -0.747481991474731; … ; -3.5504427268225025 -1.3219289313234115 … -11.011681230319526 -8.06878895093237; -1.8819719173662737 -0.747481991474731 … -8.06878895093237 -4.5798976647669045;;; -0.5702190219244254 -0.2646141643947948 … -2.2919928811326855 -1.1751172086054256; -0.2646141643947947 -0.16512256718815055 … -0.8632000905877295 -0.48985938561676046; … ; -2.2919928811326855 -0.8632000905877297 … -11.026309596728632 -6.029372075563462; -1.1751172086054253 -0.4898593856167603 … -6.029372075563462 -2.8292222589777416;;; -0.3686976079512518 -0.2539389812456165 … -1.1751172086054256 -0.6560706269776427; -0.25393898124561626 -0.3156574377442714 … -0.4898593856167604 -0.31565743774427135; … ; -1.1751172086054256 -0.48985938561676057 … -6.029372075563461 -2.829222258977741; -0.6560706269776424 -0.3156574377442712 … -2.829222258977741 -1.3741022038947448]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), ComplexF64[0.11164094023604486 + 0.0im 0.1729534009156557 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.07139183057793365 - 0.07139183057793365im 0.10318729458139622 - 0.10318729458139622im … -0.035578676822652595 + 0.035578676822652595im 0.035578676822652595 - 0.035578676822652595im; … ; -0.08538801146445177 + 0.0im -0.10864081623630145 + 0.0im … 0.0 + 0.08076812854291712im 0.0 - 0.0im; -0.07139183057793365 + 0.07139183057793365im -0.10318729458139622 + 0.10318729458139622im … -0.035578676822652595 + 0.035578676822652595im -0.035578676822652595 + 0.035578676822652595im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [0.3915556370590074 0.37851742092916557 … 0.3446996003079375 0.3785174209291657; 0.3785174209291656 0.36645844069123706 … 0.3273572817423094 0.3636495426413965; … ; 0.3446996003079375 0.3273572817423093 … 0.3075192694882305 0.33438053204271134; 0.3785174209291656 0.3636495426413965 … 0.33438053204271134 0.36645844069123706;;; 0.3785174209291657 0.366458440691237 … 0.3273572817423093 0.36364954264139643; 0.36645844069123706 0.35102886347928736 … 0.3111940134732182 0.3519170663740599; … ; 0.3273572817423093 0.3111940134732181 … 0.2982412284598287 0.3214260028488039; 0.3636495426413964 0.3519170663740599 … 0.3214260028488039 0.3519170663740599;;; 0.3446996003079375 0.3343805320427113 … 0.28653515377294264 0.3273572817423094; 0.33438053204271134 0.31861604783719377 … 0.2780589188367269 0.32142600284880396; … ; 0.28653515377294264 0.2780589188367269 … 0.2559018577461467 0.2780589188367269; 0.32735728174230927 0.32142600284880396 … 0.27805891883672684 0.3111940134732181;;; … ;;; 0.3048747493337859 0.28303666898571395 … 0.2855643323939694 0.3009573705821879; 0.28303666898571395 0.25898431623070184 … 0.2726330013434142 0.2854141966681785; … ; 0.2855643323939694 0.27263300134341417 … 0.27716038923066866 0.2812108738725452; 0.3009573705821879 0.28541419666817847 … 0.2812108738725452 0.2930827263518427;;; 0.34469960030793756 0.3273572817423093 … 0.3075192694882305 0.33438053204271134; 0.3273572817423094 0.31119401347321807 … 0.29824122845982876 0.32142600284880396; … ; 0.3075192694882305 0.2982412284598287 … 0.2771603892306687 0.29313119155538103; 0.3343805320427113 0.32142600284880396 … 0.2931311915553811 0.3186160478371938;;; 0.3785174209291657 0.3636495426413964 … 0.3343805320427113 0.3664584406912371; 0.36364954264139643 0.3519170663740599 … 0.32142600284880396 0.35191706637405995; … ; 0.33438053204271134 0.3214260028488039 … 0.29313119155538103 0.3186160478371938; 0.36645844069123706 0.35191706637405995 … 0.3186160478371938 0.35102886347928736]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [-0.503308192313982 -0.4966565572311907 … -0.4771919009774658 -0.4966565572311907; -0.4966565572311907 -0.4848182087263484 … -0.4763804457677314 -0.4920413111690271; … ; -0.4771919009774658 -0.4763804457677315 … -0.4122880709063333 -0.4550700815797695; -0.4966565572311907 -0.4920413111690271 … -0.45507008157976947 -0.4848182087263484;;; -0.4966565572311907 -0.4848182087263484 … -0.4763804457677314 -0.4920413111690271; -0.4848182087263484 -0.45837440794132067 … -0.47065601570152904 -0.4861790251791354; … ; -0.4763804457677314 -0.470656015701529 … -0.4463984364571212 -0.4688943964027922; -0.4920413111690271 -0.4861790251791355 … -0.4688943964027922 -0.4861790251791354;;; -0.4771919009774657 -0.4550700815797695 … -0.4605141234167576 -0.4763804457677314; -0.4550700815797695 -0.4090661824735755 … -0.4567199083195155 -0.4688943964027922; … ; -0.4605141234167576 -0.4567199083195155 … -0.44514495661102427 -0.4567199083195155; -0.4763804457677314 -0.4688943964027922 … -0.4567199083195155 -0.47065601570152904;;; … ;;; -0.44947595085725534 -0.45514997220617465 … -0.3712598626574318 -0.41774571522991527; -0.45514997220617465 -0.44880351099219856 … -0.41743801074040043 -0.4441260993150186; … ; -0.3712598626574318 -0.41743801074040043 … -0.2536569833789929 -0.29979809112414557; -0.41774571522991527 -0.4441260993150186 … -0.2997980911241455 -0.361063432689199;;; -0.4771919009774657 -0.4763804457677314 … -0.41228807090633324 -0.4550700815797695; -0.4763804457677314 -0.47065601570152904 … -0.4463984364571212 -0.4688943964027922; … ; -0.41228807090633324 -0.4463984364571212 … -0.2536569833789929 -0.3410633023505617; -0.4550700815797695 -0.4688943964027922 … -0.3410633023505617 -0.4090661824735755;;; -0.4966565572311907 -0.49204131116902705 … -0.4550700815797695 -0.4848182087263484; -0.49204131116902705 -0.4861790251791354 … -0.4688943964027922 -0.4861790251791354; … ; -0.4550700815797695 -0.4688943964027921 … -0.3410633023505617 -0.4090661824735755; -0.4848182087263484 -0.48617902517913547 … -0.4090661824735755 -0.45837440794132067])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [0.0, 0.5625437115174675, 2.25017484606987, 2.25017484606987, 0.5625437115174675, 0.5625437115174675, 0.7500582820232901, 2.0626602755640477, 4.50034969213974, 3.5627768396106276  …  3.7502914101164504, 3.7502914101164504, 2.0626602755640477, 1.5001165640465801, 0.7500582820232901, 2.0626602755640477, 4.50034969213974, 3.5627768396106276, 1.5001165640465801, 0.5625437115174675]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [-0.41291392124254267 -0.48683674425327694 … -0.7027113225939536 -0.48683674425327694; -0.48683674425327667 -0.774430395012754 … -0.41363732842021683 -0.38233074977324694; … ; -0.7027113225939539 -0.41363732842021717 … -2.396761682550788 -1.2958067581424835; -0.48683674425327655 -0.3823307497732468 … -1.2958067581424837 -0.7744303950127538;;; -0.4868367442532767 -0.7744303950127541 … -0.4136373284202169 -0.38233074977324727; -0.7744303950127538 -1.481447748356778 … -0.3245845694164612 -0.4499193965493469; … ; -0.413637328420217 -0.3245845694164615 … -1.0113572985850219 -0.637327779170749; -0.3823307497732469 -0.449919396549347 … -0.6373277791707488 -0.44991939654934676;;; -0.7027113225939536 -1.295806758142484 … -0.2982034893606602 -0.41363732842021705; -1.2958067581424837 -2.9196723936141233 … -0.35372958464659165 -0.6373277791707487; … ; -0.2982034893606602 -0.35372958464659227 … -0.4903726080916891 -0.35372958464659215; -0.41363732842021694 -0.6373277791707487 … -0.35372958464659154 -0.3245845694164612;;; … ;;; -1.0166744212273786 -0.5332878142879491 … -3.636138257085965 -1.9987602620140013; -0.5332878142879489 -0.32174124746040894 … -1.4667339407203976 -0.9061938941215711; … ; -3.636138257085965 -1.4667339407203976 … -10.98817782446785 -8.08737616818397; -1.998760262014001 -0.9061938941215713 … -8.08737616818397 -4.647878371104261;;; -0.7027113225939536 -0.4136373284202169 … -2.396761682550788 -1.2958067581424837; -0.4136373284202167 -0.3245845694164615 … -1.0113572985850219 -0.6373277791707487; … ; -2.396761682550788 -1.0113572985850223 … -11.002806190876957 -6.077304186358642; -1.2958067581424835 -0.6373277791707486 … -6.077304186358642 -2.9196723936141233;;; -0.4868367442532768 -0.38233074977324716 … -1.2958067581424837 -0.774430395012754; -0.3823307497732469 -0.44991939654934693 … -0.6373277791707486 -0.4499193965493468; … ; -1.2958067581424837 -0.6373277791707488 … -6.077304186358641 -2.919672393614123; -0.7744303950127538 -0.4499193965493467 … -2.919672393614123 -1.481447748356778]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), ComplexF64[0.11164094023604486 + 0.0im 0.1729534009156557 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.07139183057793365 - 0.07139183057793365im 0.10318729458139622 - 0.10318729458139622im … -0.035578676822652595 + 0.035578676822652595im 0.035578676822652595 - 0.035578676822652595im; … ; -0.08538801146445177 + 0.0im -0.10864081623630145 + 0.0im … 0.0 + 0.08076812854291712im 0.0 - 0.0im; -0.07139183057793365 + 0.07139183057793365im -0.10318729458139622 + 0.10318729458139622im … -0.035578676822652595 + 0.035578676822652595im -0.035578676822652595 + 0.035578676822652595im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, (ψ_reals = Array{ComplexF64, 3}[[-0.1784763849334866 - 0.11528822978832526im 0.002468446966244502 + 0.08103205293815757im … 0.0972359067556327 + 0.14259833496472674im 0.0024684466359357546 + 0.08103204960217698im; -0.14994683147727178 - 0.1522109265585846im 0.05457568694939437 + 0.06333814687868104im … 0.04258746674080359 + 0.07410712957143603im -0.05085624319202933 - 0.02582891587200327im; … ; -0.05585186073628069 - 0.09167375553460805im -0.05177451831454209 - 0.07029617274483863im … 0.024808850288831234 + 0.01602547200104446im 0.04314902647870221 + 0.02972747569166828im; -0.14994683168031536 - 0.15221091980736964im -0.050856243082324656 - 0.025828907579453424im … 0.07018125566732128 + 0.07109522953555972im 0.054575685024791896 + 0.06333814646557456im;;; -0.10032871459097009 - 0.06775252102832126im 0.11243108704539581 + 0.1618177935952663im … 0.037265883231668365 + 0.0650488974197654im -0.03639045240010769 - 0.0012056976102903239im; -0.06528720416713171 - 0.11014669232572177im 0.14076038972995358 + 0.11206684330991477im … 0.0011218741936896983 + 0.011091079517529063im -0.07463303542075685 - 0.09054917543492126im; … ; -0.04074943884543569 - 0.0543389060346191im -0.016984862337076835 - 0.0166178789922191im … 0.016833863483620565 + 0.01604902822147955im 0.0012853740187511954 - 0.00458623777644722im; -0.08082598655473199 - 0.06920593767128351im 0.02626010074937344 + 0.06384883445879597im … 0.03575680410413502 + 0.04816581478563269im -0.00658521150249712 + 0.007940573544279154im;;; -0.006014817893078108 - 0.006842706505173294im 0.0759943405575136 + 0.08563573635585028im … 0.0007166686870404577 + 0.0068771399245094195im -0.02637697713531401 - 0.02706527671516832im; 0.0021334336329372986 - 0.027394515414618462im 0.07814774932257171 + 0.05750223518710525im … -0.015584508397056976 - 0.02017807961126218im -0.03821161892074021 - 0.058893173840587114im; … ; -0.012063855440079695 - 0.012681051993971858im 0.00639874870393143 + 0.013463169780725412im … 0.00617531980985442 + 0.007258759749847131im -0.00528201477889144 - 0.006419459443928559im; -0.010030314037569455 - 0.0020497765655502374im 0.03698844019565404 + 0.0561864004123129im … 0.008615308557677934 + 0.014847784750345329im -0.011090294807806933 - 0.006584332264336993im;;; … ;;; 0.005898865284676606 + 0.003183682758881792im -0.00938192668491419 - 0.01363684258651178im … -0.011308270063072437 - 0.021891758953476774im 0.017386215576118642 + 0.015072396519918546im; 0.003666678296638335 + 0.00633159826865658im -0.004792983625001747 - 0.004432646322034742im … 0.006773121664132028 + 0.006383441836966722im 0.016221982338190652 + 0.02116855513672121im; … ; 0.01863885022493579 + 0.02393668662597471im 0.0015224330257887595 - 0.0016517526483684382im … -0.03604726230737022 - 0.03379074822421565im 0.005817867121584478 + 0.015220420135006935im; 0.010686485351167663 + 0.004819716084118481im -0.009316978688654347 - 0.01791403187000872im … -0.03491076171911474 - 0.04710710147596687im 0.011015567437765418 + 0.006355263158629401im;;; -0.006014818278617399 - 0.006842707221680311im -0.026376977092967657 - 0.027065277071801938im … 0.024808850493242232 + 0.016025474649454873im 0.07599433890760293 + 0.0856357384043543im; -0.010030314073043552 - 0.0020497782078454157im -0.011090294971986093 - 0.006584333397620167im … 0.03404097061209107 + 0.04533842756589682im 0.036988440007231685 + 0.05618640117483239im; … ; 0.024808850444912194 + 0.016025471317061717im -0.018815247736452295 - 0.03554809516376764im … -0.04662488269596026 - 0.0513525508323706im 0.04923010474860139 + 0.056301335863833235im; 0.0021334321798451438 - 0.027394517566289862im -0.038211618890200194 - 0.05889317443132029im … -0.024630801915385674 - 0.056728915764095014im 0.07814774614717382 + 0.05750223402753711im;;; -0.10032871531039494 - 0.0677525223497874im -0.03639045277100612 - 0.0012056959274616445im … 0.0942263457871305 + 0.11202402929110167im 0.11243108498176338 + 0.16181779342467326im; -0.08082598698904307 - 0.06920594427713328im -0.006585211779948111 + 0.007940571999875926im … 0.060237849178864974 + 0.0898366824408755im 0.026260100498628064 + 0.06384883109497966im; … ; -0.006666790139164883 - 0.04237398052475678im -0.049433639784688815 - 0.07799494572679361im … -0.0005857120440326072 - 0.015800119493739495im 0.09261353647718021 + 0.08212544565305671im; -0.06528720592181501 - 0.11014669237014407im -0.0746330353357536 - 0.09054917220800915im … 0.04817800234728893 + 0.014125205625572826im 0.1407603851160148 + 0.11206684061760246im]],)), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [0.06250485683527418, 1.000077709364387, 3.062737984928434, 4.000310837457548, 1.562621420881854, 0.2500194273410967, 0.5000388546821934, 1.0625825661996608, 2.750213700752063, 2.7502137007520635  …  2.5001942734109663, 4.5628545489750145, 3.062737984928434, 1.7501359913876768, 1.5626214208818543, 1.062582566199661, 2.750213700752063, 2.750213700752064, 1.0625825661996608, 0.5000388546821934]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [-0.30116136598756804 -0.36869760795125184 … -0.5702190219244254 -0.36869760795125195; -0.3686976079512516 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456163; … ; -0.5702190219244256 -0.264614164394795 … -2.291992881132685 -1.1751172086054253; -0.3686976079512515 -0.2539389812456162 … -1.1751172086054256 -0.6560706269776425;;; -0.3686976079512517 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456166; -0.6560706269776425 -1.3741022038947448 … -0.1651225671881503 -0.31565743774427135; … ; -0.2646141643947949 -0.16512256718815066 … -0.8632000905877295 -0.4898593856167607; -0.25393898124561615 -0.31565743774427135 … -0.48985938561676046 -0.31565743774427124;;; -0.5702190219244254 -1.1751172086054258 … -0.1242245197168452 -0.264614164394795; -1.1751172086054256 -2.8292222589777416 … -0.1750685951638031 -0.48985938561676046; … ; -0.1242245197168452 -0.1750685951638037 … -0.30112950922681153 -0.17506859516380358; -0.2646141643947948 -0.48985938561676046 … -0.17506859516380294 -0.1651225671881503;;; … ;;; -0.8720732197039092 -0.36117451106748844 … -3.5504427268225025 -1.881971917366274; -0.3611745110674882 -0.13192205269891222 … -1.3219289313234115 -0.747481991474731; … ; -3.5504427268225025 -1.3219289313234115 … -11.011681230319526 -8.06878895093237; -1.8819719173662737 -0.747481991474731 … -8.06878895093237 -4.5798976647669045;;; -0.5702190219244254 -0.2646141643947948 … -2.2919928811326855 -1.1751172086054256; -0.2646141643947947 -0.16512256718815055 … -0.8632000905877295 -0.48985938561676046; … ; -2.2919928811326855 -0.8632000905877297 … -11.026309596728632 -6.029372075563462; -1.1751172086054253 -0.4898593856167603 … -6.029372075563462 -2.8292222589777416;;; -0.3686976079512518 -0.2539389812456165 … -1.1751172086054256 -0.6560706269776427; -0.25393898124561626 -0.3156574377442714 … -0.4898593856167604 -0.31565743774427135; … ; -1.1751172086054256 -0.48985938561676057 … -6.029372075563461 -2.829222258977741; -0.6560706269776424 -0.3156574377442712 … -2.829222258977741 -1.3741022038947448]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), ComplexF64[0.10663902257822168 - 0.028573839981478756im 0.16397423109777803 - 0.0439367628021639im … -0.0048810168633526265 + 0.01821620292663248im 0.0048810168633526265 - 0.01821620292663248im; 0.04668482831007231 - 0.08086049457567514im 0.06370661418591363 - 0.11034309254819058im … -0.05243363114037364 + 0.030272571053484264im 0.05243363114037364 - 0.030272571053484264im; … ; -0.08918635851135279 + 0.023897412738989543im -0.12067576411442682 + 0.03233497354046929im … -0.019302751901532963 + 0.07203885082241784im -0.0038605503803065926 + 0.014407770164483566im; -0.051048693065027635 + 0.08841893004861681im -0.0743729428832569 + 0.128817715782219im … -0.02947884616601673 + 0.017019619769349337im -0.05895769233203346 + 0.034039239538698675im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [0.3915556370590074 0.37851742092916557 … 0.3446996003079375 0.3785174209291657; 0.3785174209291656 0.36645844069123706 … 0.3273572817423094 0.3636495426413965; … ; 0.3446996003079375 0.3273572817423093 … 0.3075192694882305 0.33438053204271134; 0.3785174209291656 0.3636495426413965 … 0.33438053204271134 0.36645844069123706;;; 0.3785174209291657 0.366458440691237 … 0.3273572817423093 0.36364954264139643; 0.36645844069123706 0.35102886347928736 … 0.3111940134732182 0.3519170663740599; … ; 0.3273572817423093 0.3111940134732181 … 0.2982412284598287 0.3214260028488039; 0.3636495426413964 0.3519170663740599 … 0.3214260028488039 0.3519170663740599;;; 0.3446996003079375 0.3343805320427113 … 0.28653515377294264 0.3273572817423094; 0.33438053204271134 0.31861604783719377 … 0.2780589188367269 0.32142600284880396; … ; 0.28653515377294264 0.2780589188367269 … 0.2559018577461467 0.2780589188367269; 0.32735728174230927 0.32142600284880396 … 0.27805891883672684 0.3111940134732181;;; … ;;; 0.3048747493337859 0.28303666898571395 … 0.2855643323939694 0.3009573705821879; 0.28303666898571395 0.25898431623070184 … 0.2726330013434142 0.2854141966681785; … ; 0.2855643323939694 0.27263300134341417 … 0.27716038923066866 0.2812108738725452; 0.3009573705821879 0.28541419666817847 … 0.2812108738725452 0.2930827263518427;;; 0.34469960030793756 0.3273572817423093 … 0.3075192694882305 0.33438053204271134; 0.3273572817423094 0.31119401347321807 … 0.29824122845982876 0.32142600284880396; … ; 0.3075192694882305 0.2982412284598287 … 0.2771603892306687 0.29313119155538103; 0.3343805320427113 0.32142600284880396 … 0.2931311915553811 0.3186160478371938;;; 0.3785174209291657 0.3636495426413964 … 0.3343805320427113 0.3664584406912371; 0.36364954264139643 0.3519170663740599 … 0.32142600284880396 0.35191706637405995; … ; 0.33438053204271134 0.3214260028488039 … 0.29313119155538103 0.3186160478371938; 0.36645844069123706 0.35191706637405995 … 0.3186160478371938 0.35102886347928736]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [-0.503308192313982 -0.4966565572311907 … -0.4771919009774658 -0.4966565572311907; -0.4966565572311907 -0.4848182087263484 … -0.4763804457677314 -0.4920413111690271; … ; -0.4771919009774658 -0.4763804457677315 … -0.4122880709063333 -0.4550700815797695; -0.4966565572311907 -0.4920413111690271 … -0.45507008157976947 -0.4848182087263484;;; -0.4966565572311907 -0.4848182087263484 … -0.4763804457677314 -0.4920413111690271; -0.4848182087263484 -0.45837440794132067 … -0.47065601570152904 -0.4861790251791354; … ; -0.4763804457677314 -0.470656015701529 … -0.4463984364571212 -0.4688943964027922; -0.4920413111690271 -0.4861790251791355 … -0.4688943964027922 -0.4861790251791354;;; -0.4771919009774657 -0.4550700815797695 … -0.4605141234167576 -0.4763804457677314; -0.4550700815797695 -0.4090661824735755 … -0.4567199083195155 -0.4688943964027922; … ; -0.4605141234167576 -0.4567199083195155 … -0.44514495661102427 -0.4567199083195155; -0.4763804457677314 -0.4688943964027922 … -0.4567199083195155 -0.47065601570152904;;; … ;;; -0.44947595085725534 -0.45514997220617465 … -0.3712598626574318 -0.41774571522991527; -0.45514997220617465 -0.44880351099219856 … -0.41743801074040043 -0.4441260993150186; … ; -0.3712598626574318 -0.41743801074040043 … -0.2536569833789929 -0.29979809112414557; -0.41774571522991527 -0.4441260993150186 … -0.2997980911241455 -0.361063432689199;;; -0.4771919009774657 -0.4763804457677314 … -0.41228807090633324 -0.4550700815797695; -0.4763804457677314 -0.47065601570152904 … -0.4463984364571212 -0.4688943964027922; … ; -0.41228807090633324 -0.4463984364571212 … -0.2536569833789929 -0.3410633023505617; -0.4550700815797695 -0.4688943964027922 … -0.3410633023505617 -0.4090661824735755;;; -0.4966565572311907 -0.49204131116902705 … -0.4550700815797695 -0.4848182087263484; -0.49204131116902705 -0.4861790251791354 … -0.4688943964027922 -0.4861790251791354; … ; -0.4550700815797695 -0.4688943964027921 … -0.3410633023505617 -0.4090661824735755; -0.4848182087263484 -0.48617902517913547 … -0.4090661824735755 -0.45837440794132067])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [0.06250485683527418, 1.000077709364387, 3.062737984928434, 4.000310837457548, 1.562621420881854, 0.2500194273410967, 0.5000388546821934, 1.0625825661996608, 2.750213700752063, 2.7502137007520635  …  2.5001942734109663, 4.5628545489750145, 3.062737984928434, 1.7501359913876768, 1.5626214208818543, 1.062582566199661, 2.750213700752063, 2.750213700752064, 1.0625825661996608, 0.5000388546821934]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [-0.41291392124254267 -0.48683674425327694 … -0.7027113225939536 -0.48683674425327694; -0.48683674425327667 -0.774430395012754 … -0.41363732842021683 -0.38233074977324694; … ; -0.7027113225939539 -0.41363732842021717 … -2.396761682550788 -1.2958067581424835; -0.48683674425327655 -0.3823307497732468 … -1.2958067581424837 -0.7744303950127538;;; -0.4868367442532767 -0.7744303950127541 … -0.4136373284202169 -0.38233074977324727; -0.7744303950127538 -1.481447748356778 … -0.3245845694164612 -0.4499193965493469; … ; -0.413637328420217 -0.3245845694164615 … -1.0113572985850219 -0.637327779170749; -0.3823307497732469 -0.449919396549347 … -0.6373277791707488 -0.44991939654934676;;; -0.7027113225939536 -1.295806758142484 … -0.2982034893606602 -0.41363732842021705; -1.2958067581424837 -2.9196723936141233 … -0.35372958464659165 -0.6373277791707487; … ; -0.2982034893606602 -0.35372958464659227 … -0.4903726080916891 -0.35372958464659215; -0.41363732842021694 -0.6373277791707487 … -0.35372958464659154 -0.3245845694164612;;; … ;;; -1.0166744212273786 -0.5332878142879491 … -3.636138257085965 -1.9987602620140013; -0.5332878142879489 -0.32174124746040894 … -1.4667339407203976 -0.9061938941215711; … ; -3.636138257085965 -1.4667339407203976 … -10.98817782446785 -8.08737616818397; -1.998760262014001 -0.9061938941215713 … -8.08737616818397 -4.647878371104261;;; -0.7027113225939536 -0.4136373284202169 … -2.396761682550788 -1.2958067581424837; -0.4136373284202167 -0.3245845694164615 … -1.0113572985850219 -0.6373277791707487; … ; -2.396761682550788 -1.0113572985850223 … -11.002806190876957 -6.077304186358642; -1.2958067581424835 -0.6373277791707486 … -6.077304186358642 -2.9196723936141233;;; -0.4868367442532768 -0.38233074977324716 … -1.2958067581424837 -0.774430395012754; -0.3823307497732469 -0.44991939654934693 … -0.6373277791707486 -0.4499193965493468; … ; -1.2958067581424837 -0.6373277791707488 … -6.077304186358641 -2.919672393614123; -0.7744303950127538 -0.4499193965493467 … -2.919672393614123 -1.481447748356778]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), ComplexF64[0.10663902257822168 - 0.028573839981478756im 0.16397423109777803 - 0.0439367628021639im … -0.0048810168633526265 + 0.01821620292663248im 0.0048810168633526265 - 0.01821620292663248im; 0.04668482831007231 - 0.08086049457567514im 0.06370661418591363 - 0.11034309254819058im … -0.05243363114037364 + 0.030272571053484264im 0.05243363114037364 - 0.030272571053484264im; … ; -0.08918635851135279 + 0.023897412738989543im -0.12067576411442682 + 0.03233497354046929im … -0.019302751901532963 + 0.07203885082241784im -0.0038605503803065926 + 0.014407770164483566im; -0.051048693065027635 + 0.08841893004861681im -0.0743729428832569 + 0.128817715782219im … -0.02947884616601673 + 0.017019619769349337im -0.05895769233203346 + 0.034039239538698675im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, (ψ_reals = Array{ComplexF64, 3}[[-0.10177434939443192 - 0.008712619193419644im -0.0540544042059237 - 0.14961220286786153im … 0.031234232144059168 - 0.07441676828591604im -0.025596847054311977 - 0.05863344485215788im; -0.0812063318732431 - 0.013049243957041587im 0.01613122664915622 - 0.09792273442231002im … -0.01209308653036405 - 0.02420978257983602im -0.05955917702014768 - 0.003152826147071786im; … ; 0.07376114461273792 + 0.025045367394509514im 0.04154308445119079 + 0.023884832688968564im … 0.006245999290875539 - 0.027789742181220014im 0.059922104328269984 - 0.07056111634603854im; 0.049708109902039055 + 0.029290363191994795im 0.02970553105054697 - 0.04691590861372022im … 0.0725870012699169 - 0.09213674017309811im 0.12527723284747533 - 0.09787798218525394im;;; 0.028031261677511465 + 0.08206366722901547im 0.0830648515775646 - 0.054534844312483885im … -0.0012432675766668065 - 0.03166162854754262im 0.0067215934369993565 + 0.04203181678574777im; 0.07454205551034386 + 0.0669340569008018im 0.12082299202143285 - 0.011029320421007953im … -0.007467590437227412 + 0.0068664684601838725im 0.007429285951705068 + 0.058144710053490554im; … ; 0.03662566302176007 + 0.010006065205618543im 0.03646063323695663 + 0.004738492304877922im … -0.0010608490947431248 - 0.04626001393941294im 0.015425041655378256 - 0.04801226867294048im; 0.06649323453970449 + 0.056912490363326074im 0.07030993992231302 - 0.024710245173280944im … 0.010693307776897356 - 0.06729209995791102im 0.03425864252783753 - 0.03833503496676867im;;; 0.07491162284658065 + 0.07517839738768169im 0.04035827644634358 - 0.016251034368659243im … 0.008437102511307292 + 0.012761664503185197im 0.038407954580750296 + 0.06502926715756746im; 0.043314688652148714 + 0.02276244077490984im -0.015784379956050087 - 0.0354019270555511im … 0.008169886820029055 + 0.024525465142021512im 0.030154666467856722 + 0.04907891639271603im; … ; 0.02823324793973418 + 0.01782284557460695im 0.027654575037646366 + 0.007014197780546248im … -0.001169789209900591 - 0.022515647231118874im 0.011742517240376185 - 0.005840320257125033im; 0.05884376198375011 + 0.05476913432035461im 0.04534291503273048 + 0.0035574189629213335im … 0.005767080101798432 - 0.013307299739122048im 0.030163725530525615 + 0.027289881778478242im;;; … ;;; 0.037948845400534253 + 0.024685585470305756im 0.02062772121121756 + 0.02507112321536492im … -0.003976296272132808 - 0.0011915188014175345im 0.030731108080356274 + 0.002761513230500001im; 0.01623531503211291 + 0.013891019760637042im 0.002623099131794173 + 0.006449253629161716im … 0.015332662332886705 + 0.0008365588729318896im 0.024440518241211497 + 0.006701743599878992im; … ; -0.032141170153559745 - 0.023176671812243546im 0.002071815477117742 + 0.009265291727623023im … -0.12077629899148251 - 0.004052639017311781im -0.098446646851547 - 0.04097512682130801im; 0.021445233192910973 + 0.010483041751377029im 0.024222535540323005 + 0.029993473368576055im … -0.07418115062467409 - 0.006008985653629345im -0.023212420079237045 - 0.02065718722487956im;;; 0.07902740785987186 + 0.060473109213140044im 0.018512224929370866 + 0.024095618781800082im … 0.05724073942468097 - 0.0004117207652936222im 0.11794449963534626 + 0.014986476070432643im; 0.0006896420392425464 + 0.011867766676082598im -0.014965351614120437 - 0.014294965720060636im … 0.033549511692757106 - 0.003494825327545921im 0.03136293618929152 + 0.005818286839652062im; … ; 0.02153059494576208 + 0.015348995946740194im 0.03210977335211526 + 0.04735965430605833im … -0.17799335210017758 + 0.015000415805741251im -0.08028845617015143 - 0.04495856281151896im; 0.13555793393622328 + 0.0855903383417145im 0.05922095168454801 + 0.06967071709265438im … -0.020606853297613817 + 0.0075525015737660725im 0.12284137553467694 - 0.0024163429705503408im;;; 0.010125498932818883 + 0.04218812124358623im -0.03109508640643665 - 0.0647007323988811im … 0.1011906940481728 - 0.03229891095629857im 0.13957629838123353 - 0.015985235825899086im; -0.06351786630806285 - 0.014325701146324303im -0.03895571627523793 - 0.07277078694674775im … 0.022206302350037406 - 0.02002509341250327im -0.011356660024853981 - 0.010446711683460702im; … ; 0.10877627274214122 + 0.06732327335918617im 0.05578389511579181 + 0.06589522477888406im … -0.05229728432655157 + 0.0340427942222471im 0.06836057068422915 - 0.02482443095718308im; 0.20343295357716518 + 0.12270613907696036im 0.06717070046887805 + 0.05455486780171893im … 0.11944163703836604 - 0.012011653634046129im 0.272872663609927 - 0.01046447893620268im]],)), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [0.0833398091136989, 0.8959029479722631, 2.8335535098657623, 4.396174930747617, 1.8334758005013758, 0.3958640932900698, 0.8959029479722631, 1.3334369458191824, 2.8960583667010367, 3.39609722138323  …  1.89598065733665, 3.833631219230149, 2.8335535098657623, 1.3959418026544566, 1.0834175184780857, 0.8333980911369889, 2.3960195120188432, 2.8960583667010367, 1.0834175184780857, 0.3958640932900698]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [-0.30116136598756804 -0.36869760795125184 … -0.5702190219244254 -0.36869760795125195; -0.3686976079512516 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456163; … ; -0.5702190219244256 -0.264614164394795 … -2.291992881132685 -1.1751172086054253; -0.3686976079512515 -0.2539389812456162 … -1.1751172086054256 -0.6560706269776425;;; -0.3686976079512517 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456166; -0.6560706269776425 -1.3741022038947448 … -0.1651225671881503 -0.31565743774427135; … ; -0.2646141643947949 -0.16512256718815066 … -0.8632000905877295 -0.4898593856167607; -0.25393898124561615 -0.31565743774427135 … -0.48985938561676046 -0.31565743774427124;;; -0.5702190219244254 -1.1751172086054258 … -0.1242245197168452 -0.264614164394795; -1.1751172086054256 -2.8292222589777416 … -0.1750685951638031 -0.48985938561676046; … ; -0.1242245197168452 -0.1750685951638037 … -0.30112950922681153 -0.17506859516380358; -0.2646141643947948 -0.48985938561676046 … -0.17506859516380294 -0.1651225671881503;;; … ;;; -0.8720732197039092 -0.36117451106748844 … -3.5504427268225025 -1.881971917366274; -0.3611745110674882 -0.13192205269891222 … -1.3219289313234115 -0.747481991474731; … ; -3.5504427268225025 -1.3219289313234115 … -11.011681230319526 -8.06878895093237; -1.8819719173662737 -0.747481991474731 … -8.06878895093237 -4.5798976647669045;;; -0.5702190219244254 -0.2646141643947948 … -2.2919928811326855 -1.1751172086054256; -0.2646141643947947 -0.16512256718815055 … -0.8632000905877295 -0.48985938561676046; … ; -2.2919928811326855 -0.8632000905877297 … -11.026309596728632 -6.029372075563462; -1.1751172086054253 -0.4898593856167603 … -6.029372075563462 -2.8292222589777416;;; -0.3686976079512518 -0.2539389812456165 … -1.1751172086054256 -0.6560706269776427; -0.25393898124561626 -0.3156574377442714 … -0.4898593856167604 -0.31565743774427135; … ; -1.1751172086054256 -0.48985938561676057 … -6.029372075563461 -2.829222258977741; -0.6560706269776424 -0.3156574377442712 … -2.829222258977741 -1.3741022038947448]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), ComplexF64[0.09525460347564817 - 0.05499527095821653im 0.14610260131202302 - 0.08435237619680104im … -0.018766875445216862 + 0.032505181770432406im 5.2088543048880615e-19 - 9.022000305289992e-19im; 0.024619950292842606 - 0.09188290537270884im 0.03407002323540016 - 0.12715105772956556im … -0.07491066001757686 + 0.02007225085619212im 0.04494639601054611 - 0.012043350513715271im; … ; -0.07966512642409461 + 0.045994682185976576im -0.10748648020277889 + 0.06205734827931975im … -0.02968662889946843 + 0.05141874955932189im 0.0 - 0.0im; -0.026921300372532365 + 0.10047166079611371im -0.039739321889381986 + 0.14830916834950758im … -0.016846285674482424 + 0.0045139486419415575im -0.05053885702344723 + 0.013541845925824664im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [0.3915556370590074 0.37851742092916557 … 0.3446996003079375 0.3785174209291657; 0.3785174209291656 0.36645844069123706 … 0.3273572817423094 0.3636495426413965; … ; 0.3446996003079375 0.3273572817423093 … 0.3075192694882305 0.33438053204271134; 0.3785174209291656 0.3636495426413965 … 0.33438053204271134 0.36645844069123706;;; 0.3785174209291657 0.366458440691237 … 0.3273572817423093 0.36364954264139643; 0.36645844069123706 0.35102886347928736 … 0.3111940134732182 0.3519170663740599; … ; 0.3273572817423093 0.3111940134732181 … 0.2982412284598287 0.3214260028488039; 0.3636495426413964 0.3519170663740599 … 0.3214260028488039 0.3519170663740599;;; 0.3446996003079375 0.3343805320427113 … 0.28653515377294264 0.3273572817423094; 0.33438053204271134 0.31861604783719377 … 0.2780589188367269 0.32142600284880396; … ; 0.28653515377294264 0.2780589188367269 … 0.2559018577461467 0.2780589188367269; 0.32735728174230927 0.32142600284880396 … 0.27805891883672684 0.3111940134732181;;; … ;;; 0.3048747493337859 0.28303666898571395 … 0.2855643323939694 0.3009573705821879; 0.28303666898571395 0.25898431623070184 … 0.2726330013434142 0.2854141966681785; … ; 0.2855643323939694 0.27263300134341417 … 0.27716038923066866 0.2812108738725452; 0.3009573705821879 0.28541419666817847 … 0.2812108738725452 0.2930827263518427;;; 0.34469960030793756 0.3273572817423093 … 0.3075192694882305 0.33438053204271134; 0.3273572817423094 0.31119401347321807 … 0.29824122845982876 0.32142600284880396; … ; 0.3075192694882305 0.2982412284598287 … 0.2771603892306687 0.29313119155538103; 0.3343805320427113 0.32142600284880396 … 0.2931311915553811 0.3186160478371938;;; 0.3785174209291657 0.3636495426413964 … 0.3343805320427113 0.3664584406912371; 0.36364954264139643 0.3519170663740599 … 0.32142600284880396 0.35191706637405995; … ; 0.33438053204271134 0.3214260028488039 … 0.29313119155538103 0.3186160478371938; 0.36645844069123706 0.35191706637405995 … 0.3186160478371938 0.35102886347928736]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [-0.503308192313982 -0.4966565572311907 … -0.4771919009774658 -0.4966565572311907; -0.4966565572311907 -0.4848182087263484 … -0.4763804457677314 -0.4920413111690271; … ; -0.4771919009774658 -0.4763804457677315 … -0.4122880709063333 -0.4550700815797695; -0.4966565572311907 -0.4920413111690271 … -0.45507008157976947 -0.4848182087263484;;; -0.4966565572311907 -0.4848182087263484 … -0.4763804457677314 -0.4920413111690271; -0.4848182087263484 -0.45837440794132067 … -0.47065601570152904 -0.4861790251791354; … ; -0.4763804457677314 -0.470656015701529 … -0.4463984364571212 -0.4688943964027922; -0.4920413111690271 -0.4861790251791355 … -0.4688943964027922 -0.4861790251791354;;; -0.4771919009774657 -0.4550700815797695 … -0.4605141234167576 -0.4763804457677314; -0.4550700815797695 -0.4090661824735755 … -0.4567199083195155 -0.4688943964027922; … ; -0.4605141234167576 -0.4567199083195155 … -0.44514495661102427 -0.4567199083195155; -0.4763804457677314 -0.4688943964027922 … -0.4567199083195155 -0.47065601570152904;;; … ;;; -0.44947595085725534 -0.45514997220617465 … -0.3712598626574318 -0.41774571522991527; -0.45514997220617465 -0.44880351099219856 … -0.41743801074040043 -0.4441260993150186; … ; -0.3712598626574318 -0.41743801074040043 … -0.2536569833789929 -0.29979809112414557; -0.41774571522991527 -0.4441260993150186 … -0.2997980911241455 -0.361063432689199;;; -0.4771919009774657 -0.4763804457677314 … -0.41228807090633324 -0.4550700815797695; -0.4763804457677314 -0.47065601570152904 … -0.4463984364571212 -0.4688943964027922; … ; -0.41228807090633324 -0.4463984364571212 … -0.2536569833789929 -0.3410633023505617; -0.4550700815797695 -0.4688943964027922 … -0.3410633023505617 -0.4090661824735755;;; -0.4966565572311907 -0.49204131116902705 … -0.4550700815797695 -0.4848182087263484; -0.49204131116902705 -0.4861790251791354 … -0.4688943964027922 -0.4861790251791354; … ; -0.4550700815797695 -0.4688943964027921 … -0.3410633023505617 -0.4090661824735755; -0.4848182087263484 -0.48617902517913547 … -0.4090661824735755 -0.45837440794132067])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [0.0833398091136989, 0.8959029479722631, 2.8335535098657623, 4.396174930747617, 1.8334758005013758, 0.3958640932900698, 0.8959029479722631, 1.3334369458191824, 2.8960583667010367, 3.39609722138323  …  1.89598065733665, 3.833631219230149, 2.8335535098657623, 1.3959418026544566, 1.0834175184780857, 0.8333980911369889, 2.3960195120188432, 2.8960583667010367, 1.0834175184780857, 0.3958640932900698]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [-0.41291392124254267 -0.48683674425327694 … -0.7027113225939536 -0.48683674425327694; -0.48683674425327667 -0.774430395012754 … -0.41363732842021683 -0.38233074977324694; … ; -0.7027113225939539 -0.41363732842021717 … -2.396761682550788 -1.2958067581424835; -0.48683674425327655 -0.3823307497732468 … -1.2958067581424837 -0.7744303950127538;;; -0.4868367442532767 -0.7744303950127541 … -0.4136373284202169 -0.38233074977324727; -0.7744303950127538 -1.481447748356778 … -0.3245845694164612 -0.4499193965493469; … ; -0.413637328420217 -0.3245845694164615 … -1.0113572985850219 -0.637327779170749; -0.3823307497732469 -0.449919396549347 … -0.6373277791707488 -0.44991939654934676;;; -0.7027113225939536 -1.295806758142484 … -0.2982034893606602 -0.41363732842021705; -1.2958067581424837 -2.9196723936141233 … -0.35372958464659165 -0.6373277791707487; … ; -0.2982034893606602 -0.35372958464659227 … -0.4903726080916891 -0.35372958464659215; -0.41363732842021694 -0.6373277791707487 … -0.35372958464659154 -0.3245845694164612;;; … ;;; -1.0166744212273786 -0.5332878142879491 … -3.636138257085965 -1.9987602620140013; -0.5332878142879489 -0.32174124746040894 … -1.4667339407203976 -0.9061938941215711; … ; -3.636138257085965 -1.4667339407203976 … -10.98817782446785 -8.08737616818397; -1.998760262014001 -0.9061938941215713 … -8.08737616818397 -4.647878371104261;;; -0.7027113225939536 -0.4136373284202169 … -2.396761682550788 -1.2958067581424837; -0.4136373284202167 -0.3245845694164615 … -1.0113572985850219 -0.6373277791707487; … ; -2.396761682550788 -1.0113572985850223 … -11.002806190876957 -6.077304186358642; -1.2958067581424835 -0.6373277791707486 … -6.077304186358642 -2.9196723936141233;;; -0.4868367442532768 -0.38233074977324716 … -1.2958067581424837 -0.774430395012754; -0.3823307497732469 -0.44991939654934693 … -0.6373277791707486 -0.4499193965493468; … ; -1.2958067581424837 -0.6373277791707488 … -6.077304186358641 -2.919672393614123; -0.7744303950127538 -0.4499193965493467 … -2.919672393614123 -1.481447748356778]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), ComplexF64[0.09525460347564817 - 0.05499527095821653im 0.14610260131202302 - 0.08435237619680104im … -0.018766875445216862 + 0.032505181770432406im 5.2088543048880615e-19 - 9.022000305289992e-19im; 0.024619950292842606 - 0.09188290537270884im 0.03407002323540016 - 0.12715105772956556im … -0.07491066001757686 + 0.02007225085619212im 0.04494639601054611 - 0.012043350513715271im; … ; -0.07966512642409461 + 0.045994682185976576im -0.10748648020277889 + 0.06205734827931975im … -0.02968662889946843 + 0.05141874955932189im 0.0 - 0.0im; -0.026921300372532365 + 0.10047166079611371im -0.039739321889381986 + 0.14830916834950758im … -0.016846285674482424 + 0.0045139486419415575im -0.05053885702344723 + 0.013541845925824664im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, (ψ_reals = Array{ComplexF64, 3}[[0.09426872185420476 - 0.034537411793972156im 0.0667249674122186 + 0.03654087836046777im … -0.0004205589417354957 - 0.028038204117971213im 0.04267787814378331 - 0.0655490295454403im; 0.055149640418966674 + 0.0013493165830904574im 0.002594691024378138 + 0.008986590209889189im … 0.023508320161807615 + 0.038552859420209695im 0.05457479922304234 + 0.0439996607979803im; … ; -0.06067467793589102 - 0.21122409444081092im -0.02734161937342003 - 0.11604223870323438im … -0.009306716477913096 + 0.00340971941598032im -0.055146552790723696 - 0.13798319191990815im; -0.03514724769789436 - 0.3021546788119017im 0.0006569345706981508 - 0.11992261058086141im … -0.05794402978766115 - 0.14648814227968424im -0.08746267527080741 - 0.3029228994854252im;;; 0.045064582669990534 + 0.07236632220041461im 0.023541277998206465 + 0.145880331451962im … 0.010420858744319757 + 0.0029888711563077416im 0.02554074207383008 + 0.013019725920722964im; -0.02823927255227543 - 0.011544030291791147im -0.04741532238902653 + 0.0447215028461712im … 0.010565805144258443 + 0.021597626813240192im 0.002025296161274017 + 0.0012379541839887681im; … ; -0.03426653175849832 - 0.13287071050756163im -0.015560698101046983 - 0.05783273952073631im … -0.008609095900991287 - 0.04346931153245481im -0.028658517887515805 - 0.11689132081194233im; -0.01915483313701149 - 0.12286473900843292im 0.007330065184478518 + 0.017365628878096395im … -0.014468220466853147 - 0.07374966816768941im -0.030491900001166285 - 0.1551452560825966im;;; -0.0040307298398161015 + 0.05983565629778814im 0.012504312342202114 + 0.10115614287574706im … -0.00021409627489374795 + 0.006685454036498046im -0.005880283900346202 + 0.018472772332299117im; -0.022287058934492936 - 0.004617344661586397im -0.0047510474059782384 + 0.03874064794101098im … -0.0035497832482566036 + 0.0017895990518872458im -0.01582561545521948 - 0.013258974893967015im; … ; -0.013410795848542443 - 0.03343544044086531im -0.0032576407792114393 + 0.002677777061728711im … -0.0049195037245100895 - 0.027012035965914914im -0.012744877973512012 - 0.043974632544340156im; -0.007382598714222161 + 0.013905402108615841im 0.009117196988544924 + 0.06257270885858504im … -0.0048086810266914515 - 0.019846833071433586im -0.011477854682316723 - 0.02105424513133276im;;; … ;;; -0.016474667520413905 - 0.011809737856172783im -0.005146455490159015 - 0.004948303501121206im … -0.00867455344300038 - 0.015062333452930298im -0.020772607366717138 - 0.019552659011909064im; -0.0024411429543311786 + 0.0032764467988426692im 0.00319637528527984 + 0.00338080960327696im … -0.010059153424191003 - 0.012293178062848539im -0.00955322238967953 - 0.00412033575389052im; … ; 0.005117273275233996 + 0.026867879739054003im -0.004560559162118897 + 0.004423768496874801im … 0.05396015448736686 + 0.08083159593161553im 0.032902292443064765 + 0.06378527322026634im; -0.01705090105565019 - 0.008237846073266135im -0.011253351605590043 - 0.009289105704786714im … 0.02223507309337744 + 0.0313545596722165im -0.004875386660648029 + 0.00631711061541935im;;; -0.020858453307139584 - 0.02967618732254269im 0.0041166423598661215 - 0.012327239295243509im … -0.03889935095691806 - 0.04743517792100487im -0.053306972665568636 - 0.0506470907534083im; 0.012420446005440611 + 0.012918166164390215im 0.01378415558665266 + 0.0037123455685557846im … -0.012667212007055471 - 0.007684039061602825im -0.0030657289949474155 + 0.009937271240996198im; … ; -0.017671497637314577 + 0.017102205935602896im -0.01594078096463889 - 0.017636414921956504im … 0.07957142678567955 + 0.17413423249332502im 0.01986464099931627 + 0.11121898260920479im; -0.05976818845159486 - 0.0702906201587325im -0.019606931073802628 - 0.04035165293567093im … -0.0149267302575871 + 0.005445494937222914im -0.07956169691836258 - 0.06353842066599466im;;; 0.031354639908037545 - 0.0666792279226075im 0.037168494917952884 - 0.01938810151110125im … -0.050298073422121274 - 0.06723517163875764im -0.043605868514061105 - 0.08668067678241767im; 0.048694575453611014 + 0.015653740861459445im 0.024975825235236143 - 0.0016185918117696215im … 0.003381338931111413 + 0.017451748944156624im 0.030198064544285076 + 0.037406078835075865im; … ; -0.05560284240212108 - 0.08336284643838282im -0.02731089793411168 - 0.07585946071447096im … 0.026610420926939757 + 0.14983860421002804im -0.042859955876107636 + 0.03807981984622042im; -0.0953864190283073 - 0.24410503864931796im -0.017092344572273738 - 0.10636725714768819im … -0.08755553111067915 - 0.09780464510266754im -0.1530463847577787 - 0.219996081308254im]],)), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [0.1666796182273978, 0.22918447506267198, 1.4167767549328811, 3.7294564578380256, 3.416932173661655, 1.2292621844270586, 1.2292621844270586, 0.9167379002506877, 1.729301039109252, 3.6669516010027516  …  4.729534167202412, 4.417009883026042, 2.2293398937914453, 1.1667573275917844, 0.41669904556849446, 1.2292621844270588, 3.1669127463205577, 4.729534167202412, 2.1668350369561713, 0.7292233297448653]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [-0.30116136598756804 -0.36869760795125184 … -0.5702190219244254 -0.36869760795125195; -0.3686976079512516 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456163; … ; -0.5702190219244256 -0.264614164394795 … -2.291992881132685 -1.1751172086054253; -0.3686976079512515 -0.2539389812456162 … -1.1751172086054256 -0.6560706269776425;;; -0.3686976079512517 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456166; -0.6560706269776425 -1.3741022038947448 … -0.1651225671881503 -0.31565743774427135; … ; -0.2646141643947949 -0.16512256718815066 … -0.8632000905877295 -0.4898593856167607; -0.25393898124561615 -0.31565743774427135 … -0.48985938561676046 -0.31565743774427124;;; -0.5702190219244254 -1.1751172086054258 … -0.1242245197168452 -0.264614164394795; -1.1751172086054256 -2.8292222589777416 … -0.1750685951638031 -0.48985938561676046; … ; -0.1242245197168452 -0.1750685951638037 … -0.30112950922681153 -0.17506859516380358; -0.2646141643947948 -0.48985938561676046 … -0.17506859516380294 -0.1651225671881503;;; … ;;; -0.8720732197039092 -0.36117451106748844 … -3.5504427268225025 -1.881971917366274; -0.3611745110674882 -0.13192205269891222 … -1.3219289313234115 -0.747481991474731; … ; -3.5504427268225025 -1.3219289313234115 … -11.011681230319526 -8.06878895093237; -1.8819719173662737 -0.747481991474731 … -8.06878895093237 -4.5798976647669045;;; -0.5702190219244254 -0.2646141643947948 … -2.2919928811326855 -1.1751172086054256; -0.2646141643947947 -0.16512256718815055 … -0.8632000905877295 -0.48985938561676046; … ; -2.2919928811326855 -0.8632000905877297 … -11.026309596728632 -6.029372075563462; -1.1751172086054253 -0.4898593856167603 … -6.029372075563462 -2.8292222589777416;;; -0.3686976079512518 -0.2539389812456165 … -1.1751172086054256 -0.6560706269776427; -0.25393898124561626 -0.3156574377442714 … -0.4898593856167604 -0.31565743774427135; … ; -1.1751172086054256 -0.48985938561676057 … -6.029372075563461 -2.829222258977741; -0.6560706269776424 -0.3156574377442712 … -2.829222258977741 -1.3741022038947448]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), ComplexF64[0.10836454158744746 + 0.0im 0.16454392299317003 + 0.0im … -0.0 - 1.0216068167279948e-18im 0.0 + 0.03680726463308285im; 0.0757741533540503 - 0.0757741533540503im 0.1141835519100639 - 0.1141835519100639im … -0.03847188688271061 + 0.03847188688271061im 0.012823962294236874 - 0.012823962294236874im; … ; -0.07579695351601741 + 0.0im -0.08711072462387971 + 0.0im … 0.0 + 0.06907686686237845im 0.0 - 0.02302562228745948im; -0.0692966484992815 + 0.0692966484992815im -0.09802716364420207 + 0.09802716364420207im … -0.03421471645670587 + 0.03421471645670587im -0.011404905485568627 + 0.011404905485568627im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [0.3915556370590074 0.37851742092916557 … 0.3446996003079375 0.3785174209291657; 0.3785174209291656 0.36645844069123706 … 0.3273572817423094 0.3636495426413965; … ; 0.3446996003079375 0.3273572817423093 … 0.3075192694882305 0.33438053204271134; 0.3785174209291656 0.3636495426413965 … 0.33438053204271134 0.36645844069123706;;; 0.3785174209291657 0.366458440691237 … 0.3273572817423093 0.36364954264139643; 0.36645844069123706 0.35102886347928736 … 0.3111940134732182 0.3519170663740599; … ; 0.3273572817423093 0.3111940134732181 … 0.2982412284598287 0.3214260028488039; 0.3636495426413964 0.3519170663740599 … 0.3214260028488039 0.3519170663740599;;; 0.3446996003079375 0.3343805320427113 … 0.28653515377294264 0.3273572817423094; 0.33438053204271134 0.31861604783719377 … 0.2780589188367269 0.32142600284880396; … ; 0.28653515377294264 0.2780589188367269 … 0.2559018577461467 0.2780589188367269; 0.32735728174230927 0.32142600284880396 … 0.27805891883672684 0.3111940134732181;;; … ;;; 0.3048747493337859 0.28303666898571395 … 0.2855643323939694 0.3009573705821879; 0.28303666898571395 0.25898431623070184 … 0.2726330013434142 0.2854141966681785; … ; 0.2855643323939694 0.27263300134341417 … 0.27716038923066866 0.2812108738725452; 0.3009573705821879 0.28541419666817847 … 0.2812108738725452 0.2930827263518427;;; 0.34469960030793756 0.3273572817423093 … 0.3075192694882305 0.33438053204271134; 0.3273572817423094 0.31119401347321807 … 0.29824122845982876 0.32142600284880396; … ; 0.3075192694882305 0.2982412284598287 … 0.2771603892306687 0.29313119155538103; 0.3343805320427113 0.32142600284880396 … 0.2931311915553811 0.3186160478371938;;; 0.3785174209291657 0.3636495426413964 … 0.3343805320427113 0.3664584406912371; 0.36364954264139643 0.3519170663740599 … 0.32142600284880396 0.35191706637405995; … ; 0.33438053204271134 0.3214260028488039 … 0.29313119155538103 0.3186160478371938; 0.36645844069123706 0.35191706637405995 … 0.3186160478371938 0.35102886347928736]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [-0.503308192313982 -0.4966565572311907 … -0.4771919009774658 -0.4966565572311907; -0.4966565572311907 -0.4848182087263484 … -0.4763804457677314 -0.4920413111690271; … ; -0.4771919009774658 -0.4763804457677315 … -0.4122880709063333 -0.4550700815797695; -0.4966565572311907 -0.4920413111690271 … -0.45507008157976947 -0.4848182087263484;;; -0.4966565572311907 -0.4848182087263484 … -0.4763804457677314 -0.4920413111690271; -0.4848182087263484 -0.45837440794132067 … -0.47065601570152904 -0.4861790251791354; … ; -0.4763804457677314 -0.470656015701529 … -0.4463984364571212 -0.4688943964027922; -0.4920413111690271 -0.4861790251791355 … -0.4688943964027922 -0.4861790251791354;;; -0.4771919009774657 -0.4550700815797695 … -0.4605141234167576 -0.4763804457677314; -0.4550700815797695 -0.4090661824735755 … -0.4567199083195155 -0.4688943964027922; … ; -0.4605141234167576 -0.4567199083195155 … -0.44514495661102427 -0.4567199083195155; -0.4763804457677314 -0.4688943964027922 … -0.4567199083195155 -0.47065601570152904;;; … ;;; -0.44947595085725534 -0.45514997220617465 … -0.3712598626574318 -0.41774571522991527; -0.45514997220617465 -0.44880351099219856 … -0.41743801074040043 -0.4441260993150186; … ; -0.3712598626574318 -0.41743801074040043 … -0.2536569833789929 -0.29979809112414557; -0.41774571522991527 -0.4441260993150186 … -0.2997980911241455 -0.361063432689199;;; -0.4771919009774657 -0.4763804457677314 … -0.41228807090633324 -0.4550700815797695; -0.4763804457677314 -0.47065601570152904 … -0.4463984364571212 -0.4688943964027922; … ; -0.41228807090633324 -0.4463984364571212 … -0.2536569833789929 -0.3410633023505617; -0.4550700815797695 -0.4688943964027922 … -0.3410633023505617 -0.4090661824735755;;; -0.4966565572311907 -0.49204131116902705 … -0.4550700815797695 -0.4848182087263484; -0.49204131116902705 -0.4861790251791354 … -0.4688943964027922 -0.4861790251791354; … ; -0.4550700815797695 -0.4688943964027921 … -0.3410633023505617 -0.4090661824735755; -0.4848182087263484 -0.48617902517913547 … -0.4090661824735755 -0.45837440794132067])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [0.1666796182273978, 0.22918447506267198, 1.4167767549328811, 3.7294564578380256, 3.416932173661655, 1.2292621844270586, 1.2292621844270586, 0.9167379002506877, 1.729301039109252, 3.6669516010027516  …  4.729534167202412, 4.417009883026042, 2.2293398937914453, 1.1667573275917844, 0.41669904556849446, 1.2292621844270588, 3.1669127463205577, 4.729534167202412, 2.1668350369561713, 0.7292233297448653]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [-0.41291392124254267 -0.48683674425327694 … -0.7027113225939536 -0.48683674425327694; -0.48683674425327667 -0.774430395012754 … -0.41363732842021683 -0.38233074977324694; … ; -0.7027113225939539 -0.41363732842021717 … -2.396761682550788 -1.2958067581424835; -0.48683674425327655 -0.3823307497732468 … -1.2958067581424837 -0.7744303950127538;;; -0.4868367442532767 -0.7744303950127541 … -0.4136373284202169 -0.38233074977324727; -0.7744303950127538 -1.481447748356778 … -0.3245845694164612 -0.4499193965493469; … ; -0.413637328420217 -0.3245845694164615 … -1.0113572985850219 -0.637327779170749; -0.3823307497732469 -0.449919396549347 … -0.6373277791707488 -0.44991939654934676;;; -0.7027113225939536 -1.295806758142484 … -0.2982034893606602 -0.41363732842021705; -1.2958067581424837 -2.9196723936141233 … -0.35372958464659165 -0.6373277791707487; … ; -0.2982034893606602 -0.35372958464659227 … -0.4903726080916891 -0.35372958464659215; -0.41363732842021694 -0.6373277791707487 … -0.35372958464659154 -0.3245845694164612;;; … ;;; -1.0166744212273786 -0.5332878142879491 … -3.636138257085965 -1.9987602620140013; -0.5332878142879489 -0.32174124746040894 … -1.4667339407203976 -0.9061938941215711; … ; -3.636138257085965 -1.4667339407203976 … -10.98817782446785 -8.08737616818397; -1.998760262014001 -0.9061938941215713 … -8.08737616818397 -4.647878371104261;;; -0.7027113225939536 -0.4136373284202169 … -2.396761682550788 -1.2958067581424837; -0.4136373284202167 -0.3245845694164615 … -1.0113572985850219 -0.6373277791707487; … ; -2.396761682550788 -1.0113572985850223 … -11.002806190876957 -6.077304186358642; -1.2958067581424835 -0.6373277791707486 … -6.077304186358642 -2.9196723936141233;;; -0.4868367442532768 -0.38233074977324716 … -1.2958067581424837 -0.774430395012754; -0.3823307497732469 -0.44991939654934693 … -0.6373277791707486 -0.4499193965493468; … ; -1.2958067581424837 -0.6373277791707488 … -6.077304186358641 -2.919672393614123; -0.7744303950127538 -0.4499193965493467 … -2.919672393614123 -1.481447748356778]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), ComplexF64[0.10836454158744746 + 0.0im 0.16454392299317003 + 0.0im … -0.0 - 1.0216068167279948e-18im 0.0 + 0.03680726463308285im; 0.0757741533540503 - 0.0757741533540503im 0.1141835519100639 - 0.1141835519100639im … -0.03847188688271061 + 0.03847188688271061im 0.012823962294236874 - 0.012823962294236874im; … ; -0.07579695351601741 + 0.0im -0.08711072462387971 + 0.0im … 0.0 + 0.06907686686237845im 0.0 - 0.02302562228745948im; -0.0692966484992815 + 0.0692966484992815im -0.09802716364420207 + 0.09802716364420207im … -0.03421471645670587 + 0.03421471645670587im -0.011404905485568627 + 0.011404905485568627im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, (ψ_reals = Array{ComplexF64, 3}[[-0.13175736561245405 + 0.022735234787199222im -0.10823330705374161 - 0.038658273932293014im … 0.08850660594306284 + 0.1304081876720437im 0.06784532115981409 + 0.19038937116623345im; -0.17975426830898542 - 0.025623978850419584im -0.06291320317458896 + 0.00397627272112609im … 0.05295326825880534 + 0.10038026163995545im -0.017177764017765475 + 0.12416071256021188im; … ; 0.005309733626812897 + 0.01645353627499115im -0.017992947233352295 - 0.010386934094062637im … -0.0038076615526987283 - 0.026559719186016788im 0.03222758849207544 + 0.03161182205046865im; -0.044576952201963026 + 0.016877449940858505im -0.06083198300204752 - 0.0334786410667194im … 0.031336233186309015 + 0.022483848948022914im 0.08776995156123785 + 0.13543680180149414im;;; -0.138452548702662 + 0.026978246845381797im -0.043155199925503686 + 0.04593895666087411im … 0.053013986438638236 + 0.07150623967580531im 0.0064901725881380355 + 0.10688240158719894im; -0.16236486250564078 + 0.01985043641706783im 0.018052390006876928 + 0.07950224713321341im … 0.021214259273159796 + 0.05945374875453638im -0.07280350558106341 + 0.07485425109871433im; … ; -0.007191459838994305 - 0.0028465430965843243im -0.016057102503791297 - 0.009608553637920974im … 0.007566566721912075 - 0.0012554370839323913im 0.014924001702806854 + 0.01165424232261281im; -0.045226082318051475 + 0.001962946443837566im -0.035981167974813454 - 0.0024507309970487915im … 0.033468621225007364 + 0.028572374756578728im 0.03002857021900196 + 0.05064550496505569im;;; -0.05313163474326905 + 0.035448730018864776im 0.00500794260254843 + 0.03955559857418347im … 0.011741030288527424 + 0.029374067814211383im -0.023788503484491567 + 0.036989927475928386im; -0.058250409673511465 + 0.023029366087934704im 0.05179209557376033 + 0.008834078539327533im … -0.0072285335380626245 + 0.024388710697860104im -0.05304956628459877 + 0.025890389258772274im; … ; -0.006276907074544528 + 0.00039910690984380336im -0.006917175264177919 + 0.0017884783131265451im … 0.007458138645550008 + 0.002399222818424724im 0.004665801412587132 + 0.004232781023302897im; -0.021691097061531824 + 0.013788088225890978im -0.008348330849269026 + 0.017848914605135553im … 0.015251998572952953 + 0.015386235673335903im 0.0010617586234943008 + 0.019335717050911257im;;; … ;;; 0.011105886686993627 + 0.027063898636346485im -0.0032993686283524556 + 0.013941375667185531im … -0.001247074353543166 - 0.06357834346215155im 0.016417678292378918 - 0.002711996604820785im; 0.0007341165979999974 + 0.024637286144714263im -0.007656756580716178 + 0.007014545721521097im … 0.002244609953944307 - 0.009908305578801731im 0.008671678439662166 + 0.022625960991409313im; … ; 0.015069451075108035 - 0.010228525713317983im 0.009481971681230494 + 0.00649823218683989im … -0.010309695629597599 - 0.06799739502116012im 0.003909075255988914 - 0.05602428874734097im; 0.01969914733142957 + 0.007718677216668178im 0.005454194853252734 + 0.013244784868286692im … -0.007259064760291908 - 0.11118211988381538im 0.015975600712863077 - 0.05146213856635212im;;; 0.004464488269819424 + 0.08569732502469518im -0.024765777119002012 + 0.011105644707536083im … 0.003203746050393053 - 0.03862911145589071im 0.04958253403425574 + 0.11710607845567653im; -0.015532569106997695 + 0.04419265382949315im -0.023967911916904075 - 0.002500922383560032im … 0.010584939284202967 + 0.031927007138445596im 0.018764691223706213 + 0.08854331365453846im; … ; 0.02859766044753672 + 0.018757506790021167im 0.007876675602461834 + 0.016049287798686106im … -0.018547651307592013 - 0.1380593444139504im 0.022666673081222437 - 0.04903836788360495im; 0.03108346200566353 + 0.06230466793851233im -0.006868532388733235 + 0.019139935360690617im … -0.018676766971161204 - 0.17551185884647552im 0.05179209618103969 + 0.00883407862086413im;;; -0.053967747347407405 + 0.10068533599996662im -0.07272098895671897 - 0.022024439245195523im … 0.04091235904880884 + 0.08514384239428006im 0.10752007977847475 + 0.2553062003618942im; -0.08584862258527916 + 0.026323251799002703im -0.05430378117976854 - 0.022928582014144744im … 0.035641234271492475 + 0.0942884325135348im 0.026095129420249958 + 0.16113640346581315im; … ; 0.02775215184938601 + 0.04373576024769733im -0.0045394780854464516 + 0.009158976945990693im … -0.020938174416977182 - 0.09625208012669997im 0.04076267000250727 + 0.0204300243962595im; 0.014769173304553719 + 0.09647392678244437im -0.037475038944744674 - 0.0037540291119407473im … -0.012148054661371461 - 0.07849676775293818im 0.10253719213276367 + 0.15320933642882772im]],))]), basis = PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), energies = Energies(total = -7.852646686729848), converged = true, ρ = [0.09132316917851177 0.087474191343932 … 0.07684754936619667 0.087474191343932; 0.087474191343932 0.08089966873007913 … 0.07642471017020991 0.08486944834404268; … ; 0.07684754936619667 0.0764247101702099 … 0.04778466668326015 0.0658789534341498; 0.087474191343932 0.08486944834404268 … 0.06587895343414979 0.08089966873007913;;; 0.08747419134393199 0.08089966873007913 … 0.07642471017020991 0.08486944834404268; 0.08089966873007913 0.06744471471038586 … 0.07348669934492112 0.08163768629205773; … ; 0.07642471017020991 0.07348669934492111 … 0.06188804120938292 0.07259829029012868; 0.08486944834404268 0.08163768629205775 … 0.07259829029012868 0.08163768629205773;;; 0.07684754936619666 0.0658789534341498 … 0.06847203698688446 0.07642471017020991; 0.0658789534341498 0.04657864266259074 … 0.06665759371554977 0.07259829029012868; … ; 0.06847203698688446 0.06665759371554976 … 0.06132515314718231 0.06665759371554977; 0.07642471017020991 0.07259829029012868 … 0.06665759371554977 0.07348669934492112;;; … ;;; 0.06328495230633412 0.06591651446172944 … 0.03394064889233095 0.04987593487054628; 0.06591651446172944 0.06297790959854108 … 0.049756397895749434 0.060870204578696255; … ; 0.03394064889233095 0.049756397895749434 … 0.009696353226074601 0.01683133880451805; 0.04987593487054628 0.060870204578696255 … 0.01683133880451804 0.0309857218966117;;; 0.07684754936619666 0.07642471017020991 … 0.047784666683260146 0.0658789534341498; 0.07642471017020991 0.07348669934492112 … 0.06188804120938292 0.07259829029012868; … ; 0.047784666683260146 