{ "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 -1.743049206561 -1.28 4.5\n", " 2 -1.743508573912 -3.34 -1.70 2.2\n", " 3 -1.743614250565 -3.98 -2.86 4.0\n", " 4 -1.743616736389 -5.60 -3.62 4.0\n", " 5 -1.743616766065 -7.53 -4.50 3.0\n", " 6 -1.743616766633 -9.25 -5.36 3.7\n", " 7 -1.743616766645 -10.90 -6.65 3.2\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 1.9985518379590979\n 1.9905514318683495\n 1.2449683477421603e-17\n 1.2448831230215372e-17\n 1.028948307523417e-17\n 1.0288607188670483e-17\n 2.988420150176951e-19\n 1.6623009195159607e-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 -1.743616766645" }, "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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