{ "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_size_from_minimal_spacing(lattice, kspacing)\n", "basis = PlaneWaveBasis(model, Ecut, kgrid=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." ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n Free energy Eₙ-Eₙ₋₁ ρout-ρin Diag\n", "--- --------------- --------- -------- ----\n", " 1 -1.761874773713 NaN 5.05e-02 4.3 \n", " 2 -1.762193548127 -3.19e-04 9.85e-03 1.0 \n", " 3 -1.762239415455 -4.59e-05 6.59e-04 3.3 \n", " 4 -1.762241618385 -2.20e-06 1.01e-04 4.0 \n", " 5 -1.762241620267 -1.88e-09 1.40e-05 2.0 \n" ] } ], "cell_type": "code", "source": [ "scfres = self_consistent_field(basis);" ], "metadata": {}, "execution_count": 3 }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "9-element Array{Float64,1}:\n 1.9999999999077955\n 1.9999975862974597\n 0.0040168936933824345\n 3.0005329349330653e-15\n 1.1115502453242078e-18\n 1.1114778778170435e-18\n 7.978062534654398e-19\n 7.977469277846154e-19\n 3.2787344247217545e-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:\n Kinetic 0.7180665 \n AtomicLocal 0.3145422 \n AtomicNonlocal 0.3265708 \n Ewald -2.1544222\n PspCorrection -0.1026056\n Hartree 0.0055004 \n Xc -0.8610492\n Entropy -0.0088446\n\n total -1.762241620267\n" }, "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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