{ "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 => [[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, [:gga_x_pbe, :gga_c_pbe];\n", " temperature=temperature,\n", " smearing=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 Free energy Eₙ-Eₙ₋₁ ρout-ρin α Diag\n", "--- --------------- --------- -------- ---- ----\n", " 1 -1.761861656702 NaN 5.05e-02 0.80 4.7\n", " 2 -1.762135813125 -2.74e-04 1.89e-02 0.80 1.0\n", " 3 -1.762239104077 -1.03e-04 1.53e-03 0.80 3.7\n", " 4 -1.762241583523 -2.48e-06 3.06e-04 0.80 2.7\n", " 5 -1.762241619938 -3.64e-08 1.86e-05 0.80 2.7\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 1.9999999999077946\n 1.9999975862950239\n 0.004016909834600165\n 3.0004366901408106e-15\n 1.1115722503194756e-18\n 1.1115080779620295e-18\n 7.978891575274669e-19\n 7.978268177428276e-19\n 3.340492423634927e-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 (in Ha):\n Kinetic 0.7180620 \n AtomicLocal 0.3145392 \n AtomicNonlocal 0.3265780 \n Ewald -2.1544222\n PspCorrection -0.1026056\n Hartree 0.0055001 \n Xc -0.8610486\n Entropy -0.0088446\n\n total -1.762241619938" }, "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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