{ "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 -7.900554246366 -0.70 4.6 2.48s\n", " 2 -7.905009594604 -2.35 -1.52 1.0 3.49s\n", " 3 -7.905178476053 -3.77 -2.52 1.1 53.7ms\n", " 4 -7.905210460349 -4.50 -2.83 2.8 47.8ms\n", " 5 -7.905211107704 -6.19 -2.99 1.0 23.0ms\n", " 6 -7.905211518427 -6.39 -4.53 1.0 22.8ms\n", " 7 -7.905211531088 -7.90 -4.60 2.8 43.6ms\n", " 8 -7.905211531385 -9.53 -5.21 1.0 24.1ms\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 3.1020964 \n AtomicLocal -2.1987852\n AtomicNonlocal 1.7296100 \n Ewald -8.3979253\n PspCorrection -0.2946254\n Hartree 0.5530393 \n Xc -2.3986213\n\n total -7.905211531385" }, "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 -0.0911692 … -0.101219 -0.023977 -0.018408\n 0.261073 0.116914 0.00482506 0.0611643 -0.023977 -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 0.389829 0.384601 … 0.436926 0.285692 0.417428\n 0.354538 0.389829 0.384601 0.449267 0.627555 0.443806" }, "metadata": {}, "execution_count": 4 } ], "cell_type": "code", "source": [ "stack(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).\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": [ "stack(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[ix, iy, iz, iσ], i.e. first in the 3-dimensional real-space grid\n", "and then in the spin component." ], "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", "We can get the Cartesian forces (in Hartree / Bohr):" ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "2-element Vector{StaticArraysCore.SVector{3, Float64}}:\n [-8.273860692573945e-16, 1.683575924870087e-16, 6.225291464399066e-16]\n [-1.9318342027677724e-16, -1.831991624635836e-16, -8.813908687278542e-16]" }, "metadata": {}, "execution_count": 7 } ], "cell_type": "code", "source": [ "compute_forces_cart(scfres)" ], "metadata": {}, "execution_count": 7 }, { "cell_type": "markdown", "source": [ "As expected, they are numerically zero in this highly symmetric configuration.\n", "We could also compute a band structure," ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "┌ Warning: Calling plot_bandstructure without first computing the band data is deprecated and will be removed in the next minor version bump.\n", "└ @ DFTKPlotsExt ~/work/DFTK.jl/DFTK.jl/ext/DFTKPlotsExt.jl:26\n" ] }, { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=44}", "image/png": 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plots:" ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=2}", "image/png": 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the results\n", "are much cruder:" ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=2}", "image/png": 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