{ "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": [ { "output_type": "execute_result", "data": { "text/plain": "3Γ—3 Array{Unitful.Quantity{Float64,𝐋,Unitful.FreeUnits{(β„«,),𝐋,nothing}},2}:\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 -7.905233638695 NaN 1.95e-01 4.1 \n", " 2 -7.909826171785 -4.59e-03 2.98e-02 1.0 \n", " 3 -7.910018865111 -1.93e-04 2.98e-03 1.2 \n", " 4 -7.910051976048 -3.31e-05 1.35e-03 2.6 \n", " 5 -7.910052578180 -6.02e-07 7.89e-04 1.0 \n", " 6 -7.910052845587 -2.67e-07 2.10e-05 1.0 \n", " 7 -7.910052854016 -8.43e-09 7.96e-06 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=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 3.0795085 \n AtomicLocal -2.1806177\n AtomicNonlocal 1.7339299 \n Ewald -8.3979253\n PspCorrection -0.2946254\n Hartree 0.5417515 \n Xc -2.3920744\n\n total -7.910052854016\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 Array{Float64,2}:\n -0.170181 -0.131799 -0.0883267 … -0.0562593 -0.114939 -0.0700156\n 0.201345 0.090905 0.0122933 0.0111159 0.0420628 0.0176513\n 0.249297 0.174774 0.176138 0.132965 0.220116 0.112331\n 0.249297 0.231429 0.202371 0.161044 0.220116 0.190457\n 0.350986 0.360028 0.340135 0.291807 0.320727 0.327376\n 0.369971 0.395898 0.389484 … 0.331814 0.388191 0.460327\n 0.369972 0.401677 0.412475 0.565567 0.388191 0.462725" }, "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 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": 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: 4%|β–‹ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 9%|β–ˆβ–Œ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 11%|β–ˆβ–Š | ETA: 0:00:03\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: 44%|β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ– | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 50%|β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 59%|β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–Œ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 69%|β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 76%|β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ– | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 83%|β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ– | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 93%|β–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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"\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\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": 7 } ], "cell_type": "code", "source": [ "plot_bandstructure(scfres, kline_density=5)" ], "metadata": {}, "execution_count": 7 }, { "cell_type": "markdown", "source": [ "or get the cartesian forces (in Hartree / Bohr)" ], "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 Array{StaticArrays.SArray{Tuple{3},Float64,1,3},1}:\n [0.0004495391736326617, 0.00044956037234211065, 0.00044956003331582124]\n [-0.0004495603723422416, -0.00044953917363254405, -0.0004495600333158564]" }, "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": "1.5.3" }, "kernelspec": { "name": "julia-1.5", "display_name": "Julia 1.5.3", "language": "julia" } }, "nbformat": 4 }