{ "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": "1.8.5" }, "kernelspec": { "name": "julia-1.8", "display_name": "Julia 1.8.5", "language": "julia" } }, "nbformat": 4 }