{ "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", "[density-functional theory](https://juliamolsim.github.io/DFTK.jl/dev/#density-functional-theory)\n", "chapter for some introductory lectures and 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": [ { "name": "stdout", "output_type": "stream", "text": [ "n Energy Eₙ-Eₙ₋₁ ρout-ρin Diag\n", "--- --------------- --------- -------- ----\n", " 1 -7.905267528627 NaN 1.95e-01 4.2 \n", " 2 -7.909883040413 -4.62e-03 2.99e-02 1.0 \n", " 3 -7.910076544544 -1.94e-04 3.01e-03 1.2 \n", " 4 -7.910108514618 -3.20e-05 1.30e-03 2.4 \n", " 5 -7.910109176920 -6.62e-07 6.97e-04 1.0 \n", " 6 -7.910109404342 -2.27e-07 2.94e-05 1.0 \n", " 7 -7.910109414059 -9.72e-09 9.71e-06 2.4 \n" ] } ], "cell_type": "code", "source": [ "using DFTK\n", "using Plots\n", "\n", "# 1. Define lattice and atomic positions\n", "a = 10.26 # Silicon lattice constant in Bohr\n", "lattice = a / 2 * [[0 1 1.]; # Silicon lattice vectors\n", " [1 0 1.]; # specified column by column\n", " [1 1 0.]]\n", "\n", "# 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 => [ones(3)/8, -ones(3)/8]]\n", "\n", "# 2. Select model and basis\n", "model = model_LDA(lattice, atoms)\n", "kgrid = [4, 4, 4] # k-point grid (Regular Monkhorst-Pack grid)\n", "Ecut = 7 # kinetic energy cutoff in Hartree\n", "basis = PlaneWaveBasis(model, 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": 1 }, { "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:\n Kinetic 3.0807655 \n AtomicLocal -2.1784285\n AtomicNonlocal 1.7340959 \n Ewald -8.4004648\n PspCorrection -0.2948928\n Hartree 0.5413849 \n Xc -2.3925697\n\n total -7.910109414059\n" }, "metadata": {}, "execution_count": 2 } ], "cell_type": "code", "source": [ "scfres.energies" ], "metadata": {}, "execution_count": 2 }, { "cell_type": "markdown", "source": [ "Eigenvalues:" ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "7×10 Array{Float64,2}:\n -0.170032 -0.131618 -0.0881007 … -0.0560193 -0.114742 -0.0697755\n 0.20171 0.091211 0.0125277 0.011409 0.0423191 0.0179189\n 0.249666 0.175088 0.176467 0.133227 0.220468 0.112585\n 0.249666 0.23179 0.202706 0.161341 0.220468 0.19078\n 0.351461 0.360508 0.340563 0.292133 0.321217 0.327741\n 0.37038 0.396309 0.389909 … 0.33217 0.388573 0.460957\n 0.37038 0.402094 0.412871 0.566136 0.388573 0.463185" }, "metadata": {}, "execution_count": 3 } ], "cell_type": "code", "source": [ "hcat(scfres.eigenvalues...)" ], "metadata": {}, "execution_count": 3 }, { "cell_type": "markdown", "source": [ "`eigenvalues` is an array (indexed by kpoints) 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 kpoints). There are 7 eigenvalues per kpoint 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": "7×10 Array{Float64,2}:\n 2.0 2.0 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 2.0 2.0\n 2.0 2.0 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 2.0 2.0\n 0.0 0.0 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 0.0 0.0\n 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0" }, "metadata": {}, "execution_count": 4 } ], "cell_type": "code", "source": [ "hcat(scfres.occupation...)" ], "metadata": {}, "execution_count": 4 }, { "cell_type": "markdown", "source": [ "And density:" ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=1}", "image/png": "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", "text/html": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\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": 5 } ], "cell_type": "code", "source": [ "rvecs = collect(r_vectors(basis))[:, 1, 1] # slice along the x axis\n", "x = [r[1] for r in rvecs] # only keep the x coordinate\n", "plot(x, scfres.ρ.real[:, 1, 1], label=\"\", xlabel=\"x\", ylabel=\"ρ\", marker=2)" ], "metadata": {}, "execution_count": 5 }, { "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 -> W -> K -> Γ -> L -> U -> W -> L -> K and U -> X\n", "\rDiagonalising Hamiltonian kblocks: 4%|▋ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 9%|█▌ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 19%|███ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 26%|████▏ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 33%|█████▍ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 39%|██████▎ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 41%|██████▌ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 50%|████████ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 59%|█████████▌ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 69%|███████████ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 78%|████████████▌ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 85%|█████████████▋ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 93%|██████████████▉ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 98%|███████████████▊| 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=210}", "image/png": "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", "text/html": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\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": 6 } ], "cell_type": "code", "source": [ "plot_bandstructure(scfres, kline_density=5, unit=:eV)" ], "metadata": {}, "execution_count": 6 }, { "cell_type": "markdown", "source": [ "or get the cartesian forces (in Hartree / Bohr)" ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "┌ Warning: Forces for shifted k-Grids not tested\n", "└ @ DFTK /home/runner/work/DFTK.jl/DFTK.jl/src/terms/terms.jl:72\n" ] }, { "output_type": "execute_result", "data": { "text/plain": "2-element Array{StaticArrays.SArray{Tuple{3},Float64,1,3},1}:\n [0.0004502579993381295, 0.00045026429158255885, 0.00045026536974565243]\n [-0.00045026429158306306, -0.0004502579993376688, -0.00045026536974559144]" }, "metadata": {}, "execution_count": 7 } ], "cell_type": "code", "source": [ "compute_forces_cart(scfres)[1] # Select silicon forces" ], "metadata": {}, "execution_count": 7 }, { "cell_type": "markdown", "source": [ "The `[1]` extracts the forces for the first kind of atoms,\n", "i.e. `Si` (silicon) in the setup of the `atoms` list of step 1 above.\n", "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://juliamolsim.github.io/DFTK.jl/dev/#example-index-1)\n", "to continue exploring DFTK." ], "metadata": {} } ], "nbformat_minor": 3, "metadata": { "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.5.3" }, "kernelspec": { "name": "julia-1.5", "display_name": "Julia 1.5.3", "language": "julia" } }, "nbformat": 4 }