{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generating a basic Grid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grid.ipynb\n",
    "\n",
    "- Creates a basic grid by specifying the number of points. Each grid depends on the number of radial/angular blocks that is multiplied by the number of points per block. \n",
    "\n",
    "- Naturally, with a greater number of points, the calculation is more accurate and expensive. \n",
    "\n",
    "- Here, we do an example with the Boron atom. Additionally, we include a 2D plot to see how the points are distributed in space. \n",
    "\n",
    "- Lastly, we create a 3D plot showing the convergence of the energy with respect to the number of points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import plotly.graph_objects as go\n",
    "from CADMium import Psgrid\n",
    "from CADMium import Kohnsham\n",
    "\n",
    "#Distance of the nucley from grid center\n",
    "a =  5\n",
    "\n",
    "#Grid Options\n",
    "NP = 5 #Number of points per block\n",
    "NM =  [3,3] #Number of blocks [angular, radial]\n",
    "L = np.arccosh(15./a)#Maximum radial coordinate value\n",
    "loc = np.array(range(-4,5)) #Non inclusive on upper bound\n",
    "\n",
    "#Create and initialize grid object\n",
    "grid = Psgrid(NP, NM, a, L, loc)\n",
    "grid.initialize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fa0918f9ca0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(dpi=100)\n",
    "\n",
    "ax.scatter(np.vstack((-np.flip(grid.Z), grid.Z)), \n",
    "            np.vstack((-np.flip(grid.Y), grid.Y)))\n",
    "\n",
    "# The Boron atom is located at one of the dense areas.\n",
    "# If two atoms are present, each one is located at each foci. \n",
    "# The separation distance translate into the distance between foci. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How much would our grid affect a calculation?  \n",
    "\n",
    "Let us redo the previous procedure with the ability of changing both the number of blocks and points per block. \n",
    "Don't fret too much on each of the small details of the calculation, you'll be able to abstract them as you follow more examples. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the number of points that we are going to explore. \n",
    "# We use very small values to make it go fast. \n",
    "\n",
    "points_per_block = [7]\n",
    "ang_points = [3, 5, 7]\n",
    "rad_points = [3, 5, 7]\n",
    "energy = []\n",
    "all_ang = []\n",
    "all_rad = []\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " iter    Total Energy     HOMO Eigenvalue         Res       \n",
      "\n",
      "----------------------------------------------------------- \n",
      "\n",
      "    1      -27.85187      -2.76665e-01       +1.00000e+00\n",
      "    2      -25.48169      -4.21852e-01       +1.46361e-01\n",
      "    3      -24.55273      -4.69748e-01       +7.05942e-02\n",
      "    4      -24.21184      -4.86792e-01       +3.41545e-02\n",
      "    5      -24.08530      -4.92447e-01       +1.71583e-02\n",
      "    6      -24.03953      -4.94155e-01       +8.75097e-03\n",
      "    7      -24.02406      -4.94571e-01       +4.41074e-03\n",
      "    8      -24.01737      -4.94717e-01       +2.37986e-03\n",
      "    9      -24.01626      -4.94601e-01       +1.22774e-03\n",
      "   10      -24.01604      -4.94522e-01       +6.31166e-04\n",
      "   11      -24.01606      -4.94473e-01       +3.24030e-04\n",
      "   12      -24.01612      -4.94445e-01       +1.66164e-04\n",
      "   13      -24.01617      -4.94429e-01       +8.51265e-05\n",
      "   14      -24.01620      -4.94421e-01       +4.35799e-05\n",
