{ "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 -7.900414412069 -0.70 4.1\n", " 2 -7.905010926090 -2.34 -1.52 1.0\n", " 3 -7.905210802115 -3.70 -2.52 3.1\n", " 4 -7.905211517180 -6.15 -3.34 2.9\n", " 5 -7.905211530341 -7.88 -4.66 1.4\n", " 6 -7.905211531396 -8.98 -5.16 3.9\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 3.1020979 \n AtomicLocal -2.1987873\n AtomicNonlocal 1.7296101 \n Ewald -8.3979253\n PspCorrection -0.2946254\n Hartree 0.5530400 \n Xc -2.3986216\n\n total -7.905211531396" }, "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 -0.0184079\n 0.261073 0.116915 0.00482515 0.0611644 -0.023977 -0.0184079\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€¦ 0.436925 0.285692 0.4175\n 0.354532 0.389829 0.384601 0.449266 0.62753 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: 16%|ā–ˆā–ˆā–Œ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 34%|ā–ˆā–ˆā–ˆā–ˆā–ˆā–Œ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 53%|ā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–Œ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 75%|ā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 97%|ā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–Œ| 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 [-2.191509554957525e-16, -6.001040450720518e-16, 2.7378380023287873e-16]\n [-4.5585489959038625e-16, -2.5011191789770235e-17, 1.7892568072338752e-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 }