{ "cells": [ { "cell_type": "markdown", "source": [ "# Temperature and metallic systems\n", "\n", "In this example we consider the modeling of a magnesium lattice\n", "as a simple example for a metallic system.\n", "For our treatment we will use the PBE exchange-correlation functional.\n", "First we import required packages and setup the lattice.\n", "Again notice that DFTK uses the convention that lattice vectors are\n", "specified column by column." ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "using DFTK\n", "using Plots\n", "using Unitful\n", "using UnitfulAtomic\n", "\n", "a = 3.01794 # bohr\n", "b = 5.22722 # bohr\n", "c = 9.77362 # bohr\n", "lattice = [[-a -a 0]; [-b b 0]; [0 0 -c]]\n", "Mg = ElementPsp(:Mg, psp=load_psp(\"hgh/pbe/Mg-q2\"))\n", "atoms = [Mg, Mg]\n", "positions = [[2/3, 1/3, 1/4], [1/3, 2/3, 3/4]];" ], "metadata": {}, "execution_count": 1 }, { "cell_type": "markdown", "source": [ "Next we build the PBE model and discretize it.\n", "Since magnesium is a metal we apply a small smearing\n", "temperature to ease convergence using the Fermi-Dirac\n", "smearing scheme. Note that both the `Ecut` is too small\n", "as well as the minimal ``k``-point spacing\n", "`kspacing` far too large to give a converged result.\n", "These have been selected to obtain a fast execution time.\n", "By default `PlaneWaveBasis` chooses a `kspacing`\n", "of `2π * 0.022` inverse Bohrs, which is much more reasonable." ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "kspacing = 0.945 / u\"angstrom\" # Minimal spacing of k-points,\n", "# in units of wavevectors (inverse Bohrs)\n", "Ecut = 5 # Kinetic energy cutoff in Hartree\n", "temperature = 0.01 # Smearing temperature in Hartree\n", "smearing = DFTK.Smearing.FermiDirac() # Smearing method\n", "# also supported: Gaussian,\n", "# MarzariVanderbilt,\n", "# and MethfesselPaxton(order)\n", "\n", "model = model_DFT(lattice, atoms, positions, [:gga_x_pbe, :gga_c_pbe];\n", " temperature, smearing)\n", "kgrid = kgrid_from_minimal_spacing(lattice, kspacing)\n", "basis = PlaneWaveBasis(model; Ecut, kgrid);" ], "metadata": {}, "execution_count": 2 }, { "cell_type": "markdown", "source": [ "Finally we run the SCF. Two magnesium atoms in\n", "our pseudopotential model result in four valence electrons being explicitly\n", "treated. Nevertheless this SCF will solve for eight bands by default\n", "in order to capture partial occupations beyond the Fermi level due to\n", "the employed smearing scheme. In this example we use a damping of `0.8`.\n", "The default `LdosMixing` should be suitable to converge metallic systems\n", "like the one we model here. For the sake of demonstration we still switch to\n", "Kerker mixing here." ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n Energy log10(ΔE) log10(Δρ) Diag\n", "--- --------------- --------- --------- ----\n", " 1 -1.743172150905 -1.28 4.8\n", " 2 -1.743515026251 -3.46 -1.70 1.0\n", " 3 -1.743614826371 -4.00 -2.85 3.8\n", " 4 -1.743616747227 -5.72 -3.61 4.2\n", " 5 -1.743616766532 -7.71 -4.66 3.0\n" ] } ], "cell_type": "code", "source": [ "scfres = self_consistent_field(basis, damping=0.8, mixing=KerkerMixing());" ], "metadata": {}, "execution_count": 3 }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "9-element Vector{Float64}:\n 1.9999999999941416\n 1.9985518036249525\n 1.990551857486642\n 1.2449644589570761e-17\n 1.2448792382339425e-17\n 1.0291312867674198e-17\n 1.0290436896902567e-17\n 2.9882320851247925e-19\n 1.661683474585201e-21" }, "metadata": {}, "execution_count": 4 } ], "cell_type": "code", "source": [ "scfres.occupation[1]" ], "metadata": {}, "execution_count": 4 }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Energy breakdown (in Ha):\n Kinetic 0.7450605 \n AtomicLocal 0.3193192 \n AtomicNonlocal 0.3192775 \n Ewald -2.1544222\n PspCorrection -0.1026056\n Hartree 0.0061601 \n Xc -0.8615674\n Entropy -0.0148389\n\n total -1.743616766532" }, "metadata": {}, "execution_count": 5 } ], "cell_type": "code", "source": [ "scfres.energies" ], "metadata": {}, "execution_count": 5 }, { "cell_type": "markdown", "source": [ "The fact that magnesium is a metal is confirmed\n", "by plotting the density of states around the Fermi level." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=2}", "image/png": 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