0.061888041209382905 … 0.009696353226074608 0.025710010687591628; 0.0658789534341498 0.07259829029012868 … 0.02571001068759162 0.046578642662590736;;; 0.08747419134393199 0.08486944834404267 … 0.0658789534341498 0.08089966873007913; 0.08486944834404267 0.08163768629205773 … 0.07259829029012868 0.08163768629205773; … ; 0.0658789534341498 0.07259829029012867 … 0.025710010687591624 0.04657864266259074; 0.08089966873007913 0.08163768629205774 … 0.046578642662590736 0.06744471471038586;;;;], ψ = Matrix{ComplexF64}[[0.8026148804824371 + 0.5184554166391131im -1.5146741499938443e-10 - 2.576171498347435e-10im -8.989226030209352e-11 - 5.65303012733942e-12im -1.3354606309690098e-10 + 1.907205296469705e-10im; 0.08088287230656413 + 0.05224692965965412im 0.13145793659710675 + 0.09968351797751016im -0.09118255178729814 - 0.33503582165897916im -0.05826614965370965 - 0.3178630159470161im; … ; 0.00990708101191768 + 0.006399557170764928im -0.021711543225304823 - 0.04501765160459906im 0.0032841193170807786 + 0.02729617584463845im 0.015868322383762182 - 0.0016875887399063066im; -0.08088287252630649 - 0.05224692972579233im -0.08110289040116887 - 0.3410492830940359im -0.05903029491679707 - 0.06780020174910997im 0.09708824559562132 - 0.33438484354946746im], [0.9238132293429502 + 0.09552207019595674im -0.18838911523608626 - 0.0580319803009722im 1.2002834837154808e-9 - 5.051863927185707e-10im -9.434622250115154e-10 - 1.4874816725574114e-9im; 0.06297812795255972 + 0.006511923738089346im 0.008384668488449605 + 0.0025828394860208416im 1.8231602651186396e-9 - 1.1738725148174867e-9im 4.794326353562035e-10 - 1.3194996501680878e-9im; … ; 0.00770966162811943 + 0.0007971770406797474im -0.08243605535937311 - 0.02539386422546365im -0.07533490798411964 + 0.012825013528384227im 0.041702692771229365 - 0.04548460438782392im; -0.11233316554446099 - 0.011615222826891924im 0.0866878262902132 + 0.026703592662243675im -0.4717837554729689 + 0.08031645597413711im 0.26116249613413 - 0.2848466693507251im], [0.876760106751819 - 0.32122028028857874im 7.243479843710432e-10 + 3.5485783755895284e-10im 4.737328029857935e-10 + 1.3104288487664206e-10im 5.323554930214414e-10 + 5.552211607140478e-10im; 0.06455256409803618 - 0.023650246548473947im 0.01586447794825852 + 0.05494587709325316im 0.0025424063467438087 + 0.02056910077894964im 0.01839638300004698 + 0.02486708240223449im; … ; 0.01302372046151479 - 0.0047715255771987476im 3.6159978483718547e-10 + 3.7625247362171876e-10im 0.05022431963287762 + 0.0019732858170997125im -0.09742703427857277 - 0.07581239901420736im; -0.14385778181594858 + 0.05270545102462371im 0.07964852109625244 + 0.27585894094425956im 0.39424598936795685 + 0.37601439301668244im -0.3538924727395541 - 0.08952679444605016im], [-0.7787377441840353 + 0.21924644639480784im -9.49557099616527e-11 + 1.5269285835728397e-11im 0.20043219087832784 + 0.4528765809716987im -1.5929942087655746e-10 - 9.510757459363361e-11im; -0.3729737202245188 + 0.10500731899969583im -0.47215533161116746 - 0.4119225524853651im -0.21804000414596172 - 0.4926614398417364im 1.6457391005531008e-10 + 1.3409864885183254e-10im; … ; -0.010967311315716183 + 0.003087745536805384im -0.0012385421969062862 - 0.001080541461696397im -0.008448289318473846 - 0.019088911604854757im 0.0017983325408563301 - 0.00902224713842014im; 0.06274058157035033 - 0.01766403341532607im -0.009407984346766204 - 0.00820780876040028im -0.05106273346888922 - 0.11537625870499876im 0.034930454509254666 - 0.17524632595691123im]], eigenvalues = Any[[-0.1667770759537835, 0.26427771784483406, 0.26427771784483417, 0.2642777178448343], [-0.11613218760040614, 0.07040532320986076, 0.22624813604356062, 0.22624813604356064], [-0.09588938142593603, 0.08764319969367547, 0.1731270414381932, 0.1731270414381934], [-0.04505146347346556, 0.02226952625214948, 0.09831189252079818, 0.18446409323258284]], occupation = [[2.0, 2.0, 2.0, 2.0], [2.0, 2.0, 2.0, 2.0], [2.0, 2.0, 2.0, 2.0], [2.0, 2.0, 2.0, 2.0]], εF = nothing, optim_res =  * Status: success

 * Candidate solution
    Final objective value:     -7.852647e+00

 * Found with
    Algorithm:     L-BFGS

 * Convergence measures
    |x - x'|               = 1.97e-13 ≤ 1.0e-12
    |x - x'|/|x'|          = 2.44e-13 ≰ 0.0e+00
    |f(x) - f(x')|         = 0.00e+00 ≤ 0.0e+00
    |f(x) - f(x')|/|f(x')| = 0.00e+00 ≰ -1.0e+00
    |g(x)|                 = 3.80e-09 ≰ -1.0e+00

 * Work counters
    Seconds run:   2  (vs limit Inf)
    Iterations:    43
    f(x) calls:    55
    ∇f(x) calls:   45
)

Start not too far from the solution to ensure convergence: We run first a very crude SCF to get close and then switch to Newton.

In [5]:
scfres_start = self_consistent_field(basis; tol=1e-1)
n     Energy            log10(ΔE)   log10(Δρ)   Diag
---   ---------------   ---------   ---------   ----
  1   -7.846889101620                   -0.70    4.2
  2   -7.852328456917       -2.26       -1.53    1.0
Out[5]:
(ham = Hamiltonian(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), HamiltonianBlock[DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [0.0, 0.5625437115174675, 2.25017484606987, 2.25017484606987, 0.5625437115174675, 0.5625437115174675, 0.7500582820232901, 2.0626602755640477, 4.50034969213974, 3.5627768396106276  …  3.7502914101164504, 3.7502914101164504, 2.0626602755640477, 1.5001165640465801, 0.7500582820232901, 2.0626602755640477, 4.50034969213974, 3.5627768396106276, 1.5001165640465801, 0.5625437115174675]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [-0.30116136598756804 -0.36869760795125184 … -0.5702190219244254 -0.36869760795125195; -0.3686976079512516 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456163; … ; -0.5702190219244256 -0.264614164394795 … -2.291992881132685 -1.1751172086054253; -0.3686976079512515 -0.2539389812456162 … -1.1751172086054256 -0.6560706269776425;;; -0.3686976079512517 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456166; -0.6560706269776425 -1.3741022038947448 … -0.1651225671881503 -0.31565743774427135; … ; -0.2646141643947949 -0.16512256718815066 … -0.8632000905877295 -0.4898593856167607; -0.25393898124561615 -0.31565743774427135 … -0.48985938561676046 -0.31565743774427124;;; -0.5702190219244254 -1.1751172086054258 … -0.1242245197168452 -0.264614164394795; -1.1751172086054256 -2.8292222589777416 … -0.1750685951638031 -0.48985938561676046; … ; -0.1242245197168452 -0.1750685951638037 … -0.30112950922681153 -0.17506859516380358; -0.2646141643947948 -0.48985938561676046 … -0.17506859516380294 -0.1651225671881503;;; … ;;; -0.8720732197039092 -0.36117451106748844 … -3.5504427268225025 -1.881971917366274; -0.3611745110674882 -0.13192205269891222 … -1.3219289313234115 -0.747481991474731; … ; -3.5504427268225025 -1.3219289313234115 … -11.011681230319526 -8.06878895093237; -1.8819719173662737 -0.747481991474731 … -8.06878895093237 -4.5798976647669045;;; -0.5702190219244254 -0.2646141643947948 … -2.2919928811326855 -1.1751172086054256; -0.2646141643947947 -0.16512256718815055 … -0.8632000905877295 -0.48985938561676046; … ; -2.2919928811326855 -0.8632000905877297 … -11.026309596728632 -6.029372075563462; -1.1751172086054253 -0.4898593856167603 … -6.029372075563462 -2.8292222589777416;;; -0.3686976079512518 -0.2539389812456165 … -1.1751172086054256 -0.6560706269776427; -0.25393898124561626 -0.3156574377442714 … -0.4898593856167604 -0.31565743774427135; … ; -1.1751172086054256 -0.48985938561676057 … -6.029372075563461 -2.829222258977741; -0.6560706269776424 -0.3156574377442712 … -2.829222258977741 -1.3741022038947448]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), ComplexF64[0.11164094023604486 + 0.0im 0.1729534009156557 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.07139183057793365 - 0.07139183057793365im 0.10318729458139622 - 0.10318729458139622im … -0.035578676822652595 + 0.035578676822652595im 0.035578676822652595 - 0.035578676822652595im; … ; -0.08538801146445177 + 0.0im -0.10864081623630145 + 0.0im … 0.0 + 0.08076812854291712im 0.0 - 0.0im; -0.07139183057793365 + 0.07139183057793365im -0.10318729458139622 + 0.10318729458139622im … -0.035578676822652595 + 0.035578676822652595im -0.035578676822652595 + 0.035578676822652595im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [0.39302388277194744 0.3797277034330404 … 0.3452240552353238 0.3797277034330404; 0.3797277034330404 0.36716436720652745 … 0.3281958281706473 0.364903762391868; … ; 0.3452240552353238 0.32819582817064724 … 0.3067281072469059 0.33429040739252475; 0.3797277034330404 0.364903762391868 … 0.3342904073925248 0.36716436720652745;;; 0.3797277034330404 0.36716436720652745 … 0.3281958281706472 0.364903762391868; 0.3671643672065275 0.3511148842472397 … 0.3121018034385326 0.3529233580847052; … ; 0.3281958281706472 0.3121018034385325 … 0.2978385722725771 0.321773662853778; 0.364903762391868 0.3529233580847052 … 0.321773662853778 0.35292335808470515;;; 0.34522405523532373 0.3342904073925247 … 0.2873043857457444 0.3281958281706472; 0.33429040739252475 0.31798127956183175 … 0.2786090169756932 0.321773662853778; … ; 0.2873043857457444 0.27860901697569307 … 0.2558710279806937 0.2786090169756931; 0.3281958281706472 0.321773662853778 … 0.2786090169756932 0.3121018034385325;;; … ;;; 0.30456056720565194 0.2831672125272052 … 0.28429713585871 0.3001204454959564; 0.2831672125272053 0.2594511485784294 … 0.27153606725493695 0.28495739099180784; … ; 0.28429713585870997 0.2715360672549369 … 0.27588729840244125 0.2799243436159472; 0.30012044549595646 0.28495739099180784 … 0.2799243436159472 0.29195377901336894;;; 0.3452240552353238 0.32819582817064724 … 0.306728107246906 0.33429040739252475; 0.3281958281706472 0.31210180343853255 … 0.29783857227257715 0.321773662853778; … ; 0.3067281072469059 0.29783857227257715 … 0.2758872984024413 0.29203083337138763; 0.3342904073925248 0.321773662853778 … 0.2920308333713877 0.3179812795618318;;; 0.3797277034330404 0.364903762391868 … 0.33429040739252475 0.3671643672065275; 0.36490376239186806 0.3529233580847052 … 0.32177366285377806 0.3529233580847052; … ; 0.33429040739252475 0.321773662853778 … 0.29203083337138763 0.31798127956183175; 0.36716436720652756 0.3529233580847052 … 0.3179812795618318 0.3511148842472397]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [-0.5045419279384403 -0.4977819883803615 … -0.4779533380182037 -0.4977819883803615; -0.4977819883803615 -0.4857723458993734 … -0.47720914572884726 -0.49312731227565143; … ; -0.4779533380182037 -0.47720914572884726 … -0.4122199564450144 -0.45556807237700436; -0.4977819883803615 -0.49312731227565143 … -0.45556807237700436 -0.48577234589937346;;; -0.4977819883803615 -0.4857723458993734 … -0.47720914572884726 -0.49312731227565143; -0.4857723458993734 -0.4591356345837859 … -0.4714910102746461 -0.48714812418091136; … ; -0.47720914572884726 -0.4714910102746461 … -0.44644148033264947 -0.46947764115753654; -0.4931273122756514 -0.48714812418091136 … -0.46947764115753654 -0.48714812418091136;;; -0.4779533380182037 -0.45556807237700436 … -0.4612434578024477 -0.4772091457288473; -0.45556807237700436 -0.4093360532609586 … -0.4573154919061865 -0.46947764115753665; … ; -0.4612434578024477 -0.4573154919061865 … -0.44531695487745426 -0.4573154919061865; -0.47720914572884726 -0.46947764115753665 … -0.4573154919061865 -0.4714910102746461;;; … ;;; -0.44959543965273724 -0.4554634141178493 … -0.37046290269724913 -0.41752013924753295; -0.4554634141178493 -0.4493001602680368 … -0.4167132028394187 -0.4440464187427182; … ; -0.370462902697249 -0.4167132028394187 … -0.2528529658820271 -0.2990096772360529; -0.41752013924753295 -0.4440464187427182 … -0.29900967723605293 -0.3606313897347814;;; -0.4779533380182037 -0.47720914572884726 … -0.4122199564450144 -0.4555680723770044; -0.47720914572884726 -0.47149101027464607 … -0.44644148033264947 -0.46947764115753665; … ; -0.41221995644501436 -0.44644148033264947 … -0.2528529658820272 -0.34079699332461627; -0.4555680723770043 -0.46947764115753665 … -0.34079699332461627 -0.4093360532609587;;; -0.4977819883803615 -0.49312731227565143 … -0.45556807237700436 -0.48577234589937346; -0.49312731227565143 -0.4871481241809113 … -0.46947764115753654 -0.48714812418091136; … ; -0.4555680723770043 -0.46947764115753654 … -0.34079699332461627 -0.4093360532609586; -0.4857723458993734 -0.48714812418091136 … -0.4093360532609586 -0.4591356345837859])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [0.0, 0.5625437115174675, 2.25017484606987, 2.25017484606987, 0.5625437115174675, 0.5625437115174675, 0.7500582820232901, 2.0626602755640477, 4.50034969213974, 3.5627768396106276  …  3.7502914101164504, 3.7502914101164504, 2.0626602755640477, 1.5001165640465801, 0.7500582820232901, 2.0626602755640477, 4.50034969213974, 3.5627768396106276, 1.5001165640465801, 0.5625437115174675]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), [-0.4126794111540609 -0.4867518928985729 … -0.7029483047073053 -0.486751892898573; -0.4867518928985727 -0.7746786056704886 … -0.41362748195299476 -0.38216253112939974; … ; -0.7029483047073055 -0.41362748195299504 … -2.3974847303307936 -1.296394873589905; -0.48675189289857257 -0.38216253112939963 … -1.2963948735899051 -0.7746786056704885;;; -0.4867518928985728 -0.7746786056704886 … -0.41362748195299487 -0.3821625311294; -0.7746786056704884 -1.4821229542312908 … -0.3245117740242638 -0.4498822038404775; … ; -0.413627481952995 -0.3245117740242643 … -1.0118029986478019 -0.6375633639205192; -0.3821625311293995 -0.4498822038404775 … -0.6375633639205189 -0.44988220384047745;;; -0.7029483047073054 -1.2963948735899056 … -0.29816359177354845 -0.41362748195299515; -1.2963948735899051 -2.9205770326768685 … -0.35377507009429643 -0.6375633639205192; … ; -0.29816359177354845 -0.3537750700942971 … -0.4905754361235721 -0.35377507009429693; -0.41362748195299487 -0.6375633639205192 … -0.3537750700942962 -0.3245117740242639;;; … ;;; -1.0171080921509945 -0.5334707126581325 … -3.6366084936610417 -1.9993716111178503; -0.5334707126581322 -0.32177106438851966 … -1.4671060669078932 -0.9065710192256414; … ; -3.6366084936610417 -1.4671060669078932 … -10.988646897799113 -8.087874284552477; -1.9993716111178501 -0.9065710192256414 … -8.087874284552477 -4.648575275488317;;; -0.7029483047073053 -0.4136274819529948 … -2.3974847303307936 -1.2963948735899051; -0.41362748195299476 -0.32451177402426407 … -1.0118029986478019 -0.6375633639205192; … ; -2.397484730330794 -1.011802998647802 … -11.003275264208218 -6.078138235516691; -1.296394873589905 -0.6375633639205189 … -6.078138235516691 -2.920577032676868;;; -0.48675189289857285 -0.3821625311293999 … -1.2963948735899051 -0.7746786056704886; -0.38216253112939963 -0.4498822038404775 … -0.6375633639205189 -0.4498822038404775; … ; -1.2963948735899051 -0.6375633639205192 … -6.07813823551669 -2.9205770326768676; -0.7746786056704882 -0.44988220384047733 … -2.9205770326768676 -1.4821229542312908]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([     0,      0,      0], spin = 1, num. G vectors =   137), ComplexF64[0.11164094023604486 + 0.0im 0.1729534009156557 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.07139183057793365 - 0.07139183057793365im 0.10318729458139622 - 0.10318729458139622im … -0.035578676822652595 + 0.035578676822652595im 0.035578676822652595 - 