{ "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 -1.761876145044 NaN 5.05e-02 4.7 \n", " 2 -1.762192994219 -3.17e-04 9.86e-03 1.0 \n", " 3 -1.762239585160 -4.66e-05 6.77e-04 3.0 \n", " 4 -1.762241612448 -2.03e-06 1.12e-04 3.7 \n", " 5 -1.762241620355 -7.91e-09 1.39e-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 1.999999999907795\n 1.9999975862950172\n 0.004016903744071185\n 3.000567472137584e-15\n 1.111545962358408e-18\n 1.111483508902833e-18\n 7.978004722915039e-19\n 7.977321548343777e-19\n 3.338352029476831e-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 0.7180655 \n AtomicLocal 0.3145401 \n AtomicNonlocal 0.3265738 \n Ewald -2.1544222\n PspCorrection -0.1026056\n Hartree 0.0055003 \n Xc -0.8610490\n Entropy -0.0088446\n\n total -1.762241620355\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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