{ "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 chapter](https://juliamolsim.github.io/DFTK.jl/dev/#density-functional-theory)\n", "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 -7.905191672941 NaN 1.95e-01 0.80 4.2\n", " 2 -7.909819028338 -4.63e-03 2.98e-02 0.80 1.0\n", " 3 -7.910051979756 -2.33e-04 3.06e-03 0.80 3.1\n", " 4 -7.910052832475 -8.53e-07 4.75e-04 0.80 2.5\n", " 5 -7.910052852110 -1.96e-08 4.25e-05 0.80 2.0\n", " 6 -7.910052854031 -1.92e-09 4.97e-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:\n Kinetic 3.0795157 \n AtomicLocal -2.1806381\n AtomicNonlocal 1.7339395 \n Ewald -8.3979253\n PspCorrection -0.2946254\n Hartree 0.5417572 \n Xc -2.3920764\n\n total -7.910052854031\n" }, "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 -0.0883283 … -0.0562608 -0.11494 -0.0700168\n 0.201343 0.0909036 0.0122924 0.0111144 0.0420612 0.0176494\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 0.460231\n 0.36997 0.401676 0.412474 0.565528 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 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 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 -> W -> K -> Γ -> L -> U -> W -> L -> K and U -> X\n", "\rDiagonalising Hamiltonian kblocks: 6%|▉ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 13%|██▏ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 24%|███▉ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 33%|█████▍ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 43%|██████▉ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 54%|████████▋ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 63%|██████████▏ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 72%|███████████▌ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 81%|█████████████ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 91%|██████████████▌ | 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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], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "2-element Vector{StaticArrays.SVector{3, Float64}}:\n [0.000448592021168021, 0.00044858239092464833, 0.0004485845656641904]\n [-0.0004485823909249593, -0.0004485920211675911, -0.00044858456566428096]" }, "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://juliamolsim.github.io/DFTK.jl/dev/#example-index-1)\n", "to continue exploring DFTK." ], "metadata": {} } ], "nbformat_minor": 3, 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