v0.5.8/examples/custom_potential.ipynb

{
 "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": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Main.var\"##419\".CustomPotential"
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "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, q::Real)\n",
    "    # = ∫ V(r) exp(-ix⋅q) dx\n",
    "    -el.α * exp(- (q * el.L)^2 / 2)\n",
    "end"
   ],
   "metadata": {},
   "execution_count": 4
  },
  {
   "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": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "2-element Vector{Main.var\"##419\".CustomPotential}:\n Main.var\"##419\".CustomPotential(X)\n Main.var\"##419\".CustomPotential(X)"
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "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\n",
      "---   ---------------   ---------   ---------   ----\n",
      "  1   -0.143581349776                   -0.42    8.0\n",
      "  2   -0.156036092192       -1.90       -1.10    1.0\n",
      "  3   -0.156768710397       -3.14       -1.56    2.0\n",
      "  4   -0.157045890563       -3.56       -2.32    2.0\n",
      "  5   -0.157055546819       -5.02       -2.99    2.0\n",
      "  6   -0.157056387622       -6.08       -3.71    1.0\n",
      "  7   -0.157056406098       -7.73       -4.37    1.0\n",
      "  8   -0.157056406912       -9.09       -5.40    2.0\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Energy breakdown (in Ha):\n    Kinetic             0.0380295 \n    AtomicLocal         -0.3163467\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-8, ρ=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 [-0.05568392329096156, 0.0, 0.0]\n [0.05568743546713474, 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": "Plot{Plots.GRBackend() n=4}",
      "image/png": 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      ]
     },
     "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\n",
    "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": 11
  }
 ],
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