Localisation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3030d1b5",
   "metadata": {},
   "source": [
    "# Shell Structure Indicators in Atoms\n",
    "This notebook explores various shell-structure indicators for atomic ions using [`AtomDB`](https://atomdb.qcdevs.org/api/index.html).\n",
    "\n",
    "One of the simplest, and most widely used, descriptors is the Laplacian of the electron density, $\\rho(r)$: \n",
    "$$\n",
    "\\nabla^2 \\rho(\\mathbf{r}) = \\tfrac{d^2 \\rho(r)}{dr^2} + \\tfrac{2}{r} \\tfrac{d \\rho(r)}{dr}\n",
    "$$\n",
    "One can also use the electron localization function (ELF)\n",
    "$$\n",
    "\\xi(r) = \\frac{t(r)-t_w(r)}{t_{TF}(r)}\n",
    "$$\n",
    "or the localized orbital locator (LOL) or nighness indicator,\n",
    "$$\n",
    "L(r) = \\frac{t(r)}{t_{TF}(r)}\n",
    "$$\n",
    "where $t(r)$ is the (positive-definite) kinetic energy density, \n",
    "$$\n",
    "t_{TF}(r) = \\frac{3}{10} (3 \\pi^2)^{2/3} \\rho(r)^{5/3}\n",
    "$$\n",
    "is the Thomas-Fermi kinetic energy density, and \n",
    "$$\n",
    "t_w(r) = \\frac{1}{8 \\rho(r)} \\left( \\frac{d \\rho(r)}{dr} \\right)^2\n",
    "$$\n",
    "is the Weizsäcker kinetic energy density.\n",
    "\n",
    "To map these onto a sensible interval, we choose a hyperbolic tangent mapping, though this is a bit unconventional. For an (arbitrary) shell-structure indicator $\\eta(r)$, one uses,\n",
    "\n",
    "$$\n",
    "\\tanh(\\eta(r)^{-1}-\\eta(r))\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c06afaf",
   "metadata": {},
   "source": [
    "# If using Google Co-Lab, uncomment the line below and run it to install AtomDB. \n",
    "# If AtomDB is already installed in your local environment you do not need to do this.\n",
    "#!pip install qc-atomdb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d7ea4ecb-6698-40ba-900c-7d2fd82e11cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Install key tools\n",
    "import numpy as np\n",
    "from atomdb import load\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "088b7fc0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute the Weizsacker kinetic energy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29e0e75c-1fa5-4388-b9eb-1068fe6eb5d5",
   "metadata": {},
   "source": [
    "relevant functions from AtomDB library: "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06f30a25-2628-4f43-a430-c2261b8e6bd4",
   "metadata": {},
   "source": [
    "dens_func:    Return a cubic spline of the electronic density.\\\n",
    "d_dens_func:  Return a cubic spline of the first derivative of the electronic density.\\\n",
    "dd_dens_func: Return a cubic spline of the electronic density Laplacian.\\\n",
    "ked_func:     Return a cubic spline of the kinetic energy density."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2c7093a-a887-42c6-9da4-626d3c69163f",
   "metadata": {},
   "source": [
    "\n",
    "$\\xi_{\\sigma}(r) = \\frac{\\rho_{\\sigma}(r) \\kappa_{\\sigma}^{BE}(r) [\\rho_{\\alpha}, \\rho_{\\alpha}]}{(2/3)\\{(3/10)(6\\pi^2)^{2/3} \\rho_{\\sigma}^{5/3}(r)\\}}$\\\n",
    "$\\rho(r) = $ dens\\\n",
    "$\\kappa_{\\sigma}^{BE}(r) [\\rho_{\\alpha}, \\rho_{\\alpha}]=  \\frac{2}{3} \\frac{\\tau_{\\sigma}(r) - \\tau_{\\sigma}^{W}(r)}{\\rho_{\\sigma}}$\\\n",
    "$\\tau_{\\sigma}=$ ked_func\\\n",
    "$\\tau_{\\sigma}^{W}(r)=\\sum_{i=1}^{N_{\\sigma}} \\frac{\\nabla \\rho(r) \\nabla \\rho(r)}{8 \\rho_{\\sigma}(r)}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5fac4125",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Evaluate the density and its derivatives on a grid\n",
    "def evaluate_splines(atom_obj,grid):\n",
    "    ''' Compute the density, its derivatives, and the kinetic energy density on a grid\n",
    "    Parameters\n",
    "    ----------\n",
    "    atom_obj : AtomDB object\n",
    "        AtomDB object for the species of interest.\n",
    "    grid : np.ndarray\n",
    "        Grid of points where the density and its derivatives are evaluated\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    rho : np.ndarray\n",
