{ "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" ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "#$$" ], "metadata": {}, "execution_count": 1 }, { "cell_type": "markdown", "source": [ "\\begin{equation}\n", "H_ku_k=\\varepsilon_k u_k\n", "\\end{equation}\n", "$$\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", "$\\mathcal{B}_k^{E_c}=\\{x\\mapsto e^{iG\\cdot x} \\;\\;|\\;G\\in\\mathcal{R}^*,\\;\\; |k+G|^2\\leq 2E_c\\}$\n", "whose size highly depends on the choice of $k$-point, cutoff energy $\\rm E_c$ or\n", "cell size. 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 $E_c$ is taken too small.\n", "\n", "Here is for example the variation of the ground state energy of face cubic centered\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", "Ecut = 5 # very low Ecut to display big irregularities\n", "kgrid = (2, 2, 2) # very sparse k-grid to fasten convergence\n", "n_bands = 8 # Standard number of bands for silicon\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; kwargs...).energies.total\n", "end\n", "\n", "callback = info->nothing # set SCF to non verbose\n", "E0_naive = compute_ground_state_energy.(a_list; kinetic_blowup=BlowupIdentity(),\n", " Ecut, kgrid, n_bands, callback);" ], "metadata": {}, "execution_count": 2 }, { "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": 3 }, { "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 [REF of the paper to be submitted],\n", "that is mathematically ensured to provide $C^2$ regularity of the energy bands." ], "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(),\n", " Ecut, kgrid, n_bands, callback, );" ], "metadata": {}, "execution_count": 4 }, { "cell_type": "markdown", "source": [ "!!! note \"Abinit energy cutoff smearing option\"\n", " For the sake of completeness, DFTK also provides the blow-up function proposed\n", " in the Abinit [^Abinit] quantum chemistry code. This function depends on a parameter\n", " `Ecutsm` fixed by the user. Note that for the right choice of `Ecutsm`, the Abinit\n", " blow-up function corresponds to the CHV one with a choice of coefficients\n", " ensuring $C^1$ regularity. The Abinit options is chosen\n", " with `kinetic_blowup=BlowupAbinit(Ecutsm)`\n", "\n", "[^Abinit]:\n", " Abinit software suite [user guide](https://docs.abinit.org/variables/rlx/#ecutsm)" ], "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)) # again, shift for legibility of the plot\n", "\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": 5 }, { "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": 6 } ], "nbformat_minor": 3, "metadata": { "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.8.1" }, "kernelspec": { "name": "julia-1.8", "display_name": "Julia 1.8.1", "language": "julia" } }, "nbformat": 4 }