{ "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 -1.743073529663 -1.29 4.2\n", " 2 -1.743506231352 -3.36 -1.70 1.8\n", " 3 -1.743614222787 -3.97 -2.88 5.7\n", " 4 -1.743616757979 -5.60 -3.72 3.8\n", " 5 -1.743616766428 -8.07 -4.62 3.5\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 1.998551763142325\n 1.9905522918941918\n 1.2449683567964902e-17\n 1.2448831302948839e-17\n 1.029141534947571e-17\n 1.0290539331961202e-17\n 2.9883123198645797e-19\n 1.6620889459003536e-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 0.7450594 \n AtomicLocal 0.3193157 \n AtomicNonlocal 0.3192821 \n Ewald -2.1544222\n PspCorrection -0.1026056\n Hartree 0.0061599 \n Xc -0.8615672\n Entropy -0.0148389\n\n total -1.743616766428" }, "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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