{ "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": [ { "name": "stdout", "output_type": "stream", "text": [ "┌ Warning: Package DFTK does not have Plots in its dependencies:\n", "│ - If you have DFTK checked out for development and have\n", "│ added Plots as a dependency but haven't updated your primary\n", "│ environment's manifest file, try `Pkg.resolve()`.\n", "│ - Otherwise you may need to report an issue with DFTK\n", "│ Loading Plots into DFTK from project dependency, future warnings for DFTK are suppressed.\n", "└ @ nothing nothing:910\n" ] } ], "cell_type": "code", "source": [ "using DFTK\n", "using Plots\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 = 0.5 # 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 -1.761894613329 NaN 5.04e-02 4.3 \n", " 2 -1.762197253998 -3.03e-04 9.95e-03 1.0 \n", " 3 -1.762239787579 -4.25e-05 6.20e-04 3.3 \n", " 4 -1.762241614610 -1.83e-06 9.06e-05 3.3 \n", " 5 -1.762241620435 -5.83e-09 5.06e-06 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 Array{Float64,1}:\n 1.9999999999077942\n 1.9999975862811754\n 0.004016886437895969\n 3.0004490665129514e-15\n 1.1116050558837664e-18\n 1.1115082057009666e-18\n 7.978239727238142e-19\n 7.977452887952258e-19\n 3.047413457237301e-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 0.7180633 \n AtomicLocal 0.3145366 \n AtomicNonlocal 0.3265794 \n Ewald -2.1544222\n PspCorrection -0.1026056\n Hartree 0.0055002 \n Xc -0.8610487\n Entropy -0.0088446\n\n total -1.762241620435\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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