    "        Density\n",
    "    grad_rho : np.ndarray\n",
    "        Radial gradient of the density\n",
    "    lapl_rho : np.ndarray\n",
    "        Radial Laplacian of the density\n",
    "    tau : np.ndarray\n",
    "        Positive-definite kinetic energy density\n",
    "    '''\n",
    "    # Get the cubic splines for the density and its derivatives,\n",
    "    # 't' indicates the total density (sum of spin-up and spin-down)\n",
    "    dens_spline = atom_obj.dens_func(spin=\"t\")\n",
    "    d_dens_spline = atom_obj.d_dens_func(spin=\"t\")\n",
    "    dd_dens_spline = atom_obj.dd_dens_func(spin=\"t\")\n",
    "    tau_spline = atom_obj.ked_func(spin=\"t\")\n",
    "\n",
    "    # Evaluate the density and its derivatives on the grid\n",
    "    rho = dens_spline(grid)\n",
    "    grad_rho = d_dens_spline(grid)\n",
    "    lapl_rho = dd_dens_spline(grid) + 2.0 * d_dens_spline(grid)/grid\n",
    "    tau = tau_spline(grid)\n",
    "\n",
    "    return rho, grad_rho, lapl_rho, tau\n",
    "\n",
    "# Evaluate the Weizsacker kinetic energy density\n",
    "def tau_w(rho,grad_rho):\n",
    "    ''' Compute the Weizsacker kinetic energy density\n",
    "    Parameters\n",
    "    ----------\n",
    "    rho : np.ndarray\n",
    "        Density evaluated on a grid\n",
    "    grad_rho : np.ndarray\n",
    "        Radial gradient of the density evaluated on the same grid\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    tau_W : np.ndarray\n",
    "        Weizsacker kinetic energy density\n",
    "    '''\n",
    "\n",
    "    # Check to make sure that the density and gradient of the density have the same shape/size.\n",
    "    if rho.shape != grad_rho.shape:\n",
    "        raise ValueError(\"The density and its gradient must have the same shape.\")\n",
    "\n",
    "    return grad_rho**2 / (8 * rho)\n",
    "\n",
    "\n",
    "# Evaluate the Thomas-Fermi kinetic energy density\n",
    "def tau_tf(rho):\n",
    "    ''' Compute the Thomas-Fermi kinetic energy density\n",
    "    Parameters\n",
    "    ----------\n",
    "    rho : np.ndarray\n",
    "        Density evaluated on a grid\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    tau_TF : np.ndarray\n",
    "        Thomas-Fermi kinetic energy density\n",
    "    '''\n",
    "    #I feel like the first formula is right, but the second formula seems to give\n",
    "    #a better result.\n",
    "    return (3.0 / 10.0) * (3.0 * np.pi ** 2) ** (2.0 / 3.0) * rho ** (5.0 / 3.0)\n",
    "    #return (3.0 / 10.0) * (6.0 * np.pi ** 2) ** (2.0 / 3.0) * rho ** (5.0 / 3.0)\n",
    "\n",
    "# Electron localization indicator\n",
    "def xi_elf(tau,tau_w,tau_tf):\n",
    "    ''' Compute the electron localization indicator\n",
    "    Parameters\n",
    "    ----------\n",
    "    tau : np.ndarray\n",
    "        Positive-definite kinetic energy density\n",
    "    tau_w : np.ndarray\n",
    "        Weizsacker kinetic energy density\n",
    "    tau_tf : np.ndarray\n",
    "        Thomas-Fermi kinetic energy density\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    xi_elf : np.ndarray\n",
    "        Electron localization indicator. This is the quantity,\n",
    "        which goes for 0 to +infinity, that we map to a finite\n",
    "        interval to indicate shells.\n",
    "    '''\n",
    "    # Ensure the input arrays all have the same size\n",
    "    if tau.shape != tau_w.shape or tau.shape != tau_tf.shape:\n",
    "        raise ValueError(\"The kinetic energy densities must have the same shape.\")\n",
    "\n",
    "    # We want to ensure that we don't overflow as the Thomas-Fermi k.e. density in\n",
    "    # the denominator gets too small\n",
    "    # Initialize the array to zero\n",
    "    xi_elf = np.zeros_like(tau)\n",
    "    xi_elf = np.where(tau_tf < np.finfo(float).tiny, xi_elf, (tau - tau_w) / tau_tf)\n",
    "\n",
    "    return xi_elf\n",
