{ "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": "3Γ—3 Matrix{Unitful.Quantity{Float64, 𝐋, Unitful.FreeUnits{(β„«,), 𝐋, nothing}}}:\n 0.0 β„« 2.7155 β„« 2.7155 β„«\n 2.7155 β„« 0.0 β„« 2.7155 β„«\n 2.7155 β„« 2.7155 β„« 0.0 β„«" }, "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 Eβ‚™-Eₙ₋₁ ρout-ρin Diag\n", "--- --------------- --------- -------- ----\n", " 1 -7.905202126561 NaN 1.95e-01 4.1 \n", " 2 -7.909823517293 -4.62e-03 2.98e-02 1.0 \n", " 3 -7.910019386064 -1.96e-04 3.02e-03 1.2 \n", " 4 -7.910051968896 -3.26e-05 1.32e-03 2.5 \n", " 5 -7.910052600843 -6.32e-07 7.39e-04 1.0 \n", " 6 -7.910052845044 -2.44e-07 2.45e-05 1.0 \n", " 7 -7.910052854003 -8.96e-09 8.85e-06 2.7 \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=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 3.0795073 \n AtomicLocal -2.1806151\n AtomicNonlocal 1.7339292 \n Ewald -8.3979253\n PspCorrection -0.2946254\n Hartree 0.5417506 \n Xc -2.3920740\n\n total -7.910052854003\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": "7Γ—10 Matrix{Float64}:\n -0.17018 -0.131799 -0.0883264 … -0.056259 -0.114938 -0.0700151\n 0.201345 0.0909053 0.0122937 0.0111163 0.0420629 0.0176514\n 0.249297 0.174774 0.176139 0.132965 0.220116 0.112331\n 0.249297 0.23143 0.202372 0.161044 0.220116 0.190457\n 0.350987 0.360028 0.340135 0.291807 0.320728 0.327377\n 0.369972 0.395899 0.389484 … 0.331814 0.388191 0.460442\n 0.369973 0.401677 0.412475 0.565569 0.388191 0.462739" }, "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": "7Γ—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:" ], "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.real[:, 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", " Ξ“ -> X -> W -> K -> Ξ“ -> L -> U -> W -> L -> K and U -> X\n", "\rDiagonalising Hamiltonian kblocks: 2%|β–Ž | ETA: 0:00:06\u001b[K\rDiagonalising Hamiltonian kblocks: 9%|β–ˆβ–Œ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 19%|β–ˆβ–ˆβ–ˆ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 28%|β–ˆβ–ˆβ–ˆβ–ˆβ–Œ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 37%|β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–‰ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 46%|β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ– | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 52%|β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–Ž | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 61%|β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–Š | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 70%|β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–Ž | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 80%|β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–Š | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 87%|β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–‰ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 94%|β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–| ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 100%|β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ| 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": [ { "name": "stdout", "output_type": "stream", "text": [ "β”Œ Warning: Forces for shifted k-Grids not tested\n", "β”” @ DFTK /home/runner/work/DFTK.jl/DFTK.jl/src/terms/terms.jl:72\n" ] }, { "output_type": "execute_result", "data": { "text/plain": "2-element Vector{StaticArrays.SVector{3, Float64}}:\n [0.00044931559241720247, 0.0004492864135625086, 0.0004492838745915574]\n [-0.00044928641356327387, -0.00044931559241632085, -0.0004492838745913425]" }, "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": "1.6.0" }, "kernelspec": { "name": "julia-1.6", "display_name": "Julia 1.6.0", "language": "julia" } }, "nbformat": 4 }