{ "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 -7.900412874619 -0.70 4.6 \n", " 2 -7.905008805049 -2.34 -1.52 1.0 1.69s\n", " 3 -7.905179138675 -3.77 -2.54 1.1 658ms\n", " 4 -7.905210677136 -4.50 -2.85 2.8 186ms\n", " 5 -7.905211133640 -6.34 -2.98 1.0 121ms\n", " 6 -7.905211518126 -6.42 -4.52 1.0 75.2ms\n", " 7 -7.905211531167 -7.88 -4.64 2.8 106ms\n", " 8 -7.905211531376 -9.68 -4.97 1.0 90.2ms\n", " 9 -7.905211531392 -10.78 -5.17 1.0 90.7ms\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 3.1020972 \n AtomicLocal -2.1987849\n AtomicNonlocal 1.7296088 \n Ewald -8.3979253\n PspCorrection -0.2946254\n Hartree 0.5530394 \n Xc -2.3986213\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 -0.0911691 … -0.101219 -0.023977 -0.0184079\n 0.261073 0.116915 0.00482513 0.0611644 -0.023977 -0.0184079\n 0.261073 0.23299 0.216734 0.121636 0.155532 0.117747\n 0.261073 0.23299 0.216734 0.212134 0.155532 0.117747\n 0.354532 0.335109 0.317102 0.350436 0.285692 0.417258\n 0.354532 0.389829 0.384601 … 0.436925 0.285692 0.4174\n 0.354532 0.389829 0.384601 0.449369 0.627583 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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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: 71%|███████████▍ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 96%|███████████████▍| ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 100%|████████████████| Time: 0:00:01\u001b[K\n" ] }, { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=44}", "image/png": 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"output_type": "execute_result", "data": { "text/plain": "2-element Vector{StaticArraysCore.SVector{3, Float64}}:\n [-5.263996241708808e-16, 3.823083543287027e-17, 1.3642689180449464e-16]\n [-5.323728882426328e-16, -1.7949456706303883e-17, -6.7595416621241e-16]" }, "metadata": {}, "execution_count": 8 } ], "cell_type": "code", "source": [ "compute_forces_cart(scfres)" ], "metadata": {}, "execution_count": 8 }, { "cell_type": "markdown", "source": [ "As expected, they are numerically zero in this highly symmetric configuration." ], "metadata": {} } ], "nbformat_minor": 3, "metadata": { "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.8.5" }, "kernelspec": { "name": "julia-1.8", "display_name": "Julia 1.8.5", "language": "julia" } }, "nbformat": 4 }