{ "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 Δtime\n", "--- --------------- --------- --------- ---- ------\n", " 1 -1.743010485383 -1.28 4.2 \n", " 2 -1.743500160639 -3.31 -1.70 2.2 853ms\n", " 3 -1.743614360971 -3.94 -2.85 4.0 120ms\n", " 4 -1.743616719843 -5.63 -3.59 4.0 80.9ms\n", " 5 -1.743616748962 -7.54 -4.47 2.7 63.2ms\n", " 6 -1.743616749873 -9.04 -5.52 3.5 70.7ms\n", " 7 -1.743616749884 -10.94 -6.34 3.5 77.8ms\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 1.9985518377926916\n 1.9905514365071684\n 1.2449704697181232e-17\n 1.2448852448536812e-17\n 1.0289503416324069e-17\n 1.0288627528314845e-17\n 2.988417081383523e-19\n 1.6623593169006687e-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 0.7450614 \n AtomicLocal 0.3193179 \n AtomicNonlocal 0.3192777 \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." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=2}", "image/png": 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