{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Li2 PDFT Inversion - Orbital Invert"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from CADMium import Kohnsham, Pssolver, Psgrid, Partition, Inverter\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "Perform PDFT Calculation. \n",
    "Currently the method used is \"OrbitalInvert\". \n",
    "But original code may have used \"WuYang\". \n",
    "Code should run as it is but for idential calculations increase to grid size to: [7,12,12]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----> Begin SCF calculation for *Interacting* Fragments\n",
      "\n",
      "                Total Energy (a.u.)                                Inversion                \n",
      "\n",
      "                __________________                ____________________________________     \n",
      "\n",
      "Iteration         A              B                  iters      optimality        res       \n",
      "\n",
      "___________________________________________________________________________________________ \n",
      "\n",
      "    1            -7.32464        -7.32464             9       +4.669e-11      +1.000e+00\n",
      "    2            -7.32866        -7.32866            10       +2.640e-11      +4.569e-02\n",
      "    3            -7.34060        -7.34060             8       +2.320e-11      +2.900e-02\n",
      "    4            -7.34060        -7.34060             9       +6.667e-15      +2.343e-02\n",
      "    5            -7.33583        -7.33583             8       +5.507e-14      +9.256e-03\n",
      "    6            -7.33822        -7.33822             6       +5.684e-11      +6.618e-03\n",
      "    7            -7.33610        -7.33610             6       +2.891e-12      +7.186e-03\n",
      "    8            -7.33881        -7.33881             6       +5.221e-13      +4.741e-03\n",
      "    9            -7.33881        -7.33881             6       +4.692e-14      +4.233e-03\n",
      "   10            -7.33747        -7.33747             6       +3.988e-14      +1.798e-03\n",
      "   11            -7.33727        -7.33727             5       +6.818e-15      +2.017e-03\n",
      "   12            -7.33780        -7.33780             5       +4.633e-15      +2.049e-04\n",
      "   13            -7.33806        -7.33806             4       +1.979e-14      +9.114e-04\n",
      "   14            -7.33787        -7.33787             4       +1.868e-11      +2.684e-04\n",
      "   15            -7.33769        -7.33769             4       +7.529e-13      +2.949e-04\n",
      "   16            -7.33770        -7.33770             4       +1.610e-13      +1.668e-04\n",
      "   17            -7.33779        -7.33779             4       +2.142e-14      +7.718e-05\n",
      "   18            -7.33782        -7.33782             3       +3.512e-15      +7.973e-05\n",
      "   19            -7.33780        -7.33780             3       +7.010e-15      +1.557e-05\n",
      "   20            -7.33778        -7.33778             3       +6.368e-15      +3.423e-05\n",
      "   21            -7.33778        -7.33778             3       +5.012e-15      +6.247e-06\n",
      "   22            -7.33778        -7.33778             2       +6.697e-11      +1.409e-05\n",
      "   23            -7.33778        -7.33778             3       +5.048e-15      +4.038e-06\n",
      "   24            -7.33778        -7.33778             2       +1.795e-11      +5.011e-06\n",
      "   25            -7.33779        -7.33779             2       +1.820e-11      +2.902e-06\n",
      "   26            -7.33779        -7.33779             2       +4.423e-12      +1.351e-06\n",
      "   27            -7.33779        -7.33779             2       +1.832e-12      +1.447e-06\n",
      "   28            -7.33778        -7.33778             2       +1.640e-12      +2.644e-07\n",
      "   29            -7.33778        -7.33778             2       +4.237e-14      +6.179e-07\n",
      "   30            -7.33778        -7.33778             2       +1.793e-13      +1.044e-07\n",
      "   31            -7.33778        -7.33778             2       +2.103e-14      +2.435e-07\n",
      "   32            -7.33778        -7.33778             2       +3.179e-14      +8.058e-08\n",
      "   33            -7.33778        -7.33778             2       +3.674e-15      +8.225e-08\n",
