{
"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 diamond silicon\n",
"with respect to its lattice parameter, around the experimental lattice constant."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"using AtomsBuilder\n",
"using DFTK\n",
"using PseudoPotentialData\n",
"using Statistics\n",
"using Unitful\n",
"using UnitfulAtomic\n",
"\n",
"a0 = 10.26u\"bohr\" # Experimental lattice constant of silicon\n",
"a_list = a0 * range(0.98, 1.02, length=20)\n",
"\n",
"function compute_ground_state_energy(a; Ecut, kgrid, kinetic_blowup, kwargs...)\n",
" pseudopotentials = PseudoFamily(\"cp2k.nc.sr.pbe.v0_1.semicore.gth\")\n",
" model = model_DFT(bulk(:Si; a); functionals=PBE(), kinetic_blowup, pseudopotentials)\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 = (4, 4, 4) # 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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]
},
"metadata": {},
"execution_count": 2
}
],
"cell_type": "code",
"source": [
"E0_ref = [-7.867399262300442, -7.867875504884598, -7.86831005961699,\n",
" -7.868703712435519, -7.869057235894591, -7.869371393835255,\n",
" -7.869646937992838, -7.869884611383302, -7.870085144568824,\n",
" -7.8702492593753135, -7.870377668337734, -7.870471072484817,\n",
" -7.870530163168231, -7.870555622590523, -7.870548125081617,\n",
" -7.870508333380078, -7.8704369010295006, -7.870334474350743,\n",
" -7.870201688247285, -7.870039170777946]\n",
"\n",
"using Plots\n",
"shift = mean(E0_naive - E0_ref)\n",
"p = plot(a_list, E0_naive .- shift, label=\"Ecut=5\", xlabel=\"lattice parameter a\",\n",
" ylabel=\"Ground state energy (Ha)\", color=1, legend=:topright)\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 [^CHV2024] that is mathematically ensured to provide $C^2$\n",
"regularity of the energy bands.\n",
"\n",
"[^CHV2024]:\n",
" Eric Cancès, Muhammad Hassan and Laurent Vidal;\n",
" *Modified-operator method for the calculation of band diagrams of\n",
" crystalline materials*.\n",
" Math. Comp. 93 (2024), 1203-1245\n",
" DOI: https://doi.org/10.1090/mcom/3897"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Let us launch 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": [
"> **Abinit energy cutoff smearing option**\n",
">\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 now 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}",
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]
},
"metadata": {},
"execution_count": 4
}
],
"cell_type": "code",
"source": [
"estimate_a0(E0_values) = a_list[findmin(E0_values)[2]]\n",
"a0_naive, a0_ref, a0_modified = estimate_a0.([E0_naive, E0_ref, E0_modified])\n",
"\n",
"shift = mean(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: 0.62696%\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
}
],
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"metadata": {
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.11.4"
},
"kernelspec": {
"name": "julia-1.11",
"display_name": "Julia 1.11.4",
"language": "julia"
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