v0.6.4/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": [],
   "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": [],
   "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   -0.143697315381                   -0.42    7.0         \n",
      "  2   -0.156054236401       -1.91       -1.10    1.0   2.05ms\n",
      "  3   -0.156771127149       -3.14       -1.57    1.0   1.75ms\n",
      "  4   -0.157013765528       -3.62       -2.11    1.0   1.63ms\n",
      "  5   -0.156930211636   +   -4.08       -1.91    2.0   1.93ms\n",
      "  6   -0.157056376920       -3.90       -3.61    1.0   1.46ms\n",
      "  7   -0.157056404273       -7.56       -4.03    1.0   1.48ms\n",
      "  8   -0.157056406868       -8.59       -4.80    1.0   1.53ms\n",
      "  9   -0.157056406914      -10.33       -5.34    1.0   1.74ms\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Energy breakdown (in Ha):\n    Kinetic             0.0380293 \n    AtomicLocal         -0.3163463\n    LocalNonlinearity   0.1212606 \n\n    total               -0.157056406914"
     },
     "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 [-0.055676487596999225, 0.0, 0.0]\n [0.05568269960062737, 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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