{ "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 -1.761831553939 NaN 5.05e-02 4.3 \n", " 2 -1.762191574256 -3.60e-04 9.83e-03 1.0 \n", " 3 -1.762239770074 -4.82e-05 6.74e-04 3.3 \n", " 4 -1.762241610160 -1.84e-06 1.01e-04 3.7 \n", " 5 -1.762241620334 -1.02e-08 1.44e-05 2.7 \n" ] } ], "cell_type": "code", "source": [ "scfres = self_consistent_field(basis);" ], "metadata": {}, "execution_count": 3 }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "9-element Vector{Float64}:\n 1.9999999999077955\n 1.9999975862981583\n 0.004016900060441794\n 3.0005471313076264e-15\n 1.1115596383986611e-18\n 1.1114805096537376e-18\n 7.978124995914052e-19\n 7.977408584736506e-19\n 3.3629793703030756e-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 0.7180647 \n AtomicLocal 0.3145395 \n AtomicNonlocal 0.3265751 \n Ewald -2.1544222\n PspCorrection -0.1026056\n Hartree 0.0055003 \n Xc -0.8610490\n Entropy -0.0088446\n\n total -1.762241620334\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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