{
"cells": [
{
"cell_type": "markdown",
"source": [
"# Pseudopotentials\n",
"\n",
"In this example, we'll look at how to use various pseudopotential (PSP)\n",
"formats in DFTK and discuss briefly the utility and importance of\n",
"pseudopotentials.\n",
"\n",
"Currently, DFTK supports norm-conserving (NC) PSPs in\n",
"separable (Kleinman-Bylander) form. Two file formats can currently\n",
"be read and used: analytical Hartwigsen-Goedecker-Hutter (HGH) PSPs\n",
"and numeric Unified Pseudopotential Format (UPF) PSPs.\n",
"\n",
"In brief, the pseudopotential approach replaces the all-electron\n",
"atomic potential with an effective atomic potential. In this pseudopotential,\n",
"tightly-bound core electrons are completely eliminated (\"frozen\") and\n",
"chemically-active valence electron wavefunctions are replaced with\n",
"smooth pseudo-wavefunctions whose Fourier representations decay quickly.\n",
"Both these transformations aim at reducing the number of Fourier modes required\n",
"to accurately represent the wavefunction of the system, greatly increasing\n",
"computational efficiency.\n",
"\n",
"Different PSP generation codes produce various file formats which contain the\n",
"same general quantities required for pesudopotential evaluation. HGH PSPs\n",
"are constructed from a fixed functional form based on Gaussians, and the files\n",
"simply tablulate various coefficients fitted for a given element. UPF PSPs\n",
"take a more flexible approach where the functional form used to generate the\n",
"PSP is arbitrary, and the resulting functions are tabulated on a radial grid\n",
"in the file. The UPF file format is documented\n",
"[on the Quantum Espresso Website](http://pseudopotentials.quantum-espresso.org/home/unified-pseudopotential-format).\n",
"\n",
"In this example, we will compare the convergence of an analytical HGH PSP with\n",
"a modern numeric norm-conserving PSP in UPF format from\n",
"[PseudoDojo](http://www.pseudo-dojo.org/).\n",
"Then, we will compare the bandstructure at the converged parameters calculated\n",
"using the two PSPs."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"using DFTK\n",
"using Unitful\n",
"using Plots\n",
"using LazyArtifacts\n",
"import Main: @artifact_str # hide"
],
"metadata": {},
"execution_count": 1
},
{
"cell_type": "markdown",
"source": [
"Here, we will use a Perdew-Wang LDA PSP from [PseudoDojo](http://www.pseudo-dojo.org/),\n",
"which is available in the JuliaMolSim\n",
"[PseudoLibrary](https://github.com/JuliaMolSim/PseudoLibrary).\n",
"Directories in PseudoLibrary correspond to artifacts that you can load using `artifact`\n",
"strings which evaluate to a filepath on your local machine where the artifact has been\n",
"downloaded."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"We load the HGH and UPF PSPs using `load_psp`, which determines the\n",
"file format using the file extension. The `artifact` string literal resolves to the\n",
"directory where the file is stored by the Artifacts system. So, if you have your own\n",
"pseudopotential files, you can just provide the path to them as well."
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"┌ Warning: using Pkg instead of using LazyArtifacts is deprecated\n",
"│ caller = eval at boot.jl:370 [inlined]\n",
"└ @ Core ./boot.jl:370\n",
" Downloading artifact: pd_nc_sr_lda_standard_0.4.1_upf\n"
]
}
],
"cell_type": "code",
"source": [
"psp_hgh = load_psp(\"hgh/lda/si-q4.hgh\");\n",
"psp_upf = load_psp(artifact\"pd_nc_sr_lda_standard_0.4.1_upf/Si.upf\");"
],
"metadata": {},
"execution_count": 2
},
{
"cell_type": "markdown",
"source": [
"First, we'll take a look at the energy cutoff convergence of these two pseudopotentials.\n",
"For both pseudos, a reference energy is calculated with a cutoff of 140 Hartree, and\n",
"SCF calculations are run at increasing cutoffs until 1 meV / atom convergence is reached."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"![](\"https://docs.dftk.org/stable/assets/si_pseudos_ecut_convergence.png\")
