In this example, we'll look at how to use various pseudopotential (PSP) formats in DFTK and discuss briefly the utility and importance of pseudopotentials.

Currently, DFTK supports norm-conserving (NC) PSPs in separable (Kleinman-Bylander) form. Two file formats can currently be read and used: analytical Hartwigsen-Goedecker-Hutter (HGH) PSPs and numeric Unified Pseudopotential Format (UPF) PSPs.

In brief, the pseudopotential approach replaces the all-electron atomic potential with an effective atomic potential. In this pseudopotential, tightly-bound core electrons are completely eliminated ("frozen") and chemically-active valence electron wavefunctions are replaced with smooth pseudo-wavefunctions whose Fourier representations decay quickly. Both these transformations aim at reducing the number of Fourier modes required to accurately represent the wavefunction of the system, greatly increasing computational efficiency.

Different PSP generation codes produce various file formats which contain the same general quantities required for pesudopotential evaluation. HGH PSPs are constructed from a fixed functional form based on Gaussians, and the files simply tablulate various coefficients fitted for a given element. UPF PSPs take a more flexible approach where the functional form used to generate the PSP is arbitrary, and the resulting functions are tabulated on a radial grid in the file. The UPF file format is documented on the Quantum Espresso Website.

In this example, we will compare the convergence of an analytical HGH PSP with a modern numeric norm-conserving PSP in UPF format from PseudoDojo. Then, we will compare the bandstructure at the converged parameters calculated using the two PSPs.

In [1]:

```
using DFTK
using Unitful
using Plots
using LazyArtifacts
import Main: @artifact_str # hide
```

`artifact`

strings which evaluate to a filepath on your local machine where the artifact has been
downloaded.

`load_psp`

, which determines the
file format using the file extension. The `artifact`

string literal resolves to the
directory where the file is stored by the Artifacts system. So, if you have your own
pseudopotential files, you can just provide the path to them as well.

In [2]:

```
psp_hgh = load_psp("hgh/lda/si-q4.hgh");
psp_upf = load_psp(artifact"pd_nc_sr_lda_standard_0.4.1_upf/Si.upf");
```

*harder*, i.e. it requires a higher energy cutoff, than the UPF PSP. In general,
numeric pseudopotentials tend to be softer than analytical pseudos because of the
flexibility of sampling arbitrary functions on a grid.

In [3]:

```
function run_bands(psp)
a = 10.26 # Silicon lattice constant in Bohr
lattice = a / 2 * [[0 1 1.];
[1 0 1.];
[1 1 0.]]
Si = ElementPsp(:Si; psp=psp)
atoms = [Si, Si]
positions = [ones(3)/8, -ones(3)/8]
# These are (as you saw above) completely unconverged parameters
model = model_LDA(lattice, atoms, positions; temperature=1e-2)
basis = PlaneWaveBasis(model; Ecut=12, kgrid=(4, 4, 4))
scfres = self_consistent_field(basis; tol=1e-4)
bandplot = plot_bandstructure(scfres)
(; scfres, bandplot)
end;
```

In [4]:

```
result_hgh = run_bands(psp_hgh)
result_hgh.scfres.energies
```

n Energy log10(ΔE) log10(Δρ) Diag Δtime --- --------------- --------- --------- ---- ------ 1 -7.920957479671 -0.69 5.8 2 -7.925542392116 -2.34 -1.22 1.8 255ms 3 -7.926171322515 -3.20 -2.43 2.6 310ms 4 -7.926189619175 -4.74 -3.03 3.9 353ms 5 -7.926189835143 -6.67 -4.18 2.4 293ms Computing bands along kpath: Γ -> X -> U and K -> Γ -> L -> W -> X Diagonalising Hamiltonian kblocks: 100%|████████████████| Time: 0:00:09

Out[4]:

Energy breakdown (in Ha): Kinetic 3.1590147 AtomicLocal -2.1424946 AtomicNonlocal 1.6043334 Ewald -8.4004648 PspCorrection -0.2948928 Hartree 0.5515699 Xc -2.4000934 Entropy -0.0031621 total -7.926189835143

In [5]:

```
result_upf = run_bands(psp_upf)
result_upf.scfres.energies
```

n Energy log10(ΔE) log10(Δρ) Diag Δtime --- --------------- --------- --------- ---- ------ 1 -8.515349267300 -0.93 6.0 2 -8.518471659081 -2.51 -1.44 1.5 250ms 3 -8.518846413170 -3.43 -2.78 3.2 329ms 4 -8.518860720679 -4.84 -3.19 4.6 422ms 5 -8.518860783871 -7.20 -3.52 2.2 271ms 6 -8.518860826649 -7.37 -4.82 1.4 257ms Computing bands along kpath: Γ -> X -> U and K -> Γ -> L -> W -> X Diagonalising Hamiltonian kblocks: 100%|████████████████| Time: 0:00:09

Out[5]:

Energy breakdown (in Ha): Kinetic 3.0954179 AtomicLocal -2.3650757 AtomicNonlocal 1.3082644 Ewald -8.4004648 PspCorrection 0.3951970 Hartree 0.5521859 Xc -3.1011662 Entropy -0.0032193 total -8.518860826649

In [6]:

```
plot(result_hgh.bandplot, result_upf.bandplot, titles=["HGH" "UPF"], size=(800, 400))
```

Out[6]: