{ "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_maximal_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 Δtime\n", "--- --------------- --------- --------- ---- ------\n", " 1 -1.743079952325 -1.28 5.3 8.20s\n", " 2 -1.743507641537 -3.37 -1.70 1.7 6.77s\n", " 3 -1.743612393044 -3.98 -2.82 2.7 28.0ms\n", " 4 -1.743616696799 -5.37 -3.50 4.0 34.2ms\n", " 5 -1.743616747505 -7.29 -4.44 2.7 28.3ms\n", " 6 -1.743616749863 -8.63 -5.50 3.5 45.2ms\n", " 7 -1.743616749884 -10.66 -6.44 3.7 34.6ms\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 1.9985518373727085\n 1.9905514367978212\n 1.2449691148253852e-17\n 1.2448838900357101e-17\n 1.028951022328513e-17\n 1.0288634334839753e-17\n 2.988411674323372e-19\n 1.6623578968888655e-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 0.7450615 \n AtomicLocal 0.3193180 \n AtomicNonlocal 0.3192775 \n Ewald -2.1544222\n PspCorrection -0.1026056\n Hartree 0.0061603 \n Xc -0.8615676\n Entropy -0.0148387\n\n total -1.743616749884" }, "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.\n", "To get better plots, we decrease the k spacing a bit for this step" ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=2}", "image/png": 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", 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