{ "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 => [[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", "\n", "model = model_DFT(lattice, atoms, [:gga_x_pbe, :gga_c_pbe];\n", " temperature=temperature,\n", " smearing=DFTK.Smearing.FermiDirac())\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 Free energy Eₙ-Eₙ₋₁ ρout-ρin α Diag\n", "--- --------------- --------- -------- ---- ----\n", " 1 -1.761863228971 NaN 5.04e-02 0.80 5.0\n", " 2 -1.762131120436 -2.68e-04 1.90e-02 0.80 1.0\n", " 3 -1.762239245503 -1.08e-04 1.54e-03 0.80 3.3\n", " 4 -1.762241601121 -2.36e-06 2.68e-04 0.80 3.0\n", " 5 -1.762241620084 -1.90e-08 1.19e-05 0.80 3.3\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 1.9999999999077942\n 1.99999758628245\n 0.004016890348629518\n 3.000430734635272e-15\n 1.1115954691347064e-18\n 1.1115064433247001e-18\n 7.978712841765931e-19\n 7.977850104495862e-19\n 3.288177493497056e-22" }, "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 0.7180610 \n AtomicLocal 0.3145388 \n AtomicNonlocal 0.3265794 \n Ewald -2.1544222\n PspCorrection -0.1026056\n Hartree 0.0055003 \n Xc -0.8610487\n Entropy -0.0088446\n\n total -1.762241620084" }, "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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