    "\n",
    "# Localized Orbital Locator\n",
    "def xi_lol(tau,tau_tf):\n",
    "    ''' Compute the localized orbital locator\n",
    "    Parameters\n",
    "    ----------\n",
    "    tau : np.ndarray\n",
    "        Positive-definite kinetic energy density\n",
    "    tau_tf : np.ndarray\n",
    "        Thomas-Fermi kinetic energy density\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    xi_lol : np.ndarray\n",
    "        Localized orbital locator. This is the quantity,\n",
    "        which goes for 0 to +infinity, that we map to a finite\n",
    "        interval to indicate shells.\n",
    "    '''\n",
    "    # Ensure the input arrays all have the same size\n",
    "    if tau.shape != tau_tf.shape:\n",
    "        raise ValueError(\"The kinetic energy densities must have the same shape.\")\n",
    "\n",
    "    # We want to ensure that we don't overflow as the Thomas-Fermi k.e. density in\n",
    "    # the denominator gets too small\n",
    "    # Initialize the array to zero\n",
    "    xi_lol = np.zeros_like(tau)\n",
    "    xi_lol = np.where(tau_tf < np.finfo(float).eps, xi_lol, tau / tau_tf)\n",
    "\n",
    "    return xi_lol\n",
    "\n",
    "# Mapping to [0,1] using the hyperbolic tangent\n",
    "def loc_index(xi, inverse=True):\n",
    "    ''' Map the localization index to the interval [0,1] using the hyperbolic tangent\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    xi : np.ndarray\n",
    "        Localization index\n",
    "    inverse : bool, optional\n",
    "        If True, large values of xi correspond to high localization.   `\n",
    "        If False, large values of xi correspond to low localization.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    loc_index : np.ndarray\n",
    "        Localization index mapped to the interval [0,1]\n",
    "    '''\n",
    "    loc_index = np.tanh(xi - xi**(-1))\n",
    "\n",
    "    if inverse:\n",
    "        loc_index *= -1\n",
    "\n",
    "    return loc_index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "37ac7ca5-6daa-4b83-9fda-7342c311e6ce",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load Data From Server, Neon Atom in Slater Basis\n",
    "atom_obj = load(elem=\"Zn\", charge=0, mult=1, dataset=\"gaussian\")\n",
    "\n",
    "# Choose points to evaluate points. Avoid the origin to prevent division by zero.\n",
    "rad_grid = np.linspace(0.001, 6.0, 1000)\n",
    "\n",
    "# Compute the key quantities of interest,\n",
    "rho, grad_rho, lapl_rho, tau = evaluate_splines(atom_obj,rad_grid)\n",
    "tau_w_array = tau_w(rho,grad_rho)\n",
    "tau_tf_array = tau_tf(rho)\n",
    "xi_elf_array = xi_elf(tau,tau_w_array,tau_tf_array)\n",
    "xi_lol_array = xi_lol(tau,tau_tf_array)\n",
    "loc_index_elf = loc_index(xi_elf_array, inverse=True)\n",
    "loc_index_lol = loc_index(xi_lol_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9cf13f19",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the localized orbital locator, electron localization function, and Laplacian.\n",
    "plt.figure()\n",
    "plt.plot(rad_grid, loc_index_elf, label=\"Electron Localization Function\")\n",
    "plt.plot(rad_grid, loc_index_lol, label=\"Localized Orbital Locator\")\n",
    "#plt.plot(rad_grid, lapl_rho, label=\"Laplacian of the Density\")\n",
    "# Set x and y limits\n",
    "plt.ylim(-1, 1)\n",
    "plt.xlim(0, 5)\n",
    "plt.ylabel(\"Radius (Bohr)\")\n",
    "plt.ylabel(\"Localization Index\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "# Plot the Laplacian.\n",
    "plt.figure()\n",
    "#plt.plot(rad_grid, loc_index_elf, label=\"Electron Localization Function\")\n",
    "#plt.plot(rad_grid, loc_index_lol, label=\"Localized Orbital Locator\")\n",
    "plt.ylim(-1000, 1000)\n",
    "plt.xlim(0, 5)\n",
    "plt.plot(rad_grid, lapl_rho, label=\"Laplacian of the Density\")\n",
    "plt.xlabel(\"Radius (Bohr)\")\n",
    "plt.ylabel(\"Localization Index\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}