{
"cells": [
{
"cell_type": "markdown",
"source": [
"# Custom potential"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"We solve the 1D Gross-Pitaevskii equation with a custom potential.\n",
"This is similar to Gross-Pitaevskii equation in 1D example\n",
"and we show how to define local potentials attached to atoms, which allows for\n",
"instance to compute forces.\n",
"The custom potential is actually already defined as `ElementGaussian` in DFTK, and could\n",
"be used as is."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"using DFTK\n",
"using LinearAlgebra"
],
"metadata": {},
"execution_count": 1
},
{
"cell_type": "markdown",
"source": [
"First, we define a new element which represents a nucleus generating\n",
"a Gaussian potential."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"struct CustomPotential <: DFTK.Element\n",
" α # Prefactor\n",
" L # Width of the Gaussian nucleus\n",
"end"
],
"metadata": {},
"execution_count": 2
},
{
"cell_type": "markdown",
"source": [
"Some default values"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"CustomPotential() = CustomPotential(1.0, 0.5);"
],
"metadata": {},
"execution_count": 3
},
{
"cell_type": "markdown",
"source": [
"We extend the two methods providing access to the real and Fourier\n",
"representation of the potential to DFTK."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"function DFTK.local_potential_real(el::CustomPotential, r::Real)\n",
" -el.α / (√(2π) * el.L) * exp(- (r / el.L)^2 / 2)\n",
"end\n",
"function DFTK.local_potential_fourier(el::CustomPotential, p::Real)\n",
" # = ∫ V(r) exp(-ix⋅p) dx\n",
" -el.α * exp(- (p * el.L)^2 / 2)\n",
"end"
],
"metadata": {},
"execution_count": 4
},
{
"cell_type": "markdown",
"source": [
"> **Gaussian potentials and DFTK**\n",
">\n",
"> DFTK already implements `CustomPotential` in form of the `DFTK.ElementGaussian`,\n",
"> so this explicit re-implementation is only provided for demonstration purposes."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"We set up the lattice. For a 1D case we supply two zero lattice vectors"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"a = 10\n",
"lattice = a .* [[1 0 0.]; [0 0 0]; [0 0 0]];"
],
"metadata": {},
"execution_count": 5
},
{
"cell_type": "markdown",
"source": [
"In this example, we want to generate two Gaussian potentials generated by\n",
"two \"nuclei\" localized at positions $x_1$ and $x_2$, that are expressed in\n",
"$[0,1)$ in fractional coordinates. $|x_1 - x_2|$ should be different from\n",
"$0.5$ to break symmetry and get nonzero forces."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"x1 = 0.2\n",
"x2 = 0.8\n",
"positions = [[x1, 0, 0], [x2, 0, 0]]\n",
"gauss = CustomPotential()\n",
"atoms = [gauss, gauss];"
],
"metadata": {},
"execution_count": 6
},
{
"cell_type": "markdown",
"source": [
"We setup a Gross-Pitaevskii model"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"C = 1.0\n",
"α = 2;\n",
"n_electrons = 1 # Increase this for fun\n",
"terms = [Kinetic(),\n",
" AtomicLocal(),\n",
" LocalNonlinearity(ρ -> C * ρ^α)]\n",
"model = Model(lattice, atoms, positions; n_electrons, terms,\n",
" spin_polarization=:spinless); # use \"spinless electrons\""
],
"metadata": {},
"execution_count": 7
},
{
"cell_type": "markdown",
"source": [
"We discretize using a moderate Ecut and run a SCF algorithm to compute forces\n",
"afterwards. As there is no ionic charge associated to `gauss` we have to specify\n",
"a starting density and we choose to start from a zero density."