      "   15      -24.01622      -4.94416e-01       +2.22995e-05\n",
      "   16      -24.01623      -4.94414e-01       +1.14069e-05\n",
      "   17      -24.01623      -4.94413e-01       +5.83399e-06\n",
      " iter    Total Energy     HOMO Eigenvalue         Res       \n",
      "\n",
      "----------------------------------------------------------- \n",
      "\n",
      "    1      -28.13381      -1.35263e-01       +1.00000e+00\n",
      "    2      -25.24803      -2.98326e-01       +1.59366e-01\n",
      "    3      -24.16902      -3.58970e-01       +8.33263e-02\n",
      "    4      -23.80344      -3.81395e-01       +4.15207e-02\n",
      "    5      -23.68091      -3.90414e-01       +2.08619e-02\n",
      "    6      -23.64357      -3.94111e-01       +1.07453e-02\n",
      "    7      -23.63448      -3.95609e-01       +5.61351e-03\n",
      "    8      -23.63346      -3.96210e-01       +2.84760e-03\n",
      "    9      -23.63434      -3.96493e-01       +1.64363e-03\n",
      "   10      -23.63590      -3.96559e-01       +8.62630e-04\n",
      "   11      -23.63687      -3.96581e-01       +4.50125e-04\n",
      "   12      -23.63743      -3.96587e-01       +2.34110e-04\n",
      "   13      -23.63774      -3.96589e-01       +1.21437e-04\n",
      "   14      -23.63791      -3.96589e-01       +6.28507e-05\n",
      "   15      -23.63800      -3.96588e-01       +3.24711e-05\n",
      "   16      -23.63805      -3.96588e-01       +1.67689e-05\n",
      "   17      -23.63807      -3.96588e-01       +8.65555e-06\n",
      " iter    Total Energy     HOMO Eigenvalue         Res       \n",
      "\n",
      "----------------------------------------------------------- \n",
      "\n",
      "    1      -27.83082      -2.95307e-01       +1.00000e+00\n",
      "    2      -25.71877      -4.52539e-01       +1.48269e-01\n",
      "    3      -24.86640      -5.07378e-01       +7.64401e-02\n",
      "    4      -24.55315      -5.28981e-01       +3.56528e-02\n",
      "    5      -24.44030      -5.36482e-01       +1.76132e-02\n",
      "    6      -24.40135      -5.38959e-01       +8.87665e-03\n",
      "    7      -24.38923      -5.39698e-01       +4.46973e-03\n",
      "    8      -24.38396      -5.40020e-01       +2.39187e-03\n",
      "    9      -24.38390      -5.39938e-01       +1.23567e-03\n",
      "   10      -24.38418      -5.39872e-01       +6.33072e-04\n",
      "   11      -24.38444      -5.39828e-01       +3.24961e-04\n",
      "   12      -24.38462      -5.39802e-01       +1.66727e-04\n",
      "   13      -24.38473      -5.39788e-01       +8.55058e-05\n",
      "   14      -24.38479      -5.39779e-01       +4.37975e-05\n",
      "   15      -24.38482      -5.39775e-01       +2.24166e-05\n",
      "   16      -24.38483      -5.39773e-01       +1.14660e-05\n",
      "   17      -24.38484      -5.39771e-01       +5.86277e-06\n",
      " iter    Total Energy     HOMO Eigenvalue         Res       \n",
      "\n",
      "----------------------------------------------------------- \n",
      "\n",
      "    1      -27.73104      -2.37631e-01       +1.00000e+00\n",
      "    2      -25.38780      -4.04895e-01       +1.54734e-01\n",
      "    3      -24.46449      -4.60200e-01       +7.95738e-02\n",
      "    4      -24.13455      -4.79057e-01       +3.80463e-02\n",
      "    5      -24.01586      -4.85170e-01       +1.89430e-02\n",
      "    6      -23.97468      -4.86944e-01       +9.61860e-03\n",
      "    7      -23.96196      -4.87333e-01       +4.84081e-03\n",
      "    8      -23.95601      -4.87480e-01       +2.60575e-03\n",
      "    9      -23.95569      -4.87317e-01       +1.34488e-03\n",
      "   10      -23.95584      -4.87212e-01       +6.88668e-04\n",
