{ "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_minimal_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\n", "--- --------------- --------- --------- ----\n", " 1 -1.743142208488 -1.28 4.8\n", " 2 -1.743514411425 -3.43 -1.70 1.0\n", " 3 -1.743614724580 -4.00 -2.86 4.0\n", " 4 -1.743616747554 -5.69 -3.61 3.7\n", " 5 -1.743616766400 -7.72 -4.63 3.0\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 1.998551805242226\n 1.9905518661507005\n 1.2449374538499859e-17\n 1.2448522293121468e-17\n 1.0291274348041904e-17\n 1.029039835580624e-17\n 2.988364206861077e-19\n 1.6616281502463627e-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 0.7450601 \n AtomicLocal 0.3193192 \n AtomicNonlocal 0.3192779 \n Ewald -2.1544222\n PspCorrection -0.1026056\n Hartree 0.0061601 \n Xc -0.8615673\n Entropy -0.0148389\n\n total -1.743616766400" }, "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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