{ "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": "3×3 Matrix{Unitful.Quantity{Float64, 𝐋, Unitful.FreeUnits{(Å,), 𝐋, nothing}}}:\n 0.0 Å 2.7155 Å 2.7155 Å\n 2.7155 Å 0.0 Å 2.7155 Å\n 2.7155 Å 2.7155 Å 0.0 Å" }, "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 Eₙ-Eₙ₋₁ ρout-ρin α Diag\n", "--- --------------- --------- -------- ---- ----\n", " 1 -7.905255321096 NaN 1.95e-01 0.80 4.1\n", " 2 -7.909828603784 -4.57e-03 2.98e-02 0.80 1.0\n", " 3 -7.910051948758 -2.23e-04 3.03e-03 0.80 3.0\n", " 4 -7.910052831830 -8.83e-07 4.71e-04 0.80 2.5\n", " 5 -7.910052852017 -2.02e-08 4.31e-05 0.80 2.0\n", " 6 -7.910052854035 -2.02e-09 4.36e-06 0.80 3.0\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 => [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\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 3.0795155 \n AtomicLocal -2.1806375\n AtomicNonlocal 1.7339392 \n Ewald -8.3979253\n PspCorrection -0.2946254\n Hartree 0.5417570 \n Xc -2.3920764\n\n total -7.910052854035" }, "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": "7×10 Matrix{Float64}:\n -0.170182 -0.131801 -0.0883282 … -0.0562607 -0.11494 -0.0700169\n 0.201343 0.0909036 0.0122924 0.0111144 0.0420614 0.0176496\n 0.249295 0.174773 0.176137 0.132964 0.220114 0.11233\n 0.249295 0.231428 0.20237 0.161043 0.220114 0.190456\n 0.350986 0.360027 0.340134 0.291807 0.320727 0.327376\n 0.36997 0.395897 0.389483 … 0.331814 0.38819 0.460233\n 0.36997 0.401676 0.412474 0.565522 0.38819 0.462717" }, "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": "7×10 Matrix{Float64}:\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": 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 ρ[iσ, 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.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", "for instance compute a band structure" ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing bands along kpath:\n", " Γ -> X -> U and K -> Γ -> L -> W -> X\n", "\rDiagonalising Hamiltonian kblocks: 6%|█ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 19%|███ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 38%|██████ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 50%|████████ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 66%|██████████▌ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 81%|█████████████ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 97%|███████████████▌| ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 100%|████████████████| 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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"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 [0.00044893130950365216, 0.00044893589868801357, 0.0004489321808010633]\n [-0.00044893589868828, -0.0004489313095032776, -0.0004489321808008686]" }, "metadata": {}, "execution_count": 8 } ], "cell_type": "code", "source": [ "compute_forces_cart(scfres)[1] # Select silicon forces" ], "metadata": {}, "execution_count": 8 }, { "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://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": "1.7.0" }, "kernelspec": { "name": "julia-1.7", "display_name": "Julia 1.7.0", "language": "julia" } }, "nbformat": 4 }