{ "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://juliamolsim.github.io/DFTK.jl/stable/guide/periodic_problems/)\n", "or the\n", "[density-functional theory](https://juliamolsim.github.io/DFTK.jl/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 -7.905199457661 NaN 1.95e-01 0.80 4.0\n", " 2 -7.909817921225 -4.62e-03 2.98e-02 0.80 1.0\n", " 3 -7.910051886500 -2.34e-04 3.05e-03 0.80 3.1\n", " 4 -7.910052831417 -9.45e-07 4.83e-04 0.80 2.4\n", " 5 -7.910052852174 -2.08e-08 4.20e-05 0.80 2.0\n", " 6 -7.910052854034 -1.86e-09 4.74e-06 0.80 3.1\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 -2.1806378\n AtomicNonlocal 1.7339394 \n Ewald -8.3979253\n PspCorrection -0.2946254\n Hartree 0.5417571 \n Xc -2.3920764\n\n total -7.910052854034" }, "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 -0.0700168\n 0.201343 0.0909036 0.0122924 0.0111144 0.0420613 0.0176495\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 0.460237\n 0.36997 0.401676 0.412474 0.565539 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: 9%|█▌ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 22%|███▌ | 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 [0.00044871265133819945, 0.00044870479213694894, 0.000448712376385704]\n [-0.0004487047921371896, -0.0004487126513381237, -0.00044871237638617866]" }, "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, "metadata": { "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.6.3" }, "kernelspec": { "name": "julia-1.6", "display_name": "Julia 1.6.3", "language": "julia" } }, "nbformat": 4 }