      "   11      -23.95603      -4.87150e-01       +3.52830e-04\n",
      "   12      -23.95617      -4.87116e-01       +1.80848e-04\n",
      "   13      -23.95625      -4.87097e-01       +9.26052e-05\n",
      "   14      -23.95630      -4.87087e-01       +4.73711e-05\n",
      "   15      -23.95633      -4.87081e-01       +2.42147e-05\n",
      "   16      -23.95634      -4.87078e-01       +1.23727e-05\n",
      "   17      -23.95635      -4.87077e-01       +6.32047e-06\n",
      " iter    Total Energy     HOMO Eigenvalue         Res       \n",
      "\n",
      "----------------------------------------------------------- \n",
      "\n",
      "    1      -31.15721      -4.71411e-02       +1.00000e+00\n",
      "    2      -25.04459      -2.01558e-01       +2.44070e-01\n",
      "    3      -23.05259      -2.43010e-01       +1.18335e-01\n",
      "    4      -22.39443      -2.46425e-01       +5.97137e-02\n",
      "    5      -22.17192      -2.42830e-01       +2.96003e-02\n",
      "    6      -22.09417      -2.39592e-01       +1.48213e-02\n",
      "    7      -22.06573      -2.37572e-01       +7.45135e-03\n",
      "    8      -22.05631      -2.36458e-01       +3.73692e-03\n",
      "    9      -22.05046      -2.35878e-01       +1.90525e-03\n",
      "   10      -22.04857      -2.35579e-01       +9.66113e-04\n",
      "   11      -22.04774      -2.35429e-01       +4.89302e-04\n",
      "   12      -22.04736      -2.35354e-01       +2.48034e-04\n",
      "   13      -22.04718      -2.35316e-01       +1.25817e-04\n",
      "   14      -22.04710      -2.35298e-01       +6.38668e-05\n",
      "   15      -22.04705      -2.35289e-01       +3.24417e-05\n",
      "   16      -22.04703      -2.35284e-01       +1.64907e-05\n",
      "   17      -22.04702      -2.35282e-01       +8.38777e-06\n",
      " iter    Total Energy     HOMO Eigenvalue         Res       \n",
      "\n",
      "----------------------------------------------------------- \n",
      "\n",
      "    1      -27.85810      -2.56719e-01       +1.00000e+00\n",
      "    2      -25.49116      -4.16210e-01       +1.54027e-01\n",
      "    3      -24.55624      -4.68619e-01       +7.90912e-02\n",
      "    4      -24.21984      -4.86945e-01       +3.81190e-02\n",
      "    5      -24.09901      -4.92878e-01       +1.89401e-02\n",
      "    6      -24.05728      -4.94595e-01       +9.66290e-03\n",
      "    7      -24.04457      -4.94966e-01       +4.87450e-03\n",
      "    8      -24.03864      -4.95104e-01       +2.64141e-03\n",
      "    9      -24.03841      -4.94943e-01       +1.36651e-03\n",
      "   10      -24.03862      -4.94840e-01       +7.02018e-04\n",
      "   11      -24.03885      -4.94778e-01       +3.60105e-04\n",
      "   12      -24.03901      -4.94744e-01       +1.84400e-04\n",
      "   13      -24.03911      -4.94725e-01       +9.43074e-05\n",
      "   14      -24.03917      -4.94715e-01       +4.81841e-05\n",
      "   15      -24.03920      -4.94710e-01       +2.46010e-05\n",
      "   16      -24.03921      -4.94707e-01       +1.25539e-05\n",
      "   17      -24.03922      -4.94705e-01       +6.40463e-06\n",
      " iter    Total Energy     HOMO Eigenvalue         Res       \n",
      "\n",
      "----------------------------------------------------------- \n",
      "\n",
      "    1      -27.43654      -1.65412e-01       +1.00000e+00\n",
      "    2      -24.78830      -3.33232e-01       +1.58872e-01\n",
      "    3      -23.81365      -3.83609e-01       +8.28597e-02\n",
      "    4      -23.48505      -3.98478e-01       +4.09655e-02\n",
      "    5      -23.37073      -4.02390e-01       +2.06317e-02\n",
      "    6      -23.33215      -4.03052e-01       +1.06205e-02\n",
