{ "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 Δtime\n", "--- --------------- --------- --------- ---- ------\n", " 1 -1.743049051026 -1.29 4.8 \n", " 2 -1.743502866351 -3.34 -1.70 1.5 747ms\n", " 3 -1.743614261457 -3.95 -2.84 4.7 58.2ms\n", " 4 -1.743616727737 -5.61 -3.54 3.5 55.1ms\n", " 5 -1.743616749011 -7.67 -4.48 3.2 48.4ms\n", " 6 -1.743616749881 -9.06 -5.44 3.5 118ms\n", " 7 -1.743616749884 -11.42 -6.27 3.5 51.8ms\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 1.998551837628499\n 1.9905514388804668\n 1.2449692693582234e-17\n 1.2448840445943245e-17\n 1.0289493739024323e-17\n 1.0288617851515235e-17\n 2.988419344165716e-19\n 1.6623746630872163e-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 0.7450614 \n AtomicLocal 0.3193178 \n AtomicNonlocal 0.3192778 \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." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=2}", "image/png": 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