      "   34            -7.33778        -7.33778             2       +6.347e-15      +5.243e-08\n",
      "   35            -7.33778        -7.33778             2       +4.465e-15      +2.293e-08\n",
      "   36            -7.33778        -7.33778             2       +4.829e-15      +2.604e-08\n",
      "   37            -7.33778        -7.33778             2       +3.640e-15      +4.308e-09\n",
      "   38            -7.33778        -7.33778             2       +5.013e-15      +1.112e-08\n",
      "   39            -7.33778        -7.33778             2       +4.546e-15      +1.868e-09\n",
      "   40            -7.33778        -7.33778             1       +5.572e-11      +3.127e-09\n",
      "   41            -7.33778        -7.33778             1       +7.961e-11      +3.317e-09\n",
      "   42            -7.33778        -7.33778             2       +5.179e-15      +1.781e-09\n",
      "   43            -7.33778        -7.33778             1       +6.557e-11      +3.011e-09\n",
      "   44            -7.33778        -7.33778             2       +6.550e-15      +1.382e-09\n",
      "   45            -7.33778        -7.33778             1       +3.592e-11      +2.160e-09\n",
      "   46            -7.33778        -7.33778             2       +4.416e-15      +8.979e-10\n"
     ]
    }
   ],
   "source": [
    "a = 5.122/2\n",
    "#Nuclear charge for fragments A and B\n",
    "Za, Zb = 3,3\n",
    "#Set polarization 1-Unpolarized, 2-Polarized\n",
    "pol = 2\n",
    "#Fragment a electrons [alpha, beta]\n",
    "Nmo_a = [[2,1]] #Number of molecular orbitals to calculate\n",
    "N_a   = [[2,1]]\n",
    "#Ensemble mix\n",
    "nu_a = 1\n",
    "#Fragment b electrons\n",
    "Nmo_b = [[2,1]]\n",
    "N_b   = [[2,1]]\n",
    "#Ensemble mix\n",
    "nu_b = 1\n",
    "\n",
    "#Molecular elctron configuration\n",
    "Nmo_m = [[3,3]]\n",
    "N_m   = [[3,3]]\n",
    "\n",
    "#Grid Options\n",
    "NP = 7 #Number of points per block\n",
    "NM =  [6,6] #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",
    "grid = Psgrid(NP, NM, a, L, loc)\n",
    "grid.initialize()\n",
    "\n",
    "\n",
    "\n",
    "#Initialize required objects. And make calculation in isolated fragments for initial guess. \n",
    "\n",
    "part = Partition(grid, Za, Zb, pol, Nmo_a, N_a, nu_a, Nmo_b, N_b, nu_b, { \"kinetic_part_type\" : 'inversion',\n",
    "                                                                          \"vp_calc_type\"      : \"component\",\n",
    "                                                                          \"ab_sym\"            : True,\n",
    "                                                                          \"ens_spin_sym\"      : True,})\n",
    "\n",
    "#Setup inverter object\n",
    "mol_solver = Pssolver(grid, Nmo_m, N_m)\n",
    "part.inverter = Inverter(grid, mol_solver, {\"invert_type\"     : \"orbitalinvert\",\n",
    "                                            \"tol_invert\"      : 1e-10,\n",
    "                                            \"max_iter_invert\" : 100,\n",
    "                                            \"disp\"            : False,\n",
    "                                            \"ab_sym\"          : True,\n",
    "                                            \"ens_spin_sym\"    : True,})\n",
    "\n",
    "part.optPartition.isolated = True\n",
    "part.scf({\"disp\"  : False,\n",
    "          \"alpha\" : [0.6],\n",
    "          \"e_tol\" : 1e-12})\n",
    "\n",
    "D0_frag_a = part.KSa.n.copy()\n",
    "D0_frag_b = part.KSa.n.copy()\n",
    "\n",
    "\n",
    "#Turn off iterative linear solver for each solver\n",
    "part.KSa.solver[0][0].optSolver.iter_lin_solver = False\n",
    "part.KSa.solver[0][1].optSolver.iter_lin_solver = False\n",
    "\n",
    "\n",
    "part.optPartition.isolated   = False\n",
    "\n",
    "part.scf({\"disp\"       : True,\n",
    "          \"alpha\"      : [0.6],\n",
    "          \"max_iter\"   : 200,\n",
    "          \"e_tol\"      : 1e-9,\n",
    "          \"continuing\" : True})\n",
    "\n",
    "#Store full densities under the presence of vp.\n",
    "Dvp_frag_a = part.KSa.n.copy()\n",
