{ "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 -1.743044883519 -1.28 4.7\n", " 2 -1.743499279324 -3.34 -1.70 1.8\n", " 3 -1.743615595375 -3.93 -2.85 4.8\n", " 4 -1.743616745072 -5.94 -3.60 3.3\n", " 5 -1.743616766420 -7.67 -4.52 3.8\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 1.9985518227147887\n 1.990551878747947\n 1.2449503328127137e-17\n 1.2448651237179183e-17\n 1.0290805431711096e-17\n 1.0289929306335709e-17\n 2.9884423746658185e-19\n 1.6619247684051235e-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 0.7450607 \n AtomicLocal 0.3193165 \n AtomicNonlocal 0.3192799 \n Ewald -2.1544222\n PspCorrection -0.1026056\n Hartree 0.0061600 \n Xc -0.8615673\n Entropy -0.0148389\n\n total -1.743616766420" }, "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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