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 here: http://pseudopotentials.quantum-espresso.org/home/unified-pseudopotential-format.

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

In [1]:

```
using DFTK
using Downloads
using Unitful
using Plots
```

Here, we will use Perdew-Wang LDA PSP from PseudoDojo, which is available in the JuliaMolSim PseudoLibrary.

In [2]:

```
PSEUDOLIB = "https://raw.githubusercontent.com/JuliaMolSim/PseudoLibrary"
COMMIT = "56d1774708e1adfff35d30a403004cb98de4224b"
URL_UPF = PSEUDOLIB * "/$COMMIT/pseudos/pd_nc_sr_lda_standard_04_upf/Li.upf";
```

We load the HGH and UPF PSPs using `load_psp`

, which determines the
file format using the file extension.

In [3]:

```
psp_hgh = load_psp("hgh/lda/li-q3.hgh");
path_upf = Downloads.download(URL_UPF, joinpath(tempdir(), "Li.upf"))
psp_upf = load_psp(path_upf);
```

First, we'll take a look at the energy cutoff convergence of these two pseudopotentials. For both pseudos, a reference energy is calculated with a cutoff of 140 Hartree, and SCF calculations are run at increasing cutoffs until 1 meV / atom convergence is reached.

The converged cutoffs are 128 Ha and 36 Ha for the HGH
and UPF pseudos respectively. We see that the HGH pseudopotential
is much *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.

Next, to see that the different pseudopotentials give reasonbly similar results, we'll look at the bandstructures calculated using the HGH and UPF PSPs. Even though the convered cutoffs are 128 and 36 Ha, we perform these calculations with a cutoff of 24 Ha for both PSPs.

In [4]:

```
function run_bands(psp)
a = -1.53877u"Å"
b = -2.66523u"Å"
c = -4.92295u"Å"
lattice = [ a a 0;
-b b 0;
0 0 -c]
Li = ElementPsp(:Li; psp)
atoms = [Li, Li]
positions = [[1/3, 2/3, 1/4],
[2/3, 1/3, 3/4]]
# These are (as you saw above) completely unconverged parameters
model = model_LDA(lattice, atoms, positions; temperature=1e-2)
basis = PlaneWaveBasis(model; Ecut=24, kgrid=(6, 6, 4))
scfres = self_consistent_field(basis, tol=1e-6)
bandplot = plot_bandstructure(scfres)
(; scfres, bandplot)
end;
```

The SCF and bandstructure calculations can then be performed using the two PSPs, where we notice in particular the difference in total energies.

In [5]:

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

Out[5]:

In [6]:

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

Out[6]:

But while total energies are not physical and thus allowed to differ, the bands (as an example for a physical quantity) are very similar for both pseudos:

In [7]:

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

Out[7]: