{
"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 -1.743225503977 -1.28 4.5\n",
" 2 -1.743517469827 -3.53 -1.70 1.3\n",
" 3 -1.743614435999 -4.01 -2.87 4.3\n",
" 4 -1.743616747580 -5.64 -3.58 4.0\n",
" 5 -1.743616766150 -7.73 -4.65 2.8\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 1.9985517947848144\n 1.9905518746017383\n 1.2449884671656927e-17\n 1.24490317923418e-17\n 1.0291323084695533e-17\n 1.0290447110271313e-17\n 2.9881305818677216e-19\n 1.6610462012205432e-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 0.7450577 \n AtomicLocal 0.3193176 \n AtomicNonlocal 0.3192817 \n Ewald -2.1544222\n PspCorrection -0.1026056\n Hartree 0.0061601 \n Xc -0.8615672\n Entropy -0.0148389\n\n total -1.743616766150"
},
"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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