{ "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", "[density-functional theory](https://docs.dftk.org/stable/guide/density_functional_theory/)\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": [ { "output_type": "execute_result", "data": { "text/plain": "3Ɨ3 Matrix{Unitful.Quantity{Float64, š‹, Unitful.FreeUnits{(ā„«,), š‹, nothing}}}:\n 0.0 ā„« 2.7155 ā„« 2.7155 ā„«\n 2.7155 ā„« 0.0 ā„« 2.7155 ā„«\n 2.7155 ā„« 2.7155 ā„« 0.0 ā„«" }, "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 log10(Ī”E) log10(Ī”Ļ) Diag\n", "--- --------------- --------- --------- ----\n", " 1 -7.900338533253 -0.70 4.0\n", " 2 -7.904994801173 -2.33 -1.52 1.0\n", " 3 -7.905210790861 -3.67 -2.52 3.2\n", " 4 -7.905211516166 -6.14 -3.34 2.5\n", " 5 -7.905211530364 -7.85 -4.64 1.8\n", " 6 -7.905211531397 -8.99 -5.20 3.6\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-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 (in Ha):\n Kinetic 3.1020981 \n AtomicLocal -2.1987876\n AtomicNonlocal 1.7296102 \n Ewald -8.3979253\n PspCorrection -0.2946254\n Hartree 0.5530401 \n Xc -2.3986216\n\n total -7.905211531397" }, "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": "7Ɨ8 Matrix{Float64}:\n -0.176942 -0.14744 -0.0911692 ā€¦ -0.101219 -0.023977 -0.018408\n 0.261073 0.116915 0.00482512 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 ā€¦ 0.436926 0.285692 0.417288\n 0.354532 0.389829 0.384601 0.449299 0.627527 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 k-points). There are 7 eigenvalues per k-point 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": "7Ɨ8 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 Ļ[iĻƒ, 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.Ļ[1, :, 1, 1], label=\"\", xlabel=\"x\", ylabel=\"Ļ\", 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", " Ī“ -> X -> U and K -> Ī“ -> L -> W -> X\n", "\rDiagonalising Hamiltonian kblocks: 9%|ā–ˆā–Œ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 22%|ā–ˆā–ˆā–ˆā–Œ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 38%|ā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 50%|ā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 66%|ā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–Œ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 78%|ā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–Œ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 94%|ā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 100%|ā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆ| Time: 0:00:00\u001b[K\n" ] }, { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=126}", "image/png": 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"\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\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{StaticArrays.SVector{3, Float64}}:\n [2.096934515331527e-17, -7.063728225914991e-16, -6.120294287001704e-16]\n [-9.11426051759574e-16, 3.8392546605553576e-16, 4.585016810067272e-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 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://docs.dftk.org/stable/#example-index-1)\n", "to continue exploring DFTK." ], "metadata": {} } ], "nbformat_minor": 3, "metadata": { "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.7.2" }, "kernelspec": { "name": "julia-1.7", "display_name": "Julia 1.7.2", "language": "julia" } }, "nbformat": 4 }