    "Dvp_frag_b = part.KSb.n.copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "Generate Figure 9. Parititon Potential. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-7.0, 7.0, -7.0, 7.0)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "full, x,y = grid.plotter(part.V.vp[:,0])\n",
    "fig, ax = plt.subplots(dpi=300)\n",
    "\n",
    "plot = ax.contourf(x,y,full, levels=22, cmap=\"plasma\")\n",
    "\n",
    "ax.set_aspect('equal')\n",
    "ax.set_xlim([-7,7])\n",
    "ax.set_ylim([-7,7])\n",
    "\n",
    "ax.scatter(5.122/2, 0, color='white', s=20)\n",
    "ax.scatter(-5.122/2, 0, color='white', s=15)\n",
    "\n",
    "ax.axis('off')\n",
    "\n",
    "# fig.colorbar(plot)\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "Generate Figure 9. Difference between Fragment Density and Isolated Atomic Density. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fd6d81e1b80>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x600 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "D_grid, x, y = grid.plotter(D0_frag_a[:,0])\n",
    "D_vp_grid, _, _ = grid.plotter(Dvp_frag_a[:,0])\n",
    "\n",
    "fig, ax = plt.subplots(dpi=150)\n",
    "plot = plt.contourf(x,y, D_vp_grid - D_grid, levels=100, cmap=\"jet\")\n",
    "\n",
    "ax.set_aspect('equal')\n",
    "ax.set_xlim([-5,5])\n",
    "ax.set_ylim([-5,5])\n",
    "\n",
    "fig.colorbar(plot)\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "Generate Figure 11. Components of the Partition Potential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4e24814dc598490683639ffe7a9f28be",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.plot(*args, scalex=True, scaley=True, data=None, **kwargs)>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_axis, vp      = grid.axis_plot(part.V.vp[:,0])\n",
    "x_axis, vp_kin  = grid.axis_plot(part.V.vp_kin[:,0])\n",
    "x_axis, vp_xc   = grid.axis_plot(part.V.vp_x[:,0] + part.V.vp_c[:,0] )\n",
    "x_axis, vp_hext = grid.axis_plot( part.V.vp_h[:,0] + part.V.vp_pot[:,0])\n",
    "\n",
    "fig, ax = plt.subplots(dpi=150)\n",
    "\n",
    "ax.set_title(\"Li$_2$\")\n",
    "ax.axvline(x=a, color=\"gray\", ls=':', alpha=0.5)\n",
    "\n",
    "ax.plot(x_axis, vp,  label='$v_p(r)$', lw=4, color=\"#FD9903\")\n",
    "# ax.plot(x_axis, vp_kin, label='Kinetic')\n",
    "# ax.plot(x_axis, vp_xc, label='XC')\n",
    "# ax.plot(x_axis, vp_hext, label=\"H + Vext\")\n",
    "\n",
    "ax.set_xlim(0,7)\n",
    "ax.set_ylim(-0.12, 0.12)\n",
    "\n",
    "ax.legend()\n",
    "\n",
    "plt.plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "Generate Table 9. Energies and Components of Ep, in atomic Units"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Ea': -7.337784849443342,\n",
       " 'Eb': -7.337784849443342,\n",
       " 'Ef': -14.675569698886685,\n",
       " 'Tsf': 14.51597760325188,\n",
       " 'Eksf': array([[-3.87274135, -3.62105118]]),\n",
       " 'Enucf': -33.88821469087027,\n",
       " 'Exf': -3.0418434859179895,\n",
       " 'Ecf': -0.30099393918618395,\n",
       " 'Ehf': 8.03950481383588,\n",
       " 'Vhxcf': 11.684634289090774,\n",
       " 'Ep': -1.8069182239952444,\n",
       " 'Ep_pot': -3.678211853854383,\n",
       " 'Ep_kin': 0.004784336086627761,\n",
       " 'Ep_hxc': 1.8665092937725107,\n",
       " 'Et': -16.48248792288193,\n",
       " 'Vnn': 1.757126122608356,\n",
       " 'E': -14.725361800273573,\n",
       " 'evals_a': array([-1.8178079 , -0.11856278, -1.81052559]),\n",
       " 'evals_b': array([-1.8178079 , -0.11856278, -1.81052559]),\n",
       " 'Ep_h': 1.886610621676736,\n",
       " 'Ep_x': 0.007092235124383617,\n",
       " 'Ep_c': -0.02719356302860887}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "values = {}\n",
    "for i in part.E.__dict__:\n",
    "    if i.startswith(\"__\") is False:\n",
    "        values.update({i : getattr(part.E, i)})\n",
    "values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "eebd6ff11bd34af3aa3a88b47f90f776",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib widget\n",
    "\n",
    "fig, ax = plt.subplots(subplot_kw={\"projection\": \"3d\"}, dpi=300)\n",
    "surf = ax.plot_surface(x, y, full, cmap=\"plasma\", alpha=1.0, \n",
    "                       linewidth=20, antialiased=True)\n",
    "\n",
    "ax.grid(False)\n",
    "ax.set_axis_off()\n",
    "ax.dist = 6\n",
    "ax.set_facecolor(\"white\")\n",
    "\n",
    "fig.show()"
   ]
  }
 ],
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