{
"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",
"[density-functional theory](https://juliamolsim.github.io/DFTK.jl/dev/#density-functional-theory)\n",
"chapter for some introductory lectures and 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": [
{
"output_type": "execute_result",
"data": {
"text/plain": "3Γ3 Array{Unitful.Quantity{Float64,π,Unitful.FreeUnits{(β«,),π,nothing}},2}:\n 0.0 β« 2.7155 β« 2.7155 β«\n 2.7155 β« 0.0 β« 2.7155 β«\n 2.7155 β« 2.7155 β« 0.0 β«"
},
"metadata": {},
"execution_count": 1
}
],
"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 Eβ-Eβββ Οout-Οin Diag\n",
"--- --------------- --------- -------- ----\n",
" 1 -7.905200737325 NaN 1.95e-01 4.1 \n",
" 2 -7.909824273438 -4.62e-03 2.98e-02 1.0 \n",
" 3 -7.910016987690 -1.93e-04 3.01e-03 1.1 \n",
" 4 -7.910051885136 -3.49e-05 1.40e-03 2.4 \n",
" 5 -7.910052524646 -6.40e-07 8.78e-04 1.0 \n",
" 6 -7.910052843759 -3.19e-07 2.68e-05 1.0 \n",
" 7 -7.910052853852 -1.01e-08 1.98e-05 2.8 \n",
" 8 -7.910052854038 -1.85e-10 1.73e-06 1.0 \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 => [ones(3)/8, -ones(3)/8]]\n",
"\n",
"# 2. Select model and basis\n",
"model = model_LDA(lattice, atoms)\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=kgrid)\n",
"\n",
"# 3. Run the SCF procedure to obtain the ground state\n",
"scfres = self_consistent_field(basis, tol=1e-8);"
],
"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:\n Kinetic 3.0795129 \n AtomicLocal -2.1806335\n AtomicNonlocal 1.7339387 \n Ewald -8.3979253\n PspCorrection -0.2946254\n Hartree 0.5417556 \n Xc -2.3920758\n\n total -7.910052854038\n"
},
"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": "7Γ10 Array{Float64,2}:\n -0.170182 -0.1318 -0.0883279 β¦ -0.0562604 -0.11494 -0.0700168\n 0.201344 0.0909038 0.0122924 0.0111146 0.042062 0.0176503\n 0.249295 0.174773 0.176137 0.132964 0.220114 0.11233\n 0.249295 0.231428 0.20237 0.161043 0.220114 0.190456\n 0.350986 0.360027 0.340134 0.291807 0.320726 0.327376\n 0.36997 0.395898 0.389483 β¦ 0.331814 0.38819 0.460264\n 0.369972 0.401676 0.412475 0.565561 0.38819 0.46272"
},
"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 kpoints) 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 kpoints). There are 7 eigenvalues per kpoint because\n",
"there are 4 occupied states in the system (4 valence electrons per\n",
"silicon atom, two atoms per unit cell, and paired spins), and the\n",
"eigensolver gives itself some breathing room by computing some extra\n",
"states (see `n_ep_extra` argument to `self_consistent_field`).\n",
"\n",
"We can check the occupations:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "7Γ10 Array{Float64,2}:\n 2.0 2.0 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 2.0 2.0\n 2.0 2.0 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 2.0 2.0\n 0.0 0.0 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 0.0 0.0\n 0.0 0.0 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:"
],
"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.Ο.real[:, 1, 1], label=\"\", xlabel=\"x\", ylabel=\"Ο\", 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",
" Ξ -> X -> W -> K -> Ξ -> L -> U -> W -> L -> K and U -> X\n",
"\rDiagonalising Hamiltonian kblocks: 7%|ββ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 13%|βββ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 28%|βββββ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 41%|βββββββ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 52%|βββββββββ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 65%|βββββββββββ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 80%|βββββββββββββ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 93%|βββββββββββββββ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 100%|ββββββββββββββββ| Time: 0:00:01\u001b[K\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=210}",
"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=5, unit=:eV)"
],
"metadata": {},
"execution_count": 7
},
{
"cell_type": "markdown",
"source": [
"or get the cartesian forces (in Hartree / Bohr)"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"β Warning: Forces for shifted k-Grids not tested\n",
"β @ DFTK /home/runner/work/DFTK.jl/DFTK.jl/src/terms/terms.jl:72\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": "2-element Array{StaticArrays.SArray{Tuple{3},Float64,1,3},1}:\n [0.00044923268336198737, 0.0004492233350269446, 0.0004492266109820147]\n [-0.00044922333502729324, -0.0004492326833618144, -0.000449226610981862]"
},
"metadata": {},
"execution_count": 8
}
],
"cell_type": "code",
"source": [
"compute_forces_cart(scfres)[1] # Select silicon forces"
],
"metadata": {},
"execution_count": 8
},
{
"cell_type": "markdown",
"source": [
"The `[1]` extracts the forces for the first kind of atoms,\n",
"i.e. `Si` (silicon) in the setup of the `atoms` list of step 1 above.\n",
"As expected, they are almost zero in this highly symmetric configuration."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Where to go from here\n",
"Take a look at the\n",
"[example index](https://juliamolsim.github.io/DFTK.jl/dev/#example-index-1)\n",
"to continue exploring DFTK."
],
"metadata": {}
}
],
"nbformat_minor": 3,
"metadata": {
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.5.3"
},
"kernelspec": {
"name": "julia-1.5",
"display_name": "Julia 1.5.3",
"language": "julia"
}
},
"nbformat": 4
}