{ "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 -1.743184626970 -1.28 4.7\n", " 2 -1.743515573385 -3.48 -1.70 1.3\n", " 3 -1.743614748314 -4.00 -2.87 3.8\n", " 4 -1.743616531603 -5.75 -3.61 4.0\n", " 5 -1.743616550785 -7.72 -4.68 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 1.9985518010235743\n 1.99055155427619\n 1.2448842166776565e-17\n 1.2447990153605369e-17\n 1.0291041641638486e-17\n 1.0290165852152987e-17\n 2.988479163500369e-19\n 1.6616815774633183e-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 0.7450657 \n AtomicLocal 0.3193265 \n AtomicNonlocal 0.3192652 \n Ewald -2.1544222\n PspCorrection -0.1026056\n Hartree 0.0061604 \n Xc -0.8615677\n Entropy -0.0148389\n\n total -1.743616550785" }, "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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