      "    7      -23.31975      -4.02900e-01       +5.46911e-03\n",
      "    8      -23.31684      -4.02644e-01       +2.75276e-03\n",
      "    9      -23.31487      -4.02494e-01       +1.47969e-03\n",
      "   10      -23.31495      -4.02343e-01       +7.59680e-04\n",
      "   11      -23.31508      -4.02260e-01       +3.88025e-04\n",
      "   12      -23.31518      -4.02216e-01       +1.98104e-04\n",
      "   13      -23.31524      -4.02193e-01       +1.01043e-04\n",
      "   14      -23.31527      -4.02180e-01       +5.15096e-05\n",
      "   15      -23.31529      -4.02174e-01       +2.62641e-05\n",
      "   16      -23.31530      -4.02171e-01       +1.33971e-05\n",
      "   17      -23.31530      -4.02169e-01       +6.83600e-06\n",
      " iter    Total Energy     HOMO Eigenvalue         Res       \n",
      "\n",
      "----------------------------------------------------------- \n",
      "\n",
      "    1      -27.92058      -2.58146e-01       +1.00000e+00\n",
      "    2      -25.55068      -4.12107e-01       +1.52829e-01\n",
      "    3      -24.60402      -4.63601e-01       +7.70864e-02\n",
      "    4      -24.26597      -4.82169e-01       +3.75801e-02\n",
      "    5      -24.14328      -4.88585e-01       +1.87645e-02\n",
      "    6      -24.10047      -4.90660e-01       +9.58610e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    7      -24.08707      -4.91243e-01       +4.82854e-03\n",
      "    8      -24.08116      -4.91501e-01       +2.62135e-03\n",
      "    9      -24.08098      -4.91392e-01       +1.35464e-03\n",
      "   10      -24.08123      -4.91313e-01       +6.95867e-04\n",
      "   11      -24.08150      -4.91263e-01       +3.57345e-04\n",
      "   12      -24.08168      -4.91234e-01       +1.83205e-04\n",
      "   13      -24.08179      -4.91218e-01       +9.38200e-05\n",
      "   14      -24.08185      -4.91209e-01       +4.80092e-05\n",
      "   15      -24.08189      -4.91204e-01       +2.45549e-05\n",
      "   16      -24.08191      -4.91201e-01       +1.25525e-05\n",
      "   17      -24.08192      -4.91200e-01       +6.41453e-06\n",
      " iter    Total Energy     HOMO Eigenvalue         Res       \n",
      "\n",
      "----------------------------------------------------------- \n",
      "\n",
      "    1      -25.85664      -4.28936e-02       +1.00000e+00\n",
      "    2      -22.05906      -1.51416e-01       +2.22167e-01\n",
      "    3      -20.97351      -1.46369e-01       +1.12019e-01\n",
      "    4      -20.63250      -1.29429e-01       +5.55638e-02\n",
      "    5      -20.50740      -1.18679e-01       +2.70844e-02\n",
      "    6      -20.45576      -1.13076e-01       +1.32632e-02\n",
      "    7      -20.43280      -1.10270e-01       +6.55342e-03\n",
      "    8      -20.42403      -1.08891e-01       +3.28304e-03\n",
      "    9      -20.41707      -1.08190e-01       +1.61186e-03\n",
      "   10      -20.41433      -1.07879e-01       +8.08838e-04\n",
      "   11      -20.41300      -1.07725e-01       +4.06351e-04\n",
      "   12      -20.41234      -1.07649e-01       +2.04729e-04\n",
      "   13      -20.41201      -1.07611e-01       +1.03250e-04\n",
      "   14      -20.41184      -1.07593e-01       +5.21464e-05\n",
      "   15      -20.41176      -1.07584e-01       +2.63651e-05\n",
      "   16      -20.41172      -1.07579e-01       +1.33403e-05\n",
      "   17      -20.41169      -1.07577e-01       +6.75589e-06\n",
      " iter    Total Energy     HOMO Eigenvalue         Res       \n",
      "\n",
      "----------------------------------------------------------- \n",
      "\n",
      "    1      -27.62561      -2.72600e-01       +1.00000e+00\n",
