{ "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, 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, [:gga_x_pbe, :gga_c_pbe];\n", " 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 -1.743072243047 -1.28 5.3 100ms\n", " 2 -1.743503486472 -3.37 -1.70 1.7 6.77s\n", " 3 -1.743612126035 -3.96 -2.82 3.2 29.7ms\n", " 4 -1.743616703642 -5.34 -3.50 3.7 45.2ms\n", " 5 -1.743616747787 -7.36 -4.46 3.3 31.1ms\n", " 6 -1.743616749855 -8.68 -5.49 3.5 33.8ms\n", " 7 -1.743616749884 -10.54 -6.33 3.7 33.6ms\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 1.9985518378169551\n 1.9905514383699265\n 1.2449682717047486e-17\n 1.2448830469534801e-17\n 1.0289513111821057e-17\n 1.0288637222942354e-17\n 2.988414050240186e-19\n 1.6620944541971911e-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 0.3192775 \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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