{
"cells": [
{
"cell_type": "markdown",
"source": [
"# Tutorial"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"DFTK is a Julia package for playing with plane-wave\n",
"density-functional theory algorithms. In its basic formulation it\n",
"solves periodic Kohn-Sham equations.\n",
"\n",
"This document provides an overview of the structure of the code\n",
"and how to access basic information about calculations.\n",
"Basic familiarity with the concepts of plane-wave density functional theory\n",
"is assumed throughout. Feel free to take a look at the\n",
"[Periodic problems](https://docs.dftk.org/stable/guide/periodic_problems/)\n",
"or the\n",
"[Introductory resources](https://docs.dftk.org/stable/guide/introductory_resources/)\n",
"chapters for some introductory material on the topic.\n",
"\n",
"!!! note \"Convergence parameters in the documentation\"\n",
" We use rough parameters in order to be able\n",
" to automatically generate this documentation very quickly.\n",
" Therefore results are far from converged.\n",
" Tighter thresholds and larger grids should be used for more realistic results.\n",
"\n",
"For our discussion we will use the classic example of\n",
"computing the LDA ground state of the\n",
"[silicon crystal](https://www.materialsproject.org/materials/mp-149).\n",
"Performing such a calculation roughly proceeds in three steps."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"using DFTK\n",
"using Plots\n",
"using Unitful\n",
"using UnitfulAtomic\n",
"\n",
"# 1. Define lattice and atomic positions\n",
"a = 5.431u\"angstrom\" # Silicon lattice constant\n",
"lattice = a / 2 * [[0 1 1.]; # Silicon lattice vectors\n",
" [1 0 1.]; # specified column by column\n",
" [1 1 0.]];"
],
"metadata": {},
"execution_count": 1
},
{
"cell_type": "markdown",
"source": [
"By default, all numbers passed as arguments are assumed to be in atomic\n",
"units. Quantities such as temperature, energy cutoffs, lattice vectors, and\n",
"the k-point grid spacing can optionally be annotated with Unitful units,\n",
"which are automatically converted to the atomic units used internally. For\n",
"more details, see the [Unitful package\n",
"documentation](https://painterqubits.github.io/Unitful.jl/stable/) and the\n",
"[UnitfulAtomic.jl package](https://github.com/sostock/UnitfulAtomic.jl)."
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"n Energy log10(ΔE) log10(Δρ) Diag Δtime\n",
"--- --------------- --------- --------- ---- ------\n",
" 1 -7.900328215648 -0.70 4.8 \n",
" 2 -7.904980434930 -2.33 -1.52 1.0 562ms\n",
" 3 -7.905177404407 -3.71 -2.53 1.2 88.6ms\n",
" 4 -7.905210616659 -4.48 -2.85 2.9 60.3ms\n",
" 5 -7.905211180844 -6.25 -3.02 1.0 96.3ms\n",
" 6 -7.905211520457 -6.47 -4.67 1.0 50.0ms\n",
" 7 -7.905211531256 -7.97 -4.74 3.2 87.0ms\n",
" 8 -7.905211531392 -9.87 -5.27 1.0 81.9ms\n"
]
}
],
"cell_type": "code",
"source": [
"# Load HGH pseudopotential for Silicon\n",
"Si = ElementPsp(:Si, psp=load_psp(\"hgh/lda/Si-q4\"))\n",
"\n",
"# Specify type and positions of atoms\n",
"atoms = [Si, Si]\n",
"positions = [ones(3)/8, -ones(3)/8]\n",
"\n",
"# 2. Select model and basis\n",
"model = model_LDA(lattice, atoms, positions)\n",
"kgrid = [4, 4, 4] # k-point grid (Regular Monkhorst-Pack grid)\n",
"Ecut = 7 # kinetic energy cutoff\n",
"# Ecut = 190.5u\"eV\" # Could also use eV or other energy-compatible units\n",
"basis = PlaneWaveBasis(model; Ecut, kgrid)\n",
"# Note the implicit passing of keyword arguments here:\n",
"# this is equivalent to PlaneWaveBasis(model; Ecut=Ecut, kgrid=kgrid)\n",
"\n",
"# 3. Run the SCF procedure to obtain the ground state\n",
"scfres = self_consistent_field(basis, tol=1e-5);"
],
"metadata": {},
"execution_count": 2
},
{
"cell_type": "markdown",
"source": [
"That's it! Now you can get various quantities from the result of the SCF.\n",
"For instance, the different components of the energy:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Energy breakdown (in Ha):\n Kinetic 3.1020970 \n AtomicLocal -2.1987858\n AtomicNonlocal 1.7296098 \n Ewald -8.3979253\n PspCorrection -0.2946254\n Hartree 0.5530396 \n Xc -2.3986214\n\n total -7.905211531392"
},
"metadata": {},
"execution_count": 3
}
],
"cell_type": "code",
"source": [
"scfres.energies"
],
"metadata": {},
"execution_count": 3
},
{
"cell_type": "markdown",
"source": [
"Eigenvalues:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "7×8 Matrix{Float64}:\n -0.176942 -0.14744 -0.0911693 … -0.101219 -0.0239771 -0.018408\n 0.261073 0.116914 0.00482503 0.0611643 -0.0239771 -0.018408\n 0.261073 0.23299 0.216733 0.121636 0.155532 0.117747\n 0.261073 0.23299 0.216733 0.212134 0.155532 0.117747\n 0.354532 0.335109 0.317102 0.350436 0.285692 0.417258\n 0.354532 0.389828 0.384601 … 0.436925 0.285692 0.417338\n 0.354532 0.389828 0.384601 0.449226 0.62759 0.443806"
},
"metadata": {},
"execution_count": 4
}
],
"cell_type": "code",
"source": [
"hcat(scfres.eigenvalues...)"