      "    2      -25.32017      -4.10686e-01       +1.54645e-01\n",
      "    3      -24.40633      -4.51256e-01       +7.23368e-02\n",
      "    4      -24.06370      -4.64173e-01       +3.43996e-02\n",
      "    5      -23.93178      -4.67351e-01       +1.71416e-02\n",
      "    6      -23.88120      -4.67718e-01       +8.69707e-03\n",
      "    7      -23.86322      -4.67448e-01       +4.36908e-03\n",
      "    8      -23.85354      -4.67266e-01       +2.32696e-03\n",
      "    9      -23.85107      -4.66977e-01       +1.19000e-03\n",
      "   10      -23.85008      -4.66817e-01       +6.06344e-04\n",
      "   11      -23.84967      -4.66730e-01       +3.08909e-04\n",
      "   12      -23.84950      -4.66685e-01       +1.57263e-04\n",
      "   13      -23.84943      -4.66661e-01       +8.00280e-05\n",
      "   14      -23.84939      -4.66649e-01       +4.07177e-05\n",
      "   15      -23.84938      -4.66642e-01       +2.07157e-05\n",
      "   16      -23.84937      -4.66639e-01       +1.05400e-05\n",
      "   17      -23.84937      -4.66638e-01       +5.36416e-06\n",
      " iter    Total Energy     HOMO Eigenvalue         Res       \n",
      "\n",
      "----------------------------------------------------------- \n",
      "\n",
      "    1      -27.85681      -2.56279e-01       +1.00000e+00\n",
      "    2      -25.48978      -4.16132e-01       +1.54421e-01\n",
      "    3      -24.55442      -4.68507e-01       +7.88662e-02\n",
      "    4      -24.21791      -4.86818e-01       +3.79028e-02\n",
      "    5      -24.09705      -4.92743e-01       +1.89366e-02\n",
      "    6      -24.05532      -4.94455e-01       +9.66276e-03\n",
      "    7      -24.04266      -4.94825e-01       +4.86401e-03\n",
      "    8      -24.03662      -4.94971e-01       +2.64177e-03\n",
      "    9      -24.03643      -4.94804e-01       +1.36407e-03\n",
      "   10      -24.03665      -4.94698e-01       +6.99816e-04\n",
      "   11      -24.03688      -4.94636e-01       +3.58594e-04\n",
      "   12      -24.03705      -4.94601e-01       +1.83448e-04\n",
      "   13      -24.03715      -4.94582e-01       +9.37636e-05\n",
      "   14      -24.03720      -4.94572e-01       +4.78969e-05\n",
      "   15      -24.03723      -4.94567e-01       +2.44527e-05\n",
      "   16      -24.03725      -4.94564e-01       +1.24781e-05\n",
      "   17      -24.03726      -4.94563e-01       +6.36639e-06\n",
      " iter    Total Energy     HOMO Eigenvalue         Res       \n",
      "\n",
      "----------------------------------------------------------- \n",
      "\n",
      "    1      -28.16779      -2.20862e-01       +1.00000e+00\n",
      "    2      -25.39209      -3.68727e-01       +1.58612e-01\n",
      "    3      -24.32385      -4.12442e-01       +8.16640e-02\n",
      "    4      -23.94515      -4.26379e-01       +3.90672e-02\n",
      "    5      -23.81212      -4.30137e-01       +1.94522e-02\n",
      "    6      -23.76732      -4.30815e-01       +9.91383e-03\n",
      "    7      -23.75474      -4.30701e-01       +4.99025e-03\n",
      "    8      -23.74811      -4.30605e-01       +2.69149e-03\n",
      "    9      -23.74804      -4.30346e-01       +1.38548e-03\n",
      "   10      -23.74834      -4.30199e-01       +7.08552e-04\n",
      "   11      -23.74861      -4.30118e-01       +3.62174e-04\n",
      "   12      -23.74880      -4.30075e-01       +1.84878e-04\n",
      "   13      -23.74891      -4.30052e-01       +9.43049e-05\n",
      "   14      -23.74897      -4.30040e-01       +4.80871e-05\n",
      "   15      -23.74900      -4.30034e-01       +2.45116e-05\n",
      "   16      -23.74902      -4.30031e-01       +1.24913e-05\n",