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"n Energy log10(ΔE) log10(Δρ) Diag Δtime\n",
"--- --------------- --------- --------- ---- ------\n",
" 1 -0.143553788980 -0.42 8.0 233ms\n",
" 2 -0.156032441512 -1.90 -1.10 1.0 58.2ms\n",
" 3 -0.156769355985 -3.13 -1.56 1.0 842μs\n",
" 4 -0.157045773146 -3.56 -2.32 1.0 776μs\n",
" 5 -0.157052891724 -5.15 -2.68 1.0 742μs\n",
" 6 -0.157056384471 -5.46 -3.65 1.0 748μs\n",
" 7 -0.157056405066 -7.69 -4.12 1.0 721μs\n",
" 8 -0.157056406883 -8.74 -4.95 1.0 758μs\n",
" 9 -0.157056406912 -10.53 -5.31 1.0 744μs\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": "Energy breakdown (in Ha):\n Kinetic 0.0380294 \n AtomicLocal -0.3163465\n LocalNonlinearity 0.1212608 \n\n total -0.157056406912"
},
"metadata": {},
"execution_count": 8
}
],
"cell_type": "code",
"source": [
"basis = PlaneWaveBasis(model; Ecut=500, kgrid=(1, 1, 1))\n",
"ρ = zeros(eltype(basis), basis.fft_size..., 1)\n",
"scfres = self_consistent_field(basis; tol=1e-5, ρ)\n",
"scfres.energies"
],
"metadata": {},
"execution_count": 8
},
{
"cell_type": "markdown",
"source": [
"Computing the forces can then be done as usual:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "2-element Vector{StaticArraysCore.SVector{3, Float64}}:\n [-0.05568565687478944, 0.0, 0.0]\n [0.05568660289350602, 0.0, 0.0]"
},
"metadata": {},
"execution_count": 9
}
],
"cell_type": "code",
"source": [
"compute_forces(scfres)"
],
"metadata": {},
"execution_count": 9
},
{
"cell_type": "markdown",
"source": [
"Extract the converged total local potential"
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"tot_local_pot = DFTK.total_local_potential(scfres.ham)[:, 1, 1]; # use only dimension 1"
],
"metadata": {},
"execution_count": 10
},
{
"cell_type": "markdown",
"source": [
"Extract other quantities before plotting them"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "101-element Vector{ComplexF64}:\n 0.23604326478731336 - 0.9436054290094268im\n 0.02425907548108349 - 0.09697734399682581im\n -0.02874262221672827 + 0.11490266682744071im\n -0.012486303726337864 + 0.04991458308125314im\n 0.0021788988420742656 - 0.008710671163639695im\n 0.003315696243315579 - 0.013254649020993737im\n 0.0004783799167270374 - 0.0019121913768802164im\n -0.0005321860005208545 + 0.002127501741453898im\n -0.00022922468934527792 + 0.0009163154999455728im\n 3.488976040818906e-5 - 0.00013948585671455274im\n ⋮\n 3.4889623097778416e-5 - 0.00013948495774455865im\n -0.00022920280839420075 + 0.0009163183842559104im\n -0.0005321832601997748 + 0.002127504834803301im\n 0.00047831378297903676 - 0.0019122050686719114im\n 0.003315636840205554 - 0.013254660810430115im\n 0.002179032782628568 - 0.008710625673328575im\n -0.012486082389081983 + 0.04991466317856004im\n -0.028743219992033532 + 0.11490247437051933im\n 0.024258779264420986 - 0.0969774095552969im"
},
"metadata": {},
"execution_count": 11
}
],
"cell_type": "code",
"source": [
"ρ = scfres.ρ[:, 1, 1, 1] # converged density, first spin component\n",
"ψ_fourier = scfres.ψ[1][:, 1] # first k-point, all G components, first eigenvector"
],
"metadata": {},
"execution_count": 11
},
{
"cell_type": "markdown",
"source": [
"Transform the wave function to real space and fix the phase:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=4}",
"image/png": 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]
},
"metadata": {},
"execution_count": 12
}
],
"cell_type": "code",
"source": [
"ψ = ifft(basis, basis.kpoints[1], ψ_fourier)[:, 1, 1]\n",
"ψ /= (ψ[div(end, 2)] / abs(ψ[div(end, 2)]));\n",
"\n",
"using Plots\n",
"x = a * vec(first.(DFTK.r_vectors(basis)))\n",
"p = plot(x, real.(ψ), label=\"real(ψ)\")\n",
"plot!(p, x, imag.(ψ), label=\"imag(ψ)\")\n",
"plot!(p, x, ρ, label=\"ρ\")\n",
"plot!(p, x, tot_local_pot, label=\"tot local pot\")"
],
"metadata": {},
"execution_count": 12
}
],
"nbformat_minor": 3,
"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"
}
},
"nbformat": 4
}