"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"The converged cutoffs are 26 Ha and 18 Ha for the HGH\n",
"and UPF pseudos respectively. We see that the HGH pseudopotential\n",
"is much *harder*, i.e. it requires a higher energy cutoff, than the UPF PSP. In general,\n",
"numeric pseudopotentials tend to be softer than analytical pseudos because of the\n",
"flexibility of sampling arbitrary functions on a grid."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Next, to see that the different pseudopotentials give reasonbly similar results,\n",
"we'll look at the bandstructures calculated using the HGH and UPF PSPs. Even though\n",
"the convered cutoffs are higher, we perform these calculations with a cutoff of\n",
"12 Ha for both PSPs."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"function run_bands(psp)\n",
" a = 10.26 # Silicon lattice constant in Bohr\n",
" lattice = a / 2 * [[0 1 1.];\n",
" [1 0 1.];\n",
" [1 1 0.]]\n",
" Si = ElementPsp(:Si; psp=psp)\n",
" atoms = [Si, Si]\n",
" positions = [ones(3)/8, -ones(3)/8]\n",
"\n",
" # These are (as you saw above) completely unconverged parameters\n",
" model = model_LDA(lattice, atoms, positions; temperature=1e-2)\n",
" basis = PlaneWaveBasis(model; Ecut=12, kgrid=(4, 4, 4))\n",
"\n",
" scfres = self_consistent_field(basis; tol=1e-4)\n",
" bandplot = plot_bandstructure(scfres)\n",
" (; scfres, bandplot)\n",
"end;"
],
"metadata": {},
"execution_count": 3
},
{
"cell_type": "markdown",
"source": [
"The SCF and bandstructure calculations can then be performed using the two PSPs,\n",
"where we notice in particular the difference in total energies."
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"n Energy log10(ΔE) log10(Δρ) Diag Δtime\n",
"--- --------------- --------- --------- ---- ------\n",
" 1 -7.920957479671 -0.69 5.8 \n",
" 2 -7.925542392116 -2.34 -1.22 1.8 255ms\n",
" 3 -7.926171322515 -3.20 -2.43 2.6 310ms\n",
" 4 -7.926189619175 -4.74 -3.03 3.9 353ms\n",
" 5 -7.926189835143 -6.67 -4.18 2.4 293ms\n",
"Computing bands along kpath:\n",
" Γ -> X -> U and K -> Γ -> L -> W -> X\n",
"\rDiagonalising Hamiltonian kblocks: 2%|▎ | ETA: 0:00:18\u001b[K\rDiagonalising Hamiltonian kblocks: 4%|▋ | ETA: 0:00:14\u001b[K\rDiagonalising Hamiltonian kblocks: 6%|▉ | ETA: 0:00:12\u001b[K\rDiagonalising Hamiltonian kblocks: 7%|█▏ | ETA: 0:00:11\u001b[K\rDiagonalising Hamiltonian kblocks: 9%|█▌ | ETA: 0:00:10\u001b[K\rDiagonalising Hamiltonian kblocks: 11%|█▊ | ETA: 0:00:10\u001b[K\rDiagonalising Hamiltonian kblocks: 13%|██ | ETA: 0:00:09\u001b[K\rDiagonalising Hamiltonian kblocks: 15%|██▍ | ETA: 0:00:09\u001b[K\rDiagonalising Hamiltonian kblocks: 17%|██▋ | ETA: 0:00:09\u001b[K\rDiagonalising Hamiltonian kblocks: 18%|██▉ | ETA: 0:00:08\u001b[K\rDiagonalising Hamiltonian kblocks: 20%|███▎ | ETA: 0:00:08\u001b[K\rDiagonalising Hamiltonian kblocks: 22%|███▌ | ETA: 0:00:08\u001b[K\rDiagonalising Hamiltonian kblocks: 24%|███▉ | ETA: 0:00:07\u001b[K\rDiagonalising Hamiltonian kblocks: 26%|████▏ | ETA: 0:00:07\u001b[K\rDiagonalising Hamiltonian kblocks: 28%|████▍ | ETA: 0:00:07\u001b[K\rDiagonalising Hamiltonian kblocks: 29%|████▊ | ETA: 0:00:07\u001b[K\rDiagonalising Hamiltonian kblocks: 31%|█████ | ETA: 0:00:07\u001b[K\rDiagonalising Hamiltonian kblocks: 33%|█████▎ | ETA: 0:00:07\u001b[K\rDiagonalising Hamiltonian kblocks: 35%|█████▋ | ETA: 0:00:06\u001b[K\rDiagonalising Hamiltonian kblocks: 37%|█████▉ | ETA: 0:00:06\u001b[K\rDiagonalising Hamiltonian kblocks: 39%|██████▏ | ETA: 0:00:06\u001b[K\rDiagonalising Hamiltonian kblocks: 40%|██████▌ | ETA: 0:00:06\u001b[K\rDiagonalising Hamiltonian kblocks: 42%|██████▊ | ETA: 0:00:06\u001b[K\rDiagonalising Hamiltonian kblocks: 44%|███████ | ETA: 0:00:05\u001b[K\rDiagonalising Hamiltonian kblocks: 46%|███████▍ | ETA: 0:00:05\u001b[K\rDiagonalising Hamiltonian kblocks: 48%|███████▋ | ETA: 0:00:05\u001b[K\rDiagonalising Hamiltonian kblocks: 50%|███████▉ | ETA: 0:00:05\u001b[K\rDiagonalising Hamiltonian kblocks: 51%|████████▎ | ETA: 0:00:05\u001b[K\rDiagonalising Hamiltonian kblocks: 53%|████████▌ | ETA: 0:00:05\u001b[K\rDiagonalising Hamiltonian