0.035578676822652595im; … ; -0.08538801146445177 + 0.0im -0.10864081623630145 + 0.0im … 0.0 + 0.08076812854291712im 0.0 - 0.0im; -0.07139183057793365 + 0.07139183057793365im -0.10318729458139622 + 0.10318729458139622im … -0.035578676822652595 + 0.035578676822652595im -0.035578676822652595 + 0.035578676822652595im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, (ψ_reals = Array{ComplexF64, 3}[[0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; … ;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im]],)), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [0.06250485683527418, 1.000077709364387, 3.062737984928434, 4.000310837457548, 1.562621420881854, 0.2500194273410967, 0.5000388546821934, 1.0625825661996608, 2.750213700752063, 2.7502137007520635  …  2.5001942734109663, 4.5628545489750145, 3.062737984928434, 1.7501359913876768, 1.5626214208818543, 1.062582566199661, 2.750213700752063, 2.750213700752064, 1.0625825661996608, 0.5000388546821934]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [-0.30116136598756804 -0.36869760795125184 … -0.5702190219244254 -0.36869760795125195; -0.3686976079512516 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456163; … ; -0.5702190219244256 -0.264614164394795 … -2.291992881132685 -1.1751172086054253; -0.3686976079512515 -0.2539389812456162 … -1.1751172086054256 -0.6560706269776425;;; -0.3686976079512517 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456166; -0.6560706269776425 -1.3741022038947448 … -0.1651225671881503 -0.31565743774427135; … ; -0.2646141643947949 -0.16512256718815066 … -0.8632000905877295 -0.4898593856167607; -0.25393898124561615 -0.31565743774427135 … -0.48985938561676046 -0.31565743774427124;;; -0.5702190219244254 -1.1751172086054258 … -0.1242245197168452 -0.264614164394795; -1.1751172086054256 -2.8292222589777416 … -0.1750685951638031 -0.48985938561676046; … ; -0.1242245197168452 -0.1750685951638037 … -0.30112950922681153 -0.17506859516380358; -0.2646141643947948 -0.48985938561676046 … -0.17506859516380294 -0.1651225671881503;;; … ;;; -0.8720732197039092 -0.36117451106748844 … -3.5504427268225025 -1.881971917366274; -0.3611745110674882 -0.13192205269891222 … -1.3219289313234115 -0.747481991474731; … ; -3.5504427268225025 -1.3219289313234115 … -11.011681230319526 -8.06878895093237; -1.8819719173662737 -0.747481991474731 … -8.06878895093237 -4.5798976647669045;;; -0.5702190219244254 -0.2646141643947948 … -2.2919928811326855 -1.1751172086054256; -0.2646141643947947 -0.16512256718815055 … -0.8632000905877295 -0.48985938561676046; … ; -2.2919928811326855 -0.8632000905877297 … -11.026309596728632 -6.029372075563462; -1.1751172086054253 -0.4898593856167603 … -6.029372075563462 -2.8292222589777416;;; -0.3686976079512518 -0.2539389812456165 … -1.1751172086054256 -0.6560706269776427; -0.25393898124561626 -0.3156574377442714 … -0.4898593856167604 -0.31565743774427135; … ; -1.1751172086054256 -0.48985938561676057 … -6.029372075563461 -2.829222258977741; -0.6560706269776424 -0.3156574377442712 … -2.829222258977741 -1.3741022038947448]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), ComplexF64[0.10663902257822168 - 0.028573839981478756im 0.16397423109777803 - 0.0439367628021639im … -0.0048810168633526265 + 0.01821620292663248im 0.0048810168633526265 - 0.01821620292663248im; 0.04668482831007231 - 0.08086049457567514im 0.06370661418591363 - 0.11034309254819058im … -0.05243363114037364 + 0.030272571053484264im 0.05243363114037364 - 0.030272571053484264im; … ; -0.08918635851135279 + 0.023897412738989543im -0.12067576411442682 + 0.03233497354046929im … -0.019302751901532963 + 0.07203885082241784im -0.0038605503803065926 + 0.014407770164483566im; -0.051048693065027635 + 0.08841893004861681im -0.0743729428832569 + 0.128817715782219im … -0.02947884616601673 + 0.017019619769349337im -0.05895769233203346 + 0.034039239538698675im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [0.39302388277194744 0.3797277034330404 … 0.3452240552353238 0.3797277034330404; 0.3797277034330404 0.36716436720652745 … 0.3281958281706473 0.364903762391868; … ; 0.3452240552353238 0.32819582817064724 … 0.3067281072469059 0.33429040739252475; 0.3797277034330404 0.364903762391868 … 0.3342904073925248 0.36716436720652745;;; 0.3797277034330404 0.36716436720652745 … 0.3281958281706472 0.364903762391868; 0.3671643672065275 0.3511148842472397 … 0.3121018034385326 0.3529233580847052; … ; 0.3281958281706472 0.3121018034385325 … 0.2978385722725771 0.321773662853778; 0.364903762391868 0.3529233580847052 … 0.321773662853778 0.35292335808470515;;; 0.34522405523532373 0.3342904073925247 … 0.2873043857457444 0.3281958281706472; 0.33429040739252475 0.31798127956183175 … 0.2786090169756932 0.321773662853778; … ; 0.2873043857457444 0.27860901697569307 … 0.2558710279806937 0.2786090169756931; 0.3281958281706472 0.321773662853778 … 0.2786090169756932 0.3121018034385325;;; … ;;; 0.30456056720565194 0.2831672125272052 … 0.28429713585871 0.3001204454959564; 0.2831672125272053 0.2594511485784294 … 0.27153606725493695 0.28495739099180784; … ; 0.28429713585870997 0.2715360672549369 … 0.27588729840244125 0.2799243436159472; 0.30012044549595646 0.28495739099180784 … 0.2799243436159472 0.29195377901336894;;; 0.3452240552353238 0.32819582817064724 … 0.306728107246906 0.33429040739252475; 0.3281958281706472 0.31210180343853255 … 0.29783857227257715 0.321773662853778; … ; 0.3067281072469059 0.29783857227257715 … 0.2758872984024413 0.29203083337138763; 0.3342904073925248 0.321773662853778 … 0.2920308333713877 0.3179812795618318;;; 0.3797277034330404 0.364903762391868 … 0.33429040739252475 0.3671643672065275; 0.36490376239186806 0.3529233580847052 … 0.32177366285377806 0.3529233580847052; … ; 0.33429040739252475 0.321773662853778 … 0.29203083337138763 0.31798127956183175; 0.36716436720652756 0.3529233580847052 … 0.3179812795618318 0.3511148842472397]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [-0.5045419279384403 -0.4977819883803615 … -0.4779533380182037 -0.4977819883803615; -0.4977819883803615 -0.4857723458993734 … -0.47720914572884726 -0.49312731227565143; … ; -0.4779533380182037 -0.47720914572884726 … -0.4122199564450144 -0.45556807237700436; -0.4977819883803615 -0.49312731227565143 … -0.45556807237700436 -0.48577234589937346;;; -0.4977819883803615 -0.4857723458993734 … -0.47720914572884726 -0.49312731227565143; -0.4857723458993734 -0.4591356345837859 … -0.4714910102746461 -0.48714812418091136; … ; -0.47720914572884726 -0.4714910102746461 … -0.44644148033264947 -0.46947764115753654; -0.4931273122756514 -0.48714812418091136 … -0.46947764115753654 -0.48714812418091136;;; -0.4779533380182037 -0.45556807237700436 … -0.4612434578024477 -0.4772091457288473; -0.45556807237700436 -0.4093360532609586 … -0.4573154919061865 -0.46947764115753665; … ; -0.4612434578024477 -0.4573154919061865 … -0.44531695487745426 -0.4573154919061865; -0.47720914572884726 -0.46947764115753665 … -0.4573154919061865 -0.4714910102746461;;; … ;;; -0.44959543965273724 -0.4554634141178493 … -0.37046290269724913 -0.41752013924753295; -0.4554634141178493 -0.4493001602680368 … -0.4167132028394187 -0.4440464187427182; … ; -0.370462902697249 -0.4167132028394187 … -0.2528529658820271 -0.2990096772360529; -0.41752013924753295 -0.4440464187427182 … -0.29900967723605293 -0.3606313897347814;;; -0.4779533380182037 -0.47720914572884726 … -0.4122199564450144 -0.4555680723770044; -0.47720914572884726 -0.47149101027464607 … -0.44644148033264947 -0.46947764115753665; … ; -0.41221995644501436 -0.44644148033264947 … -0.2528529658820272 -0.34079699332461627; -0.4555680723770043 -0.46947764115753665 … -0.34079699332461627 -0.4093360532609587;;; -0.4977819883803615 -0.49312731227565143 … -0.45556807237700436 -0.48577234589937346; -0.49312731227565143 -0.4871481241809113 … -0.46947764115753654 -0.48714812418091136; … ; -0.4555680723770043 -0.46947764115753654 … -0.34079699332461627 -0.4093360532609586; -0.4857723458993734 -0.48714812418091136 … -0.4093360532609586 -0.4591356345837859])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [0.06250485683527418, 1.000077709364387, 3.062737984928434, 4.000310837457548, 1.562621420881854, 0.2500194273410967, 0.5000388546821934, 1.0625825661996608, 2.750213700752063, 2.7502137007520635  …  2.5001942734109663, 4.5628545489750145, 3.062737984928434, 1.7501359913876768, 1.5626214208818543, 1.062582566199661, 2.750213700752063, 2.750213700752064, 1.0625825661996608, 0.5000388546821934]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), [-0.4126794111540609 -0.4867518928985729 … -0.7029483047073053 -0.486751892898573; -0.4867518928985727 -0.7746786056704886 … -0.41362748195299476 -0.38216253112939974; … ; -0.7029483047073055 -0.41362748195299504 … -2.3974847303307936 -1.296394873589905; -0.48675189289857257 -0.38216253112939963 … -1.2963948735899051 -0.7746786056704885;;; -0.4867518928985728 -0.7746786056704886 … -0.41362748195299487 -0.3821625311294; -0.7746786056704884 -1.4821229542312908 … -0.3245117740242638 -0.4498822038404775; … ; -0.413627481952995 -0.3245117740242643 … -1.0118029986478019 -0.6375633639205192; -0.3821625311293995 -0.4498822038404775 … -0.6375633639205189 -0.44988220384047745;;; -0.7029483047073054 -1.2963948735899056 … -0.29816359177354845 -0.41362748195299515; -1.2963948735899051 -2.9205770326768685 … -0.35377507009429643 -0.6375633639205192; … ; -0.29816359177354845 -0.3537750700942971 … -0.4905754361235721 -0.35377507009429693; -0.41362748195299487 -0.6375633639205192 … -0.3537750700942962 -0.3245117740242639;;; … ;;; -1.0171080921509945 -0.5334707126581325 … -3.6366084936610417 -1.9993716111178503; -0.5334707126581322 -0.32177106438851966 … -1.4671060669078932 -0.9065710192256414; … ; -3.6366084936610417 -1.4671060669078932 … -10.988646897799113 -8.087874284552477; -1.9993716111178501 -0.9065710192256414 … -8.087874284552477 -4.648575275488317;;; -0.7029483047073053 -0.4136274819529948 … -2.3974847303307936 -1.2963948735899051; -0.41362748195299476 -0.32451177402426407 … -1.0118029986478019 -0.6375633639205192; … ; -2.397484730330794 -1.011802998647802 … -11.003275264208218 -6.078138235516691; -1.296394873589905 -0.6375633639205189 … -6.078138235516691 -2.920577032676868;;; -0.48675189289857285 -0.3821625311293999 … -1.2963948735899051 -0.7746786056704886; -0.38216253112939963 -0.4498822038404775 … -0.6375633639205189 -0.4498822038404775; … ; -1.2963948735899051 -0.6375633639205192 … -6.07813823551669 -2.9205770326768676; -0.7746786056704882 -0.44988220384047733 … -2.9205770326768676 -1.4821229542312908]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,      0,      0], spin = 1, num. G vectors =   144), ComplexF64[0.10663902257822168 - 0.028573839981478756im 0.16397423109777803 - 0.0439367628021639im … -0.0048810168633526265 + 0.01821620292663248im 0.0048810168633526265 - 0.01821620292663248im; 0.04668482831007231 - 0.08086049457567514im 0.06370661418591363 - 0.11034309254819058im … -0.05243363114037364 + 0.030272571053484264im 0.05243363114037364 - 0.030272571053484264im; … ; -0.08918635851135279 + 0.023897412738989543im -0.12067576411442682 + 0.03233497354046929im … -0.019302751901532963 + 0.07203885082241784im -0.0038605503803065926 + 0.014407770164483566im; -0.051048693065027635 + 0.08841893004861681im -0.0743729428832569 + 0.128817715782219im … -0.02947884616601673 + 0.017019619769349337im -0.05895769233203346 + 0.034039239538698675im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, (ψ_reals = Array{ComplexF64, 3}[[0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; … ;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im]],)), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [0.0833398091136989, 0.8959029479722631, 2.8335535098657623, 4.396174930747617, 1.8334758005013758, 0.3958640932900698, 0.8959029479722631, 1.3334369458191824, 2.8960583667010367, 3.39609722138323  …  1.89598065733665, 3.833631219230149, 2.8335535098657623, 1.3959418026544566, 1.0834175184780857, 0.8333980911369889, 2.3960195120188432, 2.8960583667010367, 1.0834175184780857, 0.3958640932900698]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [-0.30116136598756804 -0.36869760795125184 … -0.5702190219244254 -0.36869760795125195; -0.3686976079512516 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456163; … ; -0.5702190219244256 -0.264614164394795 … -2.291992881132685 -1.1751172086054253; -0.3686976079512515 -0.2539389812456162 … -1.1751172086054256 -0.6560706269776425;;; -0.3686976079512517 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456166; -0.6560706269776425 -1.3741022038947448 … -0.1651225671881503 -0.31565743774427135; … ; -0.2646141643947949 -0.16512256718815066 … -0.8632000905877295 -0.4898593856167607; -0.25393898124561615 -0.31565743774427135 … -0.48985938561676046 -0.31565743774427124;;; -0.5702190219244254 -1.1751172086054258 … -0.1242245197168452 -0.264614164394795; -1.1751172086054256 -2.8292222589777416 … -0.1750685951638031 -0.48985938561676046; … ; -0.1242245197168452 -0.1750685951638037 … -0.30112950922681153 -0.17506859516380358; -0.2646141643947948 -0.48985938561676046 … -0.17506859516380294 -0.1651225671881503;;; … ;;; -0.8720732197039092 -0.36117451106748844 … -3.5504427268225025 -1.881971917366274; -0.3611745110674882 -0.13192205269891222 … -1.3219289313234115 -0.747481991474731; … ; -3.5504427268225025 -1.3219289313234115 … -11.011681230319526 -8.06878895093237; -1.8819719173662737 -0.747481991474731 … -8.06878895093237 -4.5798976647669045;;; -0.5702190219244254 -0.2646141643947948 … -2.2919928811326855 -1.1751172086054256; -0.2646141643947947 -0.16512256718815055 … -0.8632000905877295 -0.48985938561676046; … ; -2.2919928811326855 -0.8632000905877297 … -11.026309596728632 -6.029372075563462; -1.1751172086054253 -0.4898593856167603 … -6.029372075563462 -2.8292222589777416;;; -0.3686976079512518 -0.2539389812456165 … -1.1751172086054256 -0.6560706269776427; -0.25393898124561626 -0.3156574377442714 … -0.4898593856167604 -0.31565743774427135; … ; -1.1751172086054256 -0.48985938561676057 … -6.029372075563461 -2.829222258977741; -0.6560706269776424 -0.3156574377442712 … -2.829222258977741 -1.3741022038947448]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), ComplexF64[0.09525460347564817 - 0.05499527095821653im 0.14610260131202302 - 0.08435237619680104im … -0.018766875445216862 + 0.032505181770432406im 5.2088543048880615e-19 - 9.022000305289992e-19im; 0.024619950292842606 - 0.09188290537270884im 0.03407002323540016 - 0.12715105772956556im … -0.07491066001757686 + 0.02007225085619212im 0.04494639601054611 - 0.012043350513715271im; … ; -0.07966512642409461 + 0.045994682185976576im -0.10748648020277889 + 0.06205734827931975im … -0.02968662889946843 + 0.05141874955932189im 0.0 - 0.0im; -0.026921300372532365 + 0.10047166079611371im -0.039739321889381986 + 0.14830916834950758im … -0.016846285674482424 + 0.0045139486419415575im -0.05053885702344723 + 0.013541845925824664im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [0.39302388277194744 0.3797277034330404 … 0.3452240552353238 0.3797277034330404; 0.3797277034330404 0.36716436720652745 … 0.3281958281706473 0.364903762391868; … ; 0.3452240552353238 0.32819582817064724 … 0.3067281072469059 0.33429040739252475; 