{ "cells": [ { "cell_type": "markdown", "source": [ "# Energy cutoff smearing\n", "\n", "A technique that has been employed in the literature to ensure smooth energy bands\n", "for finite Ecut values is energy cutoff smearing.\n", "\n", "As recalled in the\n", "[Problems and plane-wave discretization](https://docs.dftk.org/stable/guide/periodic_problems/)\n", "section, the energy of periodic systems is computed by solving eigenvalue\n", "problems of the form\n", "$$\n", "H_k u_k = ε_k u_k,\n", "$$\n", "for each $k$-point in the first Brillouin zone of the system.\n", "Each of these eigenvalue problem is discretized with a plane-wave basis\n", "$\\mathcal{B}_k^{E_c}=\\{x ↦ e^{iG · x} \\;\\;|\\;G ∈ \\mathcal{R}^*,\\;\\; |k+G|^2 ≤ 2E_c\\}$\n", "whose size highly depends on the choice of $k$-point, cell size or\n", "cutoff energy $\\rm E_c$ (the `Ecut` parameter of DFTK).\n", "As a result, energy bands computed along a $k$-path in the Brillouin zone\n", "or with respect to the system's unit cell volume - in the case of geometry optimization\n", "for example - display big irregularities when `Ecut` is taken too small.\n", "\n", "Here is for example the variation of the ground state energy of face cubic centred\n", "(FCC) silicon with respect to its lattice parameter,\n", "around the experimental lattice constant." ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "using DFTK\n", "using Statistics\n", "\n", "a0 = 10.26 # Experimental lattice constant of silicon in bohr\n", "a_list = range(a0 - 1/2, a0 + 1/2; length=20)\n", "\n", "function compute_ground_state_energy(a; Ecut, kgrid, kinetic_blowup, kwargs...)\n", " lattice = a / 2 * [[0 1 1.];\n", " [1 0 1.];\n", " [1 1 0.]]\n", " Si = ElementPsp(:Si, psp=load_psp(\"hgh/lda/Si-q4\"))\n", " atoms = [Si, Si]\n", " positions = [ones(3)/8, -ones(3)/8]\n", " model = model_PBE(lattice, atoms, positions; kinetic_blowup)\n", " basis = PlaneWaveBasis(model; Ecut, kgrid)\n", " self_consistent_field(basis; callback=identity, kwargs...).energies.total\n", "end\n", "\n", "Ecut = 5 # Very low Ecut to display big irregularities\n", "kgrid = (2, 2, 2) # Very sparse k-grid to speed up convergence\n", "E0_naive = compute_ground_state_energy.(a_list; kinetic_blowup=BlowupIdentity(), Ecut, kgrid);" ], "metadata": {}, "execution_count": 1 }, { "cell_type": "markdown", "source": [ "To be compared with the same computation for a high `Ecut=100`. The naive approximation\n", "of the energy is shifted for the legibility of the plot." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=2}", "image/png": 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-7.859727053496513,\n", " -7.860069804791132, -7.860213631865354, -7.8601679947736915,\n", " -7.859942011410533, -7.859544518721661, -7.858984032385052,\n", " -7.858268793303855, -7.857406769423708]\n", "\n", "using Plots\n", "shift = mean(abs.(E0_naive .- E0_ref))\n", "p = plot(a_list, E0_naive .- shift, label=\"Ecut=5\", xlabel=\"lattice parameter a (bohr)\",\n", " ylabel=\"Ground state energy (Ha)\", color=1)\n", "plot!(p, a_list, E0_ref, label=\"Ecut=100\", color=2)" ], "metadata": {}, "execution_count": 2 }, { "cell_type": "markdown", "source": [ "The problem of non-smoothness of the approximated energy is typically avoided by\n", "taking a large enough `Ecut`, at the cost of a high computation time.\n", "Another method consist in introducing a modified kinetic term defined through\n", "the data of a blow-up function, a method which is also referred to as \"energy cutoff\n", "smearing\". DFTK features energy cutoff smearing using the CHV blow-up\n", "function introduced in [^CHV2022] that is mathematically ensured to provide $C^2$\n", "regularity of the energy bands.\n", "\n", "[^CHV2022]:\n", " Éric Cancès, Muhammad Hassan and Laurent Vidal\n", " *Modified-operator method for the calculation of band diagrams of\n", " crystalline materials*, 2022.\n", " [arXiv preprint.](https://arxiv.org/abs/2210.00442)" ], "metadata": {} }, { "cell_type": "markdown", "source": [ "Let us lauch the computation again with the modified kinetic term." ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "E0_modified = compute_ground_state_energy.(a_list; kinetic_blowup=BlowupCHV(), Ecut, kgrid);" ], "metadata": {}, "execution_count": 3 }, { "cell_type": "markdown", "source": [ "!!! note \"Abinit energy cutoff smearing option\"\n", " For the sake of completeness, DFTK also provides the blow-up function `BlowupAbinit`\n", " proposed in the Abinit quantum chemistry code. This function depends on a parameter\n", " `Ecutsm` fixed by the user\n", " (see [Abinit user guide](https://docs.abinit.org/variables/rlx/#ecutsm)).\n", " For the right choice of `Ecutsm`, `BlowupAbinit` corresponds to the `BlowupCHV` approach\n", " with coefficients ensuring $C^1$ regularity. To choose `BlowupAbinit`, pass\n", " `kinetic_blowup=BlowupAbinit(Ecutsm)` to the model constructors." ], "metadata": {} }, { "cell_type": "markdown", "source": [ "We can know compare the approximation of the energy as well as the estimated\n", "lattice constant for each strategy." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=7}", "image/png": 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"\n", "shift = mean(abs.(E0_modified .- E0_ref)) # Shift for legibility of the plot\n", "plot!(p, a_list, E0_modified .- shift, label=\"Ecut=5 + BlowupCHV\", color=3)\n", "vline!(p, [a0], label=\"experimental a0\", linestyle=:dash, linecolor=:black)\n", "vline!(p, [a0_naive], label=\"a0 Ecut=5\", linestyle=:dash, color=1)\n", "vline!(p, [a0_ref], label=\"a0 Ecut=100\", linestyle=:dash, color=2)\n", "vline!(p, [a0_modified], label=\"a0 Ecut=5 + BlowupCHV\", linestyle=:dash, color=3)" ], "metadata": {}, "execution_count": 4 }, { "cell_type": "markdown", "source": [ "The smoothed curve obtained with the modified kinetic term allow to clearly designate\n", "a minimal value of the energy with respect to the lattice parameter $a$, even with\n", "the low `Ecut=5` Ha." ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Error of approximation of the reference a0 with modified kinetic term: 0.50393%\n" ] } ], "cell_type": "code", "source": [ "println(\"Error of approximation of the reference a0 with modified kinetic term:\"*\n", " \" $(round((a0_modified - a0_ref)*100/a0_ref, digits=5))%\")" ], "metadata": {}, "execution_count": 5 } ], "nbformat_minor": 3, "metadata": { "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.8.3" }, "kernelspec": { "name": "julia-1.8", "display_name": "Julia 1.8.3", "language": "julia" } }, "nbformat": 4 }