kblocks: 55%|████████▊ | ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks: 57%|█████████▏ | ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks: 59%|█████████▍ | ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks: 61%|█████████▊ | ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks: 62%|██████████ | ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks: 64%|██████████▎ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 66%|██████████▋ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 68%|██████████▉ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 70%|███████████▏ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 72%|███████████▌ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 73%|███████████▊ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 74%|███████████▉ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 76%|████████████▏ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 78%|████████████▌ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 80%|████████████▊ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 82%|█████████████▏ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 83%|█████████████▍ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 85%|█████████████▋ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 87%|██████████████ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 89%|██████████████▎ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 91%|██████████████▌ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 93%|██████████████▉ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 94%|███████████████▏| ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 96%|███████████████▍| ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 98%|███████████████▊| ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 100%|████████████████| Time: 0:00:09\u001b[K\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": "Energy breakdown (in Ha):\n Kinetic 3.1590147 \n AtomicLocal -2.1424946\n AtomicNonlocal 1.6043334 \n Ewald -8.4004648\n PspCorrection -0.2948928\n Hartree 0.5515699 \n Xc -2.4000934\n Entropy -0.0031621\n\n total -7.926189835143"
},
"metadata": {},
"execution_count": 4
}
],
"cell_type": "code",
"source": [
"result_hgh = run_bands(psp_hgh)\n",
"result_hgh.scfres.energies"
],
"metadata": {},
"execution_count": 4
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"n Energy log10(ΔE) log10(Δρ) Diag Δtime\n",
"--- --------------- --------- --------- ---- ------\n",
" 1 -8.515349267300 -0.93 6.0 \n",
" 2 -8.518471659081 -2.51 -1.44 1.5 250ms\n",
" 3 -8.518846413170 -3.43 -2.78 3.2 329ms\n",
" 4 -8.518860720679 -4.84 -3.19 4.6 422ms\n",
" 5 -8.518860783871 -7.20 -3.52 2.2 271ms\n",
" 6 -8.518860826649 -7.37 -4.82 1.4 257ms\n",
"Computing bands along kpath:\n",
" Γ -> X -> U and K -> Γ -> L -> W -> X\n",
"\rDiagonalising Hamiltonian kblocks: 2%|▎ | ETA: 0:00:20\u001b[K\rDiagonalising Hamiltonian kblocks: 4%|▋ | ETA: 0:00:15\u001b[K\rDiagonalising Hamiltonian kblocks: 6%|▉ | ETA: 0:00:13\u001b[K\rDiagonalising Hamiltonian kblocks: 6%|█ | ETA: 0:00:12\u001b[K\rDiagonalising Hamiltonian kblocks: 8%|█▍ | ETA: 0:00:11\u001b[K\rDiagonalising Hamiltonian kblocks: 10%|█▋ | ETA: 0:00:11\u001b[K\rDiagonalising Hamiltonian kblocks: 12%|█▉ | ETA: 0:00:10\u001b[K\rDiagonalising Hamiltonian kblocks: 13%|██ | ETA: 0:00:10\u001b[K\rDiagonalising Hamiltonian kblocks: 15%|██▍ | ETA: 0:00:10\u001b[K\rDiagonalising Hamiltonian kblocks: 17%|██▋ | ETA: 0:00:09\u001b[K\rDiagonalising Hamiltonian kblocks: 18%|██▉ | ETA: 0:00:09\u001b[K\rDiagonalising Hamiltonian kblocks: 20%|███▎ | ETA: 0:00:09\u001b[K\rDiagonalising Hamiltonian kblocks: 22%|███▌ | ETA: 0:00:08\u001b[K\rDiagonalising Hamiltonian kblocks: 24%|███▉ | ETA: 0:00:08\u001b[K\rDiagonalising Hamiltonian kblocks: 26%|████▏ | ETA: 0:00:08\u001b[K\rDiagonalising Hamiltonian kblocks: 28%|████▍ | ETA: 0:00:08\u001b[K\rDiagonalising Hamiltonian kblocks: 29%|████▊ | ETA: 0:00:07\u001b[K\rDiagonalising Hamiltonian kblocks: 31%|█████ | ETA: 0:00:07\u001b[K\rDiagonalising Hamiltonian kblocks: 