{ "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", "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 -1.761887574360 NaN 5.04e-02 4.7 \n", " 2 -1.762194982709 -3.07e-04 9.90e-03 1.0 \n", " 3 -1.762239571128 -4.46e-05 6.48e-04 3.7 \n", " 4 -1.762241618458 -2.05e-06 1.01e-04 2.7 \n", " 5 -1.762241620310 -1.85e-09 1.48e-05 2.3 \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 1.9999975862958526\n 0.004016889344319704\n 3.0005331214502215e-15\n 1.1115532938244086e-18\n 1.1114723675357872e-18\n 7.978066056606978e-19\n 7.97745420859168e-19\n 3.3637364391321844e-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 0.7180660 \n AtomicLocal 0.3145422 \n AtomicNonlocal 0.3265713 \n Ewald -2.1544222\n PspCorrection -0.1026056\n Hartree 0.0055004 \n Xc -0.8610492\n Entropy -0.0088446\n\n total -1.762241620310\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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