{ "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 PseudoPotentialData\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", "\n", "pseudopotentials = PseudoFamily(\"cp2k.nc.sr.pbe.v0_1.largecore.gth\")\n", "Mg = ElementPsp(:Mg, pseudopotentials)\n", "atoms = [Mg, Mg]\n", "positions = [[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", "smearing = DFTK.Smearing.FermiDirac() # Smearing method\n", "# also supported: Gaussian,\n", "# MarzariVanderbilt,\n", "# and MethfesselPaxton(order)\n", "\n", "model = model_DFT(lattice, atoms, positions;\n", " functionals=[:gga_x_pbe, :gga_c_pbe], temperature, smearing)\n", "kgrid = kgrid_from_maximal_spacing(lattice, kspacing)\n", "basis = PlaneWaveBasis(model; Ecut, 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. In this example we use a damping of `0.8`.\n", "The default `LdosMixing` should be suitable to converge metallic systems\n", "like the one we model here. For the sake of demonstration we still switch to\n", "Kerker mixing here." ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n Energy log10(ΔE) log10(Δρ) Diag Δtime\n", "--- --------------- --------- --------- ---- ------\n", " 1 -1.743305221934 -1.28 4.3 137ms\n", " 2 -1.743516449116 -3.68 -1.70 3.7 4.23s\n", " 3 -1.743614792589 -4.01 -2.87 2.7 53.0ms\n", " 4 -1.743616708476 -5.72 -3.61 4.2 35.3ms\n", " 5 -1.743616748257 -7.40 -4.60 3.3 41.4ms\n", " 6 -1.743616749864 -8.79 -5.66 3.8 35.0ms\n", " 7 -1.743616749884 -10.70 -6.48 3.5 36.4ms\n" ] } ], "cell_type": "code", "source": [ "scfres = self_consistent_field(basis, damping=0.8, mixing=KerkerMixing());" ], "metadata": {}, "execution_count": 3 }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "9-element Vector{Float64}:\n 1.9999999999941416\n 1.998551836677886\n 1.9905514403751718\n 1.244967715989789e-17\n 1.2448824913103517e-17\n 1.028948902703259e-17\n 1.0288613139926875e-17\n 2.988415858657389e-19\n 1.6623503621266896e-21" }, "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 (in Ha):\n Kinetic 0.7450615 \n AtomicLocal 0.3193180 \n AtomicNonlocal 0.3192776 \n Ewald -2.1544222\n PspCorrection -0.1026056\n Hartree 0.0061603 \n Xc -0.8615676\n Entropy -0.0148387\n\n total -1.743616749884" }, "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.\n", "To get better plots, we decrease the k spacing a bit for this step" ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=2}", "image/png": 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