],
"metadata": {},
"execution_count": 4
},
{
"cell_type": "markdown",
"source": [
"`eigenvalues` is an array (indexed by k-points) of arrays (indexed by\n",
"eigenvalue number). The \"splatting\" operation `...` calls `hcat`\n",
"with all the inner arrays as arguments, which collects them into a\n",
"matrix.\n",
"\n",
"The resulting matrix is 7 (number of computed eigenvalues) by 8\n",
"(number of irreducible k-points). There are 7 eigenvalues per\n",
"k-point because there are 4 occupied states in the system (4 valence\n",
"electrons per silicon atom, two atoms per unit cell, and paired\n",
"spins), and the eigensolver gives itself some breathing room by\n",
"computing some extra states (see the `bands` argument to\n",
"`self_consistent_field` as well as the `AdaptiveBands` documentation).\n",
"There are only 8 k-points (instead of 4x4x4) because symmetry has been used to reduce the\n",
"amount of computations to just the irreducible k-points (see\n",
"[Crystal symmetries](https://docs.dftk.org/stable/developer/symmetries/)\n",
"for details).\n",
"\n",
"We can check the occupations ..."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "7×8 Matrix{Float64}:\n 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0\n 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0\n 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0\n 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0\n 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0"
},
"metadata": {},
"execution_count": 5
}
],
"cell_type": "code",
"source": [
"hcat(scfres.occupation...)"
],
"metadata": {},
"execution_count": 5
},
{
"cell_type": "markdown",
"source": [
"... and density, where we use that the density objects in DFTK are\n",
"indexed as ρ[iσ, ix, iy, iz], i.e. first in the spin component and then\n",
"in the 3-dimensional real-space grid."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=1}",
"image/png": 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",
"text/html": [
"\n",
"\n"
],
"image/svg+xml": [
"\n",
"\n"
]
},
"metadata": {},
"execution_count": 6
}
],
"cell_type": "code",
"source": [
"rvecs = collect(r_vectors(basis))[:, 1, 1] # slice along the x axis\n",
"x = [r[1] for r in rvecs] # only keep the x coordinate\n",
"plot(x, scfres.ρ[1, :, 1, 1], label=\"\", xlabel=\"x\", ylabel=\"ρ\", marker=2)"
],
"metadata": {},
"execution_count": 6
},
{
"cell_type": "markdown",
"source": [
"We can also perform various postprocessing steps:\n",
"for instance compute a band structure"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Computing bands along kpath:\n",
" Γ -> X -> U and K -> Γ -> L -> W -> X\n",
"\rDiagonalising Hamiltonian kblocks: 14%|██▎ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 100%|████████████████| Time: 0:00:00\u001b[K\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=44}",
"image/png": 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",
"text/html": [
"\n",
"\n"
],
"image/svg+xml": [
"\n",
"\n"
]
},
"metadata": {},
"execution_count": 7
}
],
"cell_type": "code",
"source": [
"plot_bandstructure(scfres; kline_density=10)"
],
"metadata": {},
"execution_count": 7
},
{
"cell_type": "markdown",
"source": [
"or get the cartesian forces (in Hartree / Bohr)"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "2-element Vector{StaticArraysCore.SVector{3, Float64}}:\n [-1.0672937781901006e-15, 3.6277266993397825e-16, 7.150784072512087e-17]\n [3.547159801310774e-16, -7.752269333691469e-16, -6.542745759111475e-16]"
},
"metadata": {},
"execution_count": 8
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