{ "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 [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(), 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": "1.8.2" }, "kernelspec": { "name": "julia-1.8", "display_name": "Julia 1.8.2", "language": "julia" } }, "nbformat": 4 }