      "   17      -23.74903      -4.30029e-01       +6.36508e-06\n",
      " iter    Total Energy     HOMO Eigenvalue         Res       \n",
      "\n",
      "----------------------------------------------------------- \n",
      "\n",
      "    1      -27.81218      -6.48243e-02       +1.00000e+00\n",
      "    2      -24.65717      -2.53466e-01       +1.83328e-01\n",
      "    3      -23.52601      -3.22381e-01       +9.09170e-02\n",
      "    4      -23.16765      -3.35203e-01       +4.75393e-02\n",
      "    5      -23.04564      -3.36579e-01       +2.40426e-02\n",
      "    6      -23.00387      -3.35972e-01       +1.23563e-02\n",
      "    7      -22.99033      -3.35153e-01       +6.35448e-03\n",
      "    8      -22.98750      -3.34551e-01       +3.20097e-03\n",
      "    9      -22.98508      -3.34230e-01       +1.71162e-03\n",
      "   10      -22.98512      -3.33987e-01       +8.75199e-04\n",
      "   11      -22.98525      -3.33857e-01       +4.46072e-04\n",
      "   12      -22.98535      -3.33790e-01       +2.27278e-04\n",
      "   13      -22.98542      -3.33755e-01       +1.15779e-04\n",
      "   14      -22.98546      -3.33737e-01       +5.89747e-05\n",
      "   15      -22.98548      -3.33729e-01       +3.00417e-05\n",
      "   16      -22.98549      -3.33724e-01       +1.53064e-05\n",
      "   17      -22.98549      -3.33722e-01       +7.80227e-06\n",
      " iter    Total Energy     HOMO Eigenvalue         Res       \n",
      "\n",
      "----------------------------------------------------------- \n",
      "\n",
      "    1      -31.03930      -5.00866e-02       +1.00000e+00\n",
      "    2      -25.06771      -1.97200e-01       +2.38218e-01\n",
      "    3      -23.08997      -2.34769e-01       +1.17563e-01\n",
      "    4      -22.42445      -2.37284e-01       +5.88306e-02\n",
      "    5      -22.19305      -2.33522e-01       +2.90469e-02\n",
      "    6      -22.10938      -2.30260e-01       +1.45201e-02\n",
      "    7      -22.07755      -2.28251e-01       +7.29077e-03\n",
      "    8      -22.06647      -2.27151e-01       +3.64971e-03\n",
      "    9      -22.05950      -2.26579e-01       +1.85852e-03\n",
      "   10      -22.05709      -2.26289e-01       +9.40777e-04\n",
      "   11      -22.05599      -2.26143e-01       +4.75680e-04\n",
      "   12      -22.05547      -2.26071e-01       +2.40791e-04\n",
      "   13      -22.05522      -2.26035e-01       +1.21992e-04\n",
      "   14      -22.05510      -2.26017e-01       +6.18635e-05\n",
      "   15      -22.05504      -2.26008e-01       +3.13979e-05\n",
      "   16      -22.05501      -2.26004e-01       +1.59468e-05\n",
      "   17      -22.05499      -2.26002e-01       +8.10485e-06\n",
      " iter    Total Energy     HOMO Eigenvalue         Res       \n",
      "\n",
      "----------------------------------------------------------- \n",
      "\n",
      "    1      -28.15547      -1.61171e-01       +1.00000e+00\n",
      "    2      -25.11139      -3.35052e-01       +1.59761e-01\n",
      "    3      -23.98812      -3.93157e-01       +8.21289e-02\n",
      "    4      -23.59137      -4.12427e-01       +4.04434e-02\n",
      "    5      -23.45067      -4.18037e-01       +2.03572e-02\n",
      "    6      -23.40166      -4.19353e-01       +1.04408e-02\n",
      "    7      -23.38494      -4.19465e-01       +5.37458e-03\n",
      "    8      -23.38005      -4.19320e-01       +2.70210e-03\n",
      "    9      -23.37736      -4.19229e-01       +1.45514e-03\n",
      "   10      -23.37708      -4.19096e-01       +7.45595e-04\n",
      "   11      -23.37704      -4.19022e-01       +3.80785e-04\n",
      "   12      -23.37705      -4.18982e-01       +1.94446e-04\n",
