v0.6.18/examples/pseudopotentials.ipynb

{
 "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\n",
    "[JuliaMolSim 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.\n",
    "\n",
    "!!! note \"Using the PseudoLibrary in your own calculations\"\n",
    "    Instructions for using the [PseudoLibrary](https://github.com/JuliaMolSim/PseudoLibrary)\n",
    "    in your own calculations can be found in its documentation."
   ],
   "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:385 [inlined]\n",
      "└ @ Core ./boot.jl:385\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": [
    "<img src=\"https://docs.dftk.org/stable/assets/si_pseudos_ecut_convergence.png\" width=600 height=400 />"
   ],
   "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)\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(compute_bands(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   -7.921038699554                   -0.69    5.8    453ms\n",
      "  2   -7.925547576200       -2.35       -1.22    1.8    213ms\n",
      "  3   -7.926172871958       -3.20       -2.42    2.9    574ms\n",
      "  4   -7.926189237389       -4.79       -3.04    3.2    333ms\n",
      "  5   -7.926189826841       -6.23       -4.08    2.5    531ms\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Energy breakdown (in Ha):\n    Kinetic             3.1589874 \n    AtomicLocal         -2.1423842\n    AtomicNonlocal      1.6042681 \n    Ewald               -8.4004648\n    PspCorrection       -0.2948928\n    Hartree             0.5515432 \n    Xc                  -2.4000842\n    Entropy             -0.0031626\n\n    total               -7.926189826841"
     },
     "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   -8.515485098741                   -0.93    6.0    1.18s\n",
      "  2   -8.518512950997       -2.52       -1.44    1.8    1.04s\n",
      "  3   -8.518865400549       -3.45       -2.83    3.1    297ms\n",
      "  4   -8.518884595936       -4.72       -3.20    4.4    368ms\n",
      "  5   -8.518884691770       -7.02       -3.53    2.0    233ms\n",
      "  6   -8.518884733365       -7.38       -4.59    1.5    213ms\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Energy breakdown (in Ha):\n    Kinetic             3.0954113 \n    AtomicLocal         -2.3650642\n    AtomicNonlocal      1.3082420 \n    Ewald               -8.4004648\n    PspCorrection       0.3951970 \n    Hartree             0.5521743 \n    Xc                  -3.1011608\n    Entropy             -0.0032195\n\n    total               -8.518884733365"
     },
     "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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     },
     "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
  }
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