{
"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 -1.743059526826 -1.29 4.8 \n",
" 2 -1.743504537817 -3.35 -1.70 1.5 443ms\n",
" 3 -1.743614416307 -3.96 -2.85 4.7 48.5ms\n",
" 4 -1.743616731787 -5.64 -3.59 3.3 56.5ms\n",
" 5 -1.743616749057 -7.76 -4.46 4.0 42.5ms\n",
" 6 -1.743616749878 -9.09 -5.47 3.2 52.4ms\n",
" 7 -1.743616749884 -11.18 -6.30 4.0 43.6ms\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 1.998551837650251\n 1.9905514370429007\n 1.2449692643706322e-17\n 1.244884039586403e-17\n 1.0289499327103308e-17\n 1.028862343930247e-17\n 2.988419185261808e-19\n 1.6623728158508557e-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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",
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],
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"source": [
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],
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}
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