      "   13      -23.37707      -4.18962e-01       +9.92569e-05\n",
      "   14      -23.37709      -4.18951e-01       +5.06598e-05\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   15      -23.37710      -4.18945e-01       +2.58550e-05\n",
      "   16      -23.37710      -4.18942e-01       +1.31965e-05\n",
      "   17      -23.37710      -4.18941e-01       +6.73864e-06\n",
      " iter    Total Energy     HOMO Eigenvalue         Res       \n",
      "\n",
      "----------------------------------------------------------- \n",
      "\n",
      "    1      -27.85737      -2.56324e-01       +1.00000e+00\n",
      "    2      -25.48978      -4.16122e-01       +1.54220e-01\n",
      "    3      -24.55444      -4.68503e-01       +7.87766e-02\n",
      "    4      -24.21794      -4.86817e-01       +3.78407e-02\n",
      "    5      -24.09708      -4.92744e-01       +1.89209e-02\n",
      "    6      -24.05535      -4.94457e-01       +9.66861e-03\n",
      "    7      -24.04273      -4.94827e-01       +4.86643e-03\n",
      "    8      -24.03662      -4.94978e-01       +2.65179e-03\n",
      "    9      -24.03645      -4.94808e-01       +1.36823e-03\n",
      "   10      -24.03668      -4.94701e-01       +7.01665e-04\n",
      "   11      -24.03692      -4.94639e-01       +3.59471e-04\n",
      "   12      -24.03708      -4.94603e-01       +1.83925e-04\n",
      "   13      -24.03718      -4.94584e-01       +9.40011e-05\n",
      "   14      -24.03724      -4.94574e-01       +4.79995e-05\n",
      "   15      -24.03727      -4.94569e-01       +2.44944e-05\n",
      "   16      -24.03728      -4.94566e-01       +1.24944e-05\n",
      "   17      -24.03729      -4.94565e-01       +6.37225e-06\n"
     ]
    }
   ],
   "source": [
    "#Nuclear charges on centers AB\n",
    "Za  = 5\n",
    "Zb = 0\n",
    "\n",
    "#Set polaization. 1 Unpolarized, 2 Polarized\n",
    "pol = 2\n",
    "\n",
    "#Assign electronic structure\n",
    "Nmo = [[3,3], [1,0]]\n",
    "N   = [[2,2], [1,0]]\n",
    "\n",
    "optKS = {}\n",
    "\n",
    "for i in ang_points:\n",
    "    for j in rad_points:\n",
    "        \n",
    "        #Grid Options\n",
    "        a =  1.0\n",
    "        NP = 7 #Number of points per block\n",
    "        NM =  [i,j] #Number of blocks [angular, radial]\n",
    "        L = np.arccosh(15./a) #Maximum radial coordinate value\n",
    "        loc = np.array(range(-4,5)) #Non inclusive on upper bound\n",
    "\n",
    "        #Create and initialize grid object\n",
    "        grid = Psgrid(NP, NM, a, L, loc)\n",
    "        grid.initialize()\n",
    "\n",
    "        #Kohn Sham object\n",
    "        KS = Kohnsham(grid, Za, Zb, pol, Nmo, N, optKS)\n",
    "        KS.scf(optKS)\n",
    "\n",
    "        energy.append(KS.E.E)\n",
    "        all_ang.append(i)\n",
    "        all_rad.append(j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(projection='3d')\n",
    "\n",
    "\n",
    "ax.scatter(all_ang, all_rad, energy)\n",
    "\n",
    "ax.set_xlabel('X Label')\n",
    "ax.set_ylabel('Y Label')\n",
    "ax.set_zlabel('Z Label')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Optional. If `plotly` is installed:\n",
    "\n",
    "# fig = go.Figure(data=[go.Scatter3d(\n",
    "#     x=all_ang,\n",
    "#     y=all_rad,\n",
    "#     z=energy,\n",
    "#     mode='markers',\n",
    "#     marker=dict(\n",
    "#         size=5,\n",
    "#         color=energy,                # set color to an array/list of desired values\n",
    "#         colorscale='Viridis',   # choose a colorscale\n",
    "#         opacity=0.8\n",
    "#     )\n",
    "# )])\n",
    "\n",
    "# fig.show()"
   ]
  }
 ],
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