{ "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 -7.900294697919 -0.70 3.9\n", " 2 -7.904985640884 -2.33 -1.52 1.0\n", " 3 -7.905210852785 -3.65 -2.52 3.2\n", " 4 -7.905211520149 -6.18 -3.38 2.5\n", " 5 -7.905211530793 -7.97 -4.76 1.6\n", " 6 -7.905211531392 -9.22 -5.24 3.8\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 3.1020968 \n AtomicLocal -2.1987842\n AtomicNonlocal 1.7296086 \n Ewald -8.3979253\n PspCorrection -0.2946254\n Hartree 0.5530392 \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": "7Ɨ8 Matrix{Float64}:\n -0.176942 -0.14744 -0.0911689 ā€¦ -0.101219 -0.0239767 -0.0184077\n 0.261074 0.116915 0.00482533 0.0611646 -0.0239767 -0.0184077\n 0.261074 0.23299 0.216734 0.121636 0.155532 0.117748\n 0.261074 0.23299 0.216734 0.212134 0.155532 0.117748\n 0.354532 0.33511 0.317103 0.350436 0.285692 0.417258\n 0.354532 0.389829 0.384601 ā€¦ 0.436926 0.285692 0.417585\n 0.354532 0.389829 0.384601 0.44925 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: 12%|ā–ˆā–ˆ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 31%|ā–ˆā–ˆā–ˆā–ˆā–ˆ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 50%|ā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 69%|ā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆā–ˆ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 88%|ā–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 [-3.195636908640615e-16, -6.01964711041252e-16, 3.265771952082316e-17]\n [-3.484135309252274e-16, -6.578714503809925e-17, -1.002783840931148e-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": "1.7.3" }, "kernelspec": { "name": "julia-1.7", "display_name": "Julia 1.7.3", "language": "julia" } }, "nbformat": 4 }