33%|█████▎ | ETA: 0:00:07\u001b[K\rDiagonalising Hamiltonian kblocks: 35%|█████▋ | ETA: 0:00:07\u001b[K\rDiagonalising Hamiltonian kblocks: 37%|█████▉ | ETA: 0:00:07\u001b[K\rDiagonalising Hamiltonian kblocks: 39%|██████▏ | ETA: 0:00:06\u001b[K\rDiagonalising Hamiltonian kblocks: 40%|██████▌ | ETA: 0:00:06\u001b[K\rDiagonalising Hamiltonian kblocks: 42%|██████▊ | ETA: 0:00:06\u001b[K\rDiagonalising Hamiltonian kblocks: 44%|███████ | ETA: 0:00:06\u001b[K\rDiagonalising Hamiltonian kblocks: 46%|███████▍ | ETA: 0:00:06\u001b[K\rDiagonalising Hamiltonian kblocks: 47%|███████▌ | ETA: 0:00:05\u001b[K\rDiagonalising Hamiltonian kblocks: 49%|███████▊ | ETA: 0:00:05\u001b[K\rDiagonalising Hamiltonian kblocks: 50%|████████▏ | ETA: 0:00:05\u001b[K\rDiagonalising Hamiltonian kblocks: 52%|████████▍ | ETA: 0:00:05\u001b[K\rDiagonalising Hamiltonian kblocks: 53%|████████▌ | ETA: 0:00:05\u001b[K\rDiagonalising Hamiltonian kblocks: 55%|████████▊ | ETA: 0:00:05\u001b[K\rDiagonalising Hamiltonian kblocks: 57%|█████████▏ | ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks: 59%|█████████▍ | ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks: 61%|█████████▊ | ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks: 62%|██████████ | ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks: 64%|██████████▎ | ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks: 66%|██████████▋ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 68%|██████████▉ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 70%|███████████▏ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 72%|███████████▌ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 73%|███████████▊ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 74%|███████████▉ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 76%|████████████▏ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 78%|████████████▌ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 80%|████████████▊ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 82%|█████████████▏ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 83%|█████████████▍ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 85%|█████████████▋ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 87%|██████████████ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 89%|██████████████▎ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 91%|██████████████▌ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 93%|██████████████▉ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 94%|███████████████▏| ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 96%|███████████████▍| ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 98%|███████████████▊| ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 100%|████████████████| Time: 0:00:09\u001b[K\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": "Energy breakdown (in Ha):\n Kinetic 3.0954179 \n AtomicLocal -2.3650757\n AtomicNonlocal 1.3082644 \n Ewald -8.4004648\n PspCorrection 0.3951970 \n Hartree 0.5521859 \n Xc -3.1011662\n Entropy -0.0032193\n\n total -8.518860826649"
},
"metadata": {},
"execution_count": 5
}
],
"cell_type": "code",
"source": [
"result_upf = run_bands(psp_upf)\n",
"result_upf.scfres.energies"
],
"metadata": {},
"execution_count": 5
},
{
"cell_type": "markdown",
"source": [
"But while total energies are not physical and thus allowed to differ,\n",
"the bands (as an example for a physical quantity) are very similar for both pseudos:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=116}",
"image/png": 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",
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]
},
"metadata": {},
"execution_count": 6
}
],
"cell_type": "code",
"source": [
"plot(result_hgh.bandplot, result_upf.bandplot, titles=[\"HGH\" \"UPF\"], size=(800, 400))"
],
"metadata": {},
"execution_count": 6
}
],
"nbformat_minor": 3,
"metadata": {
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.9.0"
},
"kernelspec": {
"name": "julia-1.9",
"display_name": "Julia 1.9.0",
"language": "julia"
}
},
"nbformat": 4
}