0.3797277034330404 0.364903762391868 … 0.3342904073925248 0.36716436720652745;;; 0.3797277034330404 0.36716436720652745 … 0.3281958281706472 0.364903762391868; 0.3671643672065275 0.3511148842472397 … 0.3121018034385326 0.3529233580847052; … ; 0.3281958281706472 0.3121018034385325 … 0.2978385722725771 0.321773662853778; 0.364903762391868 0.3529233580847052 … 0.321773662853778 0.35292335808470515;;; 0.34522405523532373 0.3342904073925247 … 0.2873043857457444 0.3281958281706472; 0.33429040739252475 0.31798127956183175 … 0.2786090169756932 0.321773662853778; … ; 0.2873043857457444 0.27860901697569307 … 0.2558710279806937 0.2786090169756931; 0.3281958281706472 0.321773662853778 … 0.2786090169756932 0.3121018034385325;;; … ;;; 0.30456056720565194 0.2831672125272052 … 0.28429713585871 0.3001204454959564; 0.2831672125272053 0.2594511485784294 … 0.27153606725493695 0.28495739099180784; … ; 0.28429713585870997 0.2715360672549369 … 0.27588729840244125 0.2799243436159472; 0.30012044549595646 0.28495739099180784 … 0.2799243436159472 0.29195377901336894;;; 0.3452240552353238 0.32819582817064724 … 0.306728107246906 0.33429040739252475; 0.3281958281706472 0.31210180343853255 … 0.29783857227257715 0.321773662853778; … ; 0.3067281072469059 0.29783857227257715 … 0.2758872984024413 0.29203083337138763; 0.3342904073925248 0.321773662853778 … 0.2920308333713877 0.3179812795618318;;; 0.3797277034330404 0.364903762391868 … 0.33429040739252475 0.3671643672065275; 0.36490376239186806 0.3529233580847052 … 0.32177366285377806 0.3529233580847052; … ; 0.33429040739252475 0.321773662853778 … 0.29203083337138763 0.31798127956183175; 0.36716436720652756 0.3529233580847052 … 0.3179812795618318 0.3511148842472397]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [-0.5045419279384403 -0.4977819883803615 … -0.4779533380182037 -0.4977819883803615; -0.4977819883803615 -0.4857723458993734 … -0.47720914572884726 -0.49312731227565143; … ; -0.4779533380182037 -0.47720914572884726 … -0.4122199564450144 -0.45556807237700436; -0.4977819883803615 -0.49312731227565143 … -0.45556807237700436 -0.48577234589937346;;; -0.4977819883803615 -0.4857723458993734 … -0.47720914572884726 -0.49312731227565143; -0.4857723458993734 -0.4591356345837859 … -0.4714910102746461 -0.48714812418091136; … ; -0.47720914572884726 -0.4714910102746461 … -0.44644148033264947 -0.46947764115753654; -0.4931273122756514 -0.48714812418091136 … -0.46947764115753654 -0.48714812418091136;;; -0.4779533380182037 -0.45556807237700436 … -0.4612434578024477 -0.4772091457288473; -0.45556807237700436 -0.4093360532609586 … -0.4573154919061865 -0.46947764115753665; … ; -0.4612434578024477 -0.4573154919061865 … -0.44531695487745426 -0.4573154919061865; -0.47720914572884726 -0.46947764115753665 … -0.4573154919061865 -0.4714910102746461;;; … ;;; -0.44959543965273724 -0.4554634141178493 … -0.37046290269724913 -0.41752013924753295; -0.4554634141178493 -0.4493001602680368 … -0.4167132028394187 -0.4440464187427182; … ; -0.370462902697249 -0.4167132028394187 … -0.2528529658820271 -0.2990096772360529; -0.41752013924753295 -0.4440464187427182 … -0.29900967723605293 -0.3606313897347814;;; -0.4779533380182037 -0.47720914572884726 … -0.4122199564450144 -0.4555680723770044; -0.47720914572884726 -0.47149101027464607 … -0.44644148033264947 -0.46947764115753665; … ; -0.41221995644501436 -0.44644148033264947 … -0.2528529658820272 -0.34079699332461627; -0.4555680723770043 -0.46947764115753665 … -0.34079699332461627 -0.4093360532609587;;; -0.4977819883803615 -0.49312731227565143 … -0.45556807237700436 -0.48577234589937346; -0.49312731227565143 -0.4871481241809113 … -0.46947764115753654 -0.48714812418091136; … ; -0.4555680723770043 -0.46947764115753654 … -0.34079699332461627 -0.4093360532609586; -0.4857723458993734 -0.48714812418091136 … -0.4093360532609586 -0.4591356345837859])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [0.0833398091136989, 0.8959029479722631, 2.8335535098657623, 4.396174930747617, 1.8334758005013758, 0.3958640932900698, 0.8959029479722631, 1.3334369458191824, 2.8960583667010367, 3.39609722138323  …  1.89598065733665, 3.833631219230149, 2.8335535098657623, 1.3959418026544566, 1.0834175184780857, 0.8333980911369889, 2.3960195120188432, 2.8960583667010367, 1.0834175184780857, 0.3958640932900698]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), [-0.4126794111540609 -0.4867518928985729 … -0.7029483047073053 -0.486751892898573; -0.4867518928985727 -0.7746786056704886 … -0.41362748195299476 -0.38216253112939974; … ; -0.7029483047073055 -0.41362748195299504 … -2.3974847303307936 -1.296394873589905; -0.48675189289857257 -0.38216253112939963 … -1.2963948735899051 -0.7746786056704885;;; -0.4867518928985728 -0.7746786056704886 … -0.41362748195299487 -0.3821625311294; -0.7746786056704884 -1.4821229542312908 … -0.3245117740242638 -0.4498822038404775; … ; -0.413627481952995 -0.3245117740242643 … -1.0118029986478019 -0.6375633639205192; -0.3821625311293995 -0.4498822038404775 … -0.6375633639205189 -0.44988220384047745;;; -0.7029483047073054 -1.2963948735899056 … -0.29816359177354845 -0.41362748195299515; -1.2963948735899051 -2.9205770326768685 … -0.35377507009429643 -0.6375633639205192; … ; -0.29816359177354845 -0.3537750700942971 … -0.4905754361235721 -0.35377507009429693; -0.41362748195299487 -0.6375633639205192 … -0.3537750700942962 -0.3245117740242639;;; … ;;; -1.0171080921509945 -0.5334707126581325 … -3.6366084936610417 -1.9993716111178503; -0.5334707126581322 -0.32177106438851966 … -1.4671060669078932 -0.9065710192256414; … ; -3.6366084936610417 -1.4671060669078932 … -10.988646897799113 -8.087874284552477; -1.9993716111178501 -0.9065710192256414 … -8.087874284552477 -4.648575275488317;;; -0.7029483047073053 -0.4136274819529948 … -2.3974847303307936 -1.2963948735899051; -0.41362748195299476 -0.32451177402426407 … -1.0118029986478019 -0.6375633639205192; … ; -2.397484730330794 -1.011802998647802 … -11.003275264208218 -6.078138235516691; -1.296394873589905 -0.6375633639205189 … -6.078138235516691 -2.920577032676868;;; -0.48675189289857285 -0.3821625311293999 … -1.2963948735899051 -0.7746786056704886; -0.38216253112939963 -0.4498822038404775 … -0.6375633639205189 -0.4498822038404775; … ; -1.2963948735899051 -0.6375633639205192 … -6.07813823551669 -2.9205770326768676; -0.7746786056704882 -0.44988220384047733 … -2.9205770326768676 -1.4821229542312908]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([ 0.333,  0.333,      0], spin = 1, num. G vectors =   141), ComplexF64[0.09525460347564817 - 0.05499527095821653im 0.14610260131202302 - 0.08435237619680104im … -0.018766875445216862 + 0.032505181770432406im 5.2088543048880615e-19 - 9.022000305289992e-19im; 0.024619950292842606 - 0.09188290537270884im 0.03407002323540016 - 0.12715105772956556im … -0.07491066001757686 + 0.02007225085619212im 0.04494639601054611 - 0.012043350513715271im; … ; -0.07966512642409461 + 0.045994682185976576im -0.10748648020277889 + 0.06205734827931975im … -0.02968662889946843 + 0.05141874955932189im 0.0 - 0.0im; -0.026921300372532365 + 0.10047166079611371im -0.039739321889381986 + 0.14830916834950758im … -0.016846285674482424 + 0.0045139486419415575im -0.05053885702344723 + 0.013541845925824664im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, (ψ_reals = Array{ComplexF64, 3}[[0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; … ;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im]],)), DFTK.DftHamiltonianBlock(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), Any[DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [0.1666796182273978, 0.22918447506267198, 1.4167767549328811, 3.7294564578380256, 3.416932173661655, 1.2292621844270586, 1.2292621844270586, 0.9167379002506877, 1.729301039109252, 3.6669516010027516  …  4.729534167202412, 4.417009883026042, 2.2293398937914453, 1.1667573275917844, 0.41669904556849446, 1.2292621844270588, 3.1669127463205577, 4.729534167202412, 2.1668350369561713, 0.7292233297448653]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [-0.30116136598756804 -0.36869760795125184 … -0.5702190219244254 -0.36869760795125195; -0.3686976079512516 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456163; … ; -0.5702190219244256 -0.264614164394795 … -2.291992881132685 -1.1751172086054253; -0.3686976079512515 -0.2539389812456162 … -1.1751172086054256 -0.6560706269776425;;; -0.3686976079512517 -0.6560706269776427 … -0.2646141643947948 -0.2539389812456166; -0.6560706269776425 -1.3741022038947448 … -0.1651225671881503 -0.31565743774427135; … ; -0.2646141643947949 -0.16512256718815066 … -0.8632000905877295 -0.4898593856167607; -0.25393898124561615 -0.31565743774427135 … -0.48985938561676046 -0.31565743774427124;;; -0.5702190219244254 -1.1751172086054258 … -0.1242245197168452 -0.264614164394795; -1.1751172086054256 -2.8292222589777416 … -0.1750685951638031 -0.48985938561676046; … ; -0.1242245197168452 -0.1750685951638037 … -0.30112950922681153 -0.17506859516380358; -0.2646141643947948 -0.48985938561676046 … -0.17506859516380294 -0.1651225671881503;;; … ;;; -0.8720732197039092 -0.36117451106748844 … -3.5504427268225025 -1.881971917366274; -0.3611745110674882 -0.13192205269891222 … -1.3219289313234115 -0.747481991474731; … ; -3.5504427268225025 -1.3219289313234115 … -11.011681230319526 -8.06878895093237; -1.8819719173662737 -0.747481991474731 … -8.06878895093237 -4.5798976647669045;;; -0.5702190219244254 -0.2646141643947948 … -2.2919928811326855 -1.1751172086054256; -0.2646141643947947 -0.16512256718815055 … -0.8632000905877295 -0.48985938561676046; … ; -2.2919928811326855 -0.8632000905877297 … -11.026309596728632 -6.029372075563462; -1.1751172086054253 -0.4898593856167603 … -6.029372075563462 -2.8292222589777416;;; -0.3686976079512518 -0.2539389812456165 … -1.1751172086054256 -0.6560706269776427; -0.25393898124561626 -0.3156574377442714 … -0.4898593856167604 -0.31565743774427135; … ; -1.1751172086054256 -0.48985938561676057 … -6.029372075563461 -2.829222258977741; -0.6560706269776424 -0.3156574377442712 … -2.829222258977741 -1.3741022038947448]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), ComplexF64[0.10836454158744746 + 0.0im 0.16454392299317003 + 0.0im … -0.0 - 1.0216068167279948e-18im 0.0 + 0.03680726463308285im; 0.0757741533540503 - 0.0757741533540503im 0.1141835519100639 - 0.1141835519100639im … -0.03847188688271061 + 0.03847188688271061im 0.012823962294236874 - 0.012823962294236874im; … ; -0.07579695351601741 + 0.0im -0.08711072462387971 + 0.0im … 0.0 + 0.06907686686237845im 0.0 - 0.02302562228745948im; -0.0692966484992815 + 0.0692966484992815im -0.09802716364420207 + 0.09802716364420207im … -0.03421471645670587 + 0.03421471645670587im -0.011404905485568627 + 0.011404905485568627im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142)), DFTK.NoopOperator{Float64}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142)), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [0.39302388277194744 0.3797277034330404 … 0.3452240552353238 0.3797277034330404; 0.3797277034330404 0.36716436720652745 … 0.3281958281706473 0.364903762391868; … ; 0.3452240552353238 0.32819582817064724 … 0.3067281072469059 0.33429040739252475; 0.3797277034330404 0.364903762391868 … 0.3342904073925248 0.36716436720652745;;; 0.3797277034330404 0.36716436720652745 … 0.3281958281706472 0.364903762391868; 0.3671643672065275 0.3511148842472397 … 0.3121018034385326 0.3529233580847052; … ; 0.3281958281706472 0.3121018034385325 … 0.2978385722725771 0.321773662853778; 0.364903762391868 0.3529233580847052 … 0.321773662853778 0.35292335808470515;;; 0.34522405523532373 0.3342904073925247 … 0.2873043857457444 0.3281958281706472; 0.33429040739252475 0.31798127956183175 … 0.2786090169756932 0.321773662853778; … ; 0.2873043857457444 0.27860901697569307 … 0.2558710279806937 0.2786090169756931; 0.3281958281706472 0.321773662853778 … 0.2786090169756932 0.3121018034385325;;; … ;;; 0.30456056720565194 0.2831672125272052 … 0.28429713585871 0.3001204454959564; 0.2831672125272053 0.2594511485784294 … 0.27153606725493695 0.28495739099180784; … ; 0.28429713585870997 0.2715360672549369 … 0.27588729840244125 0.2799243436159472; 0.30012044549595646 0.28495739099180784 … 0.2799243436159472 0.29195377901336894;;; 0.3452240552353238 0.32819582817064724 … 0.306728107246906 0.33429040739252475; 0.3281958281706472 0.31210180343853255 … 0.29783857227257715 0.321773662853778; … ; 0.3067281072469059 0.29783857227257715 … 0.2758872984024413 0.29203083337138763; 0.3342904073925248 0.321773662853778 … 0.2920308333713877 0.3179812795618318;;; 0.3797277034330404 0.364903762391868 … 0.33429040739252475 0.3671643672065275; 0.36490376239186806 0.3529233580847052 … 0.32177366285377806 0.3529233580847052; … ; 0.33429040739252475 0.321773662853778 … 0.29203083337138763 0.31798127956183175; 0.36716436720652756 0.3529233580847052 … 0.3179812795618318 0.3511148842472397]), DFTK.RealSpaceMultiplication{Float64, SubArray{Float64, 3, Array{Float64, 4}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [-0.5045419279384403 -0.4977819883803615 … -0.4779533380182037 -0.4977819883803615; -0.4977819883803615 -0.4857723458993734 … -0.47720914572884726 -0.49312731227565143; … ; -0.4779533380182037 -0.47720914572884726 … -0.4122199564450144 -0.45556807237700436; -0.4977819883803615 -0.49312731227565143 … -0.45556807237700436 -0.48577234589937346;;; -0.4977819883803615 -0.4857723458993734 … -0.47720914572884726 -0.49312731227565143; -0.4857723458993734 -0.4591356345837859 … -0.4714910102746461 -0.48714812418091136; … ; -0.47720914572884726 -0.4714910102746461 … -0.44644148033264947 -0.46947764115753654; -0.4931273122756514 -0.48714812418091136 … -0.46947764115753654 -0.48714812418091136;;; -0.4779533380182037 -0.45556807237700436 … -0.4612434578024477 -0.4772091457288473; -0.45556807237700436 -0.4093360532609586 … -0.4573154919061865 -0.46947764115753665; … ; -0.4612434578024477 -0.4573154919061865 … -0.44531695487745426 -0.4573154919061865; -0.47720914572884726 -0.46947764115753665 … -0.4573154919061865 -0.4714910102746461;;; … ;;; -0.44959543965273724 -0.4554634141178493 … -0.37046290269724913 -0.41752013924753295; -0.4554634141178493 -0.4493001602680368 … -0.4167132028394187 -0.4440464187427182; … ; -0.370462902697249 -0.4167132028394187 … -0.2528529658820271 -0.2990096772360529; -0.41752013924753295 -0.4440464187427182 … -0.29900967723605293 -0.3606313897347814;;; -0.4779533380182037 -0.47720914572884726 … -0.4122199564450144 -0.4555680723770044; -0.47720914572884726 -0.47149101027464607 … -0.44644148033264947 -0.46947764115753665; … ; -0.41221995644501436 -0.44644148033264947 … -0.2528529658820272 -0.34079699332461627; -0.4555680723770043 -0.46947764115753665 … -0.34079699332461627 -0.4093360532609587;;; -0.4977819883803615 -0.49312731227565143 … -0.45556807237700436 -0.48577234589937346; -0.49312731227565143 -0.4871481241809113 … -0.46947764115753654 -0.48714812418091136; … ; -0.4555680723770043 -0.46947764115753654 … -0.34079699332461627 -0.4093360532609586; -0.4857723458993734 -0.48714812418091136 … -0.4093360532609586 -0.4591356345837859])], DFTK.FourierMultiplication{Float64, Vector{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [0.1666796182273978, 0.22918447506267198, 1.4167767549328811, 3.7294564578380256, 3.416932173661655, 1.2292621844270586, 1.2292621844270586, 0.9167379002506877, 1.729301039109252, 3.6669516010027516  …  4.729534167202412, 4.417009883026042, 2.2293398937914453, 1.1667573275917844, 0.41669904556849446, 1.2292621844270588, 3.1669127463205577, 4.729534167202412, 2.1668350369561713, 0.7292233297448653]), DFTK.RealSpaceMultiplication{Float64, Array{Float64, 3}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), [-0.4126794111540609 -0.4867518928985729 … -0.7029483047073053 -0.486751892898573; -0.4867518928985727 -0.7746786056704886 … -0.41362748195299476 -0.38216253112939974; … ; -0.7029483047073055 -0.41362748195299504 … -2.3974847303307936 -1.296394873589905; -0.48675189289857257 -0.38216253112939963 … -1.2963948735899051 -0.7746786056704885;;; -0.4867518928985728 -0.7746786056704886 … -0.41362748195299487 -0.3821625311294; -0.7746786056704884 -1.4821229542312908 … -0.3245117740242638 -0.4498822038404775; … ; -0.413627481952995 -0.3245117740242643 … -1.0118029986478019 -0.6375633639205192; -0.3821625311293995 -0.4498822038404775 … -0.6375633639205189 -0.44988220384047745;;; -0.7029483047073054 -1.2963948735899056 … -0.29816359177354845 -0.41362748195299515; -1.2963948735899051 -2.9205770326768685 … -0.35377507009429643 -0.6375633639205192; … ; -0.29816359177354845 -0.3537750700942971 … -0.4905754361235721 -0.35377507009429693; -0.41362748195299487 -0.6375633639205192 … -0.3537750700942962 -0.3245117740242639;;; … ;;; -1.0171080921509945 -0.5334707126581325 … -3.6366084936610417 -1.9993716111178503; -0.5334707126581322 -0.32177106438851966 … -1.4671060669078932 -0.9065710192256414; … ; -3.6366084936610417 -1.4671060669078932 … -10.988646897799113 -8.087874284552477; -1.9993716111178501 -0.9065710192256414 … -8.087874284552477 -4.648575275488317;;; -0.7029483047073053 -0.4136274819529948 … -2.3974847303307936 -1.2963948735899051; -0.41362748195299476 -0.32451177402426407 … -1.0118029986478019 -0.6375633639205192; … ; -2.397484730330794 -1.011802998647802 … -11.003275264208218 -6.078138235516691; -1.296394873589905 -0.6375633639205189 … -6.078138235516691 -2.920577032676868;;; -0.48675189289857285 -0.3821625311293999 … -1.2963948735899051 -0.7746786056704886; -0.38216253112939963 -0.4498822038404775 … -0.6375633639205189 -0.4498822038404775; … ; -1.2963948735899051 -0.6375633639205192 … -6.07813823551669 -2.9205770326768676; -0.7746786056704882 -0.44988220384047733 … -2.9205770326768676 -1.4821229542312908]), DFTK.NonlocalOperator{Float64, Matrix{ComplexF64}, Matrix{Float64}}(PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), KPoint([-0.333,  0.333,      0], spin = 1, num. G vectors =   142), ComplexF64[0.10836454158744746 + 0.0im 0.16454392299317003 + 0.0im … -0.0 - 1.0216068167279948e-18im 0.0 + 0.03680726463308285im; 0.0757741533540503 - 0.0757741533540503im 0.1141835519100639 - 0.1141835519100639im … -0.03847188688271061 + 0.03847188688271061im 0.012823962294236874 - 0.012823962294236874im; … ; -0.07579695351601741 + 0.0im -0.08711072462387971 + 0.0im … 0.0 + 0.06907686686237845im 0.0 - 0.02302562228745948im; -0.0692966484992815 + 0.0692966484992815im -0.09802716364420207 + 0.09802716364420207im … -0.03421471645670587 + 0.03421471645670587im -0.011404905485568627 + 0.011404905485568627im], [5.90692831 -1.26189397 … 0.0 0.0; -1.26189397 3.25819622 … 0.0 0.0; … ; 0.0 0.0 … 2.72701346 0.0; 0.0 0.0 … 0.0 2.72701346]), nothing, (ψ_reals = Array{ComplexF64, 3}[[0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; … ;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im;;; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; … ; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im; 0.0 + 0.0im 0.0 + 0.0im … 0.0 + 0.0im 0.0 + 0.0im]],))]), basis = PlaneWaveBasis(model = Model(lda_x+lda_c_pw, spin_polarization = :none), Ecut = 5.0 Ha, kgrid = [3, 3, 3]), energies = Energies(total = -7.852328456917065), converged = true, occupation_threshold = 1.0e-6, ρ = [0.0920495156560242 0.0881175096600935 … 0.07724577112271185 0.0881175096600935; 0.0881175096600935 0.0814166519408628 … 0.0768565526396431 0.08547754607051947; … ; 0.07724577112271182 0.0768565526396431 … 0.047758951813577 0.06611332471781527; 0.0881175096600935 0.08547754607051947 … 0.06611332471781527 0.08141665194086281;;; 0.08811750966009352 0.0814166519408628 … 0.0768565526396431 0.08547754607051947; 0.0814166519408628 0.06780898306153302 … 0.07391037380997144 0.08216604762574431; … ; 0.07685655263964308 0.07391037380997144 … 0.061907432817789446 0.07289161378092368; 0.08547754607051944 0.08216604762574431 … 0.07289161378092368 0.08216604762574431;;; 0.07724577112271185 0.06611332471781527 … 0.06882462791851619 0.07685655263964311; 0.06611332471781527 0.04667885456152749 … 0.06694021471466098 0.0728916137809237; … ; 0.06882462791851618 0.06694021471466098 … 0.061402183254199785 0.06694021471466097; 0.0768565526396431 0.0728916137809237 … 0.06694021471466098 0.07391037380997144;;; … ;;; 0.06333961864006743 0.0660640219180881 … 0.033703025446653996 0.04978828400708409; 0.0660640219180881 0.06320458628448562 … 0.049475597812279615 0.06083472228903816; … ; 0.03370302544665398 0.049475597812279615 … 0.009595056908273829 0.01668607116757396; 0.04978828400708408 0.06083472228903816 … 0.016686071167573955 0.030864557817533358;;; 0.07724577112271185 0.0768565526396431 … 0.04775895181357699 0.06611332471781528; 0.0768565526396431 0.07391037380997142 … 0.061907432817789446 0.0728916137809237; … ; 0.047758951813576984 0.061907432817789446 … 0.00959505690827384 0.025644255931794986; 0.06611332471781525 0.07289161378092371 … 0.02564425593179499 0.04667885456152751;;; 0.0881175096600935 0.08547754607051945 … 0.06611332471781527 0.08141665194086281; 0.08547754607051945 0.0821660476257443 … 0.07289161378092368 0.08216604762574432; … ; 0.06611332471781525 0.07289161378092368 … 0.02564425593179499 0.0466788545615275; 0.0814166519408628 0.08216604762574432 … 0.0466788545615275 0.06780898306153303;;;;], α = 0.8, eigenvalues = [[-0.16689782644047324, 0.2643159694204391, 0.2643325800018151, 0.264371086998889, 0.3573419116058391, 0.3573441521945637, 0.3576209520025845], [-0.11620211049399586, 0.07030474177299344, 0.22627226988815372, 0.2262728600502361, 0.33637014477450244, 0.3933540560951479, 0.3933671677548217], [-0.09595851181345064, 0.08789157735121994, 0.17297338938144052, 0.17300018585446514, 0.29147257078085415, 0.3373040816572012, 0.5340068166873877], [-0.04495194017335516, 0.02236497574519555, 0.09784329248401565, 0.18445817827277294, 0.3248031647959163, 0.5030834102905085, 0.5067496847507762]], occupation = [[2.0, 2.0, 2.0, 2.0, 0.0, 0.0, 0.0], [2.0, 2.0, 2.0, 2.0, 0.0, 0.0, 0.0], [2.0, 2.0, 2.0, 2.0, 0.0, 0.0, 0.0], [2.0, 2.0, 2.0, 2.0, 0.0, 0.0, 0.0]], εF = 0.2900219028560186, n_iter = 2, n_ep_extra = 3, ψ = Matrix{ComplexF64}[[0.7881981218377464 + 0.54160573452203im 3.6113119303615216e-5 + 8.598567558635616e-5im … -5.8131763014578606e-5 + 4.615686326684516e-5im 0.00021375860805835593 - 0.0001984341159793888im; 0.07892032694884801 + 0.05397067339661399im 0.0871069141504575 - 0.23419705974182034im … -0.36144085253187175 - 0.16370954534063897im 0.09969076180919284 + 0.17969975063568136im; … ; 0.009080677957668875 + 0.006313719279539574im -0.015337870753504512 + 0.011564098386122823im … -0.037244357992847886 - 0.02058923938731761im 0.010704307982698856 - 0.016002451306296562im; -0.07873019969754566 - 0.05395527943505231im -0.06203351629196083 - 0.12133529748593629im … 0.05440250680709672 - 0.0067431248016980635im -0.01935693381668911 - 0.31534003394121557im], [-0.09787452320469162 - 0.9242519241606357im -0.05184807712587567 + 0.18961138728995938im … -5.60009446218425e-6 + 6.725321425194832e-5im 2.155812591758681e-5 - 2.594605676516242e-5im; -0.0065934410587283575 - 0.06222052525780338im 0.0029645171040498276 - 0.01102004883435065im … 0.00013229816109871123 + 0.00011111781048430565im 0.0004393565434210774 - 0.00017340386556140785im; … ; -0.0008277682736502836 - 0.007936616012087663im -0.022578289736483615 + 0.08262354006258553im … -0.05082928300885793 + 0.0240378121957455im 0.08880347958969047 - 0.0017991501240844639im; 0.01181365730212787 + 0.11166182446884176im 0.023385687190751916 - 0.08558018190847158im … -0.2252657488048014 + 0.10694093115149249im 0.3920195535614653 - 0.007881599407161816im], [0.8792188330712678 - 0.3166505395363437im 7.430491542400502e-5 - 7.338821216596809e-5im … 0.0006597737246218705 - 0.0005326231533659212im 7.682478881875659e-5 - 1.730762233202851e-7im; 0.06334387446873944 - 0.022818881687326712im 0.03855560610099889 - 0.04533096744945065im … 0.00719609621744691 - 0.004798792757501199im -0.0018809007408566209 + 0.0046133619013863664im; … ; 0.01366397076554213 - 0.004906518263019535im -5.275327554090509e-5 + 5.714881450380807e-5im … -0.005195970983481392 + 0.0036072051205219965im -0.044358079857398154 + 0.04783731692891134im; -0.1432003106779094 + 0.05157608855432317im 0.18577330947837262 - 0.21827682013870808im … -0.3128499848864874 + 0.2178904695104014im -0.1017080212107101 + 0.10851049528587532im], [-0.27375176083605757 + 0.7618408587657299im 3.924678824819837e-5 + 0.00013774517138510353im … 0.0026336094104972858 + 0.007007276049662258im -0.0715430330399434 - 0.2131734415219493im; -0.13095986912221702 + 0.36449409838431485im 0.21320260834375154 + 0.589946754463161im … -0.0027795612550057048 - 0.007044170904984991im 0.06923784688493462 + 0.20459926825144212im; … ; -0.0038280888010029076 + 0.010639613490984095im 0.00045494774835185263 + 0.0012887135557300092im … 0.0022008526368437215 + 0.04595804631690827im -0.004661452898798752 - 0.01206532665870967im; 0.021629254865559017 - 0.06023731431217379im 0.004572534650586915 + 0.012687518660843077im … 0.026067136403990908 + 0.5038825966828455im -0.1401654497881309 - 0.4083553843542853im]], diagonalization = NamedTuple{(:λ, :X, :residual_norms, :iterations, :converged, :n_matvec), Tuple{Vector{Vector{Float64}}, Vector{Matrix{ComplexF64}}, Vector{Vector{Float64}}, Vector{Int64}, Bool, Int64}}[(λ = [[-0.16689782644047324, 0.2643159694204391, 0.2643325800018151, 0.264371086998889, 0.3573419116058391, 0.3573441521945637, 0.3576209520025845], [-0.11620211049399586, 0.07030474177299344, 0.22627226988815372, 0.2262728600502361, 0.33637014477450244, 0.3933540560951479, 0.3933671677548217], [-0.09595851181345064, 0.08789157735121994, 0.17297338938144052, 0.17300018585446514, 0.29147257078085415, 0.3373040816572012, 0.5340068166873877], [-0.04495194017335516, 0.02236497574519555, 0.09784329248401565, 0.18445817827277294, 0.3248031647959163, 0.5030834102905085, 0.5067496847507762]], X = [[0.7881981218377464 + 0.54160573452203im 3.6113119303615216e-5 + 8.598567558635616e-5im … -5.8131763014578606e-5 + 4.615686326684516e-5im 0.00021375860805835593 - 0.0001984341159793888im; 0.07892032694884801 + 0.05397067339661399im 0.0871069141504575 - 0.23419705974182034im … -0.36144085253187175 - 0.16370954534063897im 0.09969076180919284 + 0.17969975063568136im; … ; 0.009080677957668875 + 0.006313719279539574im -0.015337870753504512 + 0.011564098386122823im … -0.037244357992847886 - 0.02058923938731761im 0.010704307982698856 - 0.016002451306296562im; -0.07873019969754566 - 0.05395527943505231im -0.06203351629196083 - 0.12133529748593629im … 0.05440250680709672 - 0.0067431248016980635im -0.01935693381668911 - 0.31534003394121557im], [-0.09787452320469162 - 0.9242519241606357im -0.05184807712587567 + 0.18961138728995938im … -5.60009446218425e-6 + 6.725321425194832e-5im 2.155812591758681e-5 - 2.594605676516242e-5im; -0.0065934410587283575 - 0.06222052525780338im 0.0029645171040498276 - 0.01102004883435065im … 0.00013229816109871123 + 0.00011111781048430565im 0.0004393565434210774 - 0.00017340386556140785im; … ; -0.0008277682736502836 - 0.007936616012087663im -0.022578289736483615 + 0.08262354006258553im … -0.05082928300885793 + 0.0240378121957455im 0.08880347958969047 - 0.0017991501240844639im; 0.01181365730212787 + 0.11166182446884176im 0.023385687190751916 - 0.08558018190847158im … -0.2252657488048014 + 0.10694093115149249im 0.3920195535614653 - 0.007881599407161816im], [0.8792188330712678 - 0.3166505395363437im 7.430491542400502e-5 - 7.338821216596809e-5im … 0.0006597737246218705 - 0.0005326231533659212im 7.682478881875659e-5 - 1.730762233202851e-7im; 0.06334387446873944 - 0.022818881687326712im 0.03855560610099889 - 0.04533096744945065im … 0.00719609621744691 - 0.004798792757501199im -0.0018809007408566209 + 0.0046133619013863664im; … ; 0.01366397076554213 - 0.004906518263019535im -5.275327554090509e-5 + 5.714881450380807e-5im … -0.005195970983481392 + 0.0036072051205219965im -0.044358079857398154 + 0.04783731692891134im; -0.1432003106779094 + 0.05157608855432317im 0.18577330947837262 - 0.21827682013870808im … -0.3128499848864874 + 0.2178904695104014im -0.1017080212107101 + 0.10851049528587532im], [-0.27375176083605757 + 0.7618408587657299im 3.924678824819837e-5 + 0.00013774517138510353im … 0.0026336094104972858 + 0.007007276049662258im -0.0715430330399434 - 0.2131734415219493im; -0.13095986912221702 + 0.36449409838431485im 0.21320260834375154 + 0.589946754463161im … -0.0027795612550057048 - 0.007044170904984991im 0.06923784688493462 + 0.20459926825144212im; … ; -0.0038280888010029076 + 0.010639613490984095im 0.00045494774835185263 + 0.0012887135557300092im … 0.0022008526368437215 + 0.04595804631690827im -0.004661452898798752 - 0.01206532665870967im; 0.021629254865559017 - 0.06023731431217379im 0.004572534650586915 + 0.012687518660843077im … 0.026067136403990908 + 0.5038825966828455im -0.1401654497881309 - 0.4083553843542853im]], residual_norms = [[0.01022517521944985, 0.005851765882501231, 0.008402864647199564, 0.00925381926768134, 0.0038431923236665637, 0.004215896910914291, 0.015865294045440945], [0.003978512460781444, 0.006606192063413894, 0.005895829279197241, 0.005982080215058053, 0.006755115930964504, 0.010707812963964839, 0.01121389728937602], [0.005897525065330269, 0.005765204887847177, 0.004530305601652122, 0.007291598431355004, 0.007575626007776496, 0.017914038507312834, 0.03076086020892194], [0.004950832735032369, 0.004883829133134035, 0.00833276915604035, 0.012487686693126205, 0.04153582782020897, 0.01852931474463993, 0.04845344478367099]], iterations = [1, 1, 1, 1], converged = 1, n_matvec = 56)], stage = :finalize, algorithm = "SCF", norm_Δρ = 0.0027314029698999676)

Remove the virtual orbitals (which Newton cannot treat yet)

In [6]:
ψ, _ = DFTK.select_occupied_orbitals(basis, scfres_start.ψ, scfres_start.occupation)
scfres_newton = newton(basis, ψ; tol)

# Comparison of results

println("|ρ_newton - ρ_scf|  = ", norm(scfres_newton.ρ - scfres_scf.ρ))
println("|ρ_newton - ρ_scfv| = ", norm(scfres_newton.ρ - scfres_scfv.ρ))
println("|ρ_newton - ρ_dm|   = ", norm(scfres_newton.ρ - scfres_dm.ρ))
n     Energy            log10(ΔE)   log10(Δρ)
---   ---------------   ---------   ---------
  1   -7.852646686711                   -2.54
  2   -7.852646686730      -10.72       -5.93
  3   -7.852646686730   +  -14.75      -12.66
|ρ_newton - ρ_scf|  = 2.6574363024722467e-13
|ρ_newton - ρ_scfv| = 5.4355464968945945e-14
|ρ_newton - ρ_dm|   = 3.5514212961804796e-10