Carbon.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "from sympy import oo\n",
    "import numpy as np\n",
    "from itertools import product\n",
    "from scipy.linalg import eig\n",
    "from sympy import diff\n",
    "import time as time\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy.plotting import plot\n",
    "# %matplotlib notebook \n",
    "%matplotlib inline\n",
    "from IPython.display import Math\n",
    "sp.init_printing()\n",
    "\n",
    "r, r1, r2, zeta, zeta1, zeta2 = sp.symbols(\"r, r1, r2, zeta, zeta1, zeta2\")\n",
    "n = sp.Symbol('n',integer=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def STO(zeta, n, r=r):\n",
    "    return (2*zeta)**n*(2*zeta/sp.factorial(2*n))**(1/2)*r**(n-1)*sp.exp(-zeta*r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# S Overlap Integrate\n",
    "def S_int(f1, f2):\n",
    "    return sp.integrate(f1*f2*r*r ,(r, 0, +oo))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# H core = kinetics energy + electron and nuclear potential energy\n",
    "def Hs_int(f1, f2, Z):\n",
    "    return sp.integrate(f1*(-((1/2)*(1/r)*diff(diff(r*f2, r), r))-((Z/r)*f2))*r*r, (r,0,+oo))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# H core = kinetics energy + electron and nuclear potential energy\n",
    "def Hp_int(f1, f2, Z):\n",
    "    return sp.integrate(f1*(-((1/2)*(1/r)*diff(diff(r*f2, r), r))+((1/r**2)*f2)-((Z/r)*f2))*r*r, (r,0,+oo))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Returns the core hamiltonian matrix\n",
    "def Hs_matrix(fs, Z):\n",
    "\n",
    "    H = np.zeros((len(fs),len(fs)))\n",
    "    for i in range(len(fs)):\n",
    "        for j in range(len(fs)):\n",
    "            H[i, j] =  Hs_int(fs[i], fs[j], Z)\n",
    "\n",
    "    return H    \n",
    "\n",
    "# Returns the overlap matrix\n",
    "def S_matrix(fs):\n",
    "\n",
    "    S = np.zeros((len(fs),len(fs)))\n",
    "    for i in range(len(fs)):\n",
    "        for j in range(len(fs)):\n",
    "            S[i, j] =  S_int(fs[i], fs[j])\n",
    "\n",
    "    return S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Returns the core hamiltonian matrix\n",
    "def Hp_matrix(fp, Z):\n",
    "\n",
    "    H = np.zeros((len(fp),len(fp)))\n",
    "    for i in range(len(fp)):\n",
    "        for j in range(len(fp)):\n",
    "            H[i, j] =  Hp_int(fp[i], fp[j], Z)\n",
    "\n",
    "    return H    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Repulsion_electron(zetas, l):\n",
    "    \n",
    "    f1=STO(zetas[0][0], zetas[0][1], r1)\n",
    "    f2=STO(zetas[1][0], zetas[1][1], r1)\n",
    "    f3=STO(zetas[2][0], zetas[2][1], r2)\n",
    "    f4=STO(zetas[3][0], zetas[3][1], r2)\n",
    "    fs = [f1, f2, f3, f4]\n",
    "    \n",
    "    B = (1/r1**(l+1))*sp.integrate(f3*f4*r2**(l+2) ,(r2, 0, r1)) + r1**l*sp.integrate(f3*f4*r2**(1-l) ,(r2, r1, +oo))\n",
    "    A = sp.integrate(f1*f2*r1*r1*B ,(r1, 0, +oo))\n",
    "    return A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculates Density matrix\n",
    "# P need to be changed if the atom have unpaired electron\n",
    "def Ps_matrix(Co):\n",
    "\n",
    "    P = np.zeros([Co.shape[0], Co.shape[0]])\n",
    "\n",
    "    for t in range(Co.shape[0]):\n",
    "        for u in range(Co.shape[0]):\n",
    "            P[t][u] = 2* Co[t][0]*Co[u][0] + 2* Co[t][1]*Co[u][1]\n",
    "    return P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculates Density matrix\n",
    "# P need to be changed if the atom have unpaired electron\n",
    "def Pp_matrix(Co):\n",
    "\n",
    "    P = np.zeros([Co.shape[0], Co.shape[0]])\n",
    "\n",
    "    for t in range(Co.shape[0]):\n",
    "        for u in range(Co.shape[0]):\n",
    "            P[t][u] = 2* Co[t][0]*Co[u][0]\n",
    "    return P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def J_matrix(zetai, zetaj, l):\n",
    "    J = np.zeros((len(zetai), len(zetai), len(zetaj), len(zetaj)))\n",
    "\n",
    "    rs = list(product(range(len(zetai)),repeat=2))\n",
    "    tu = list(product(range(len(zetaj)),repeat=2))\n",
    "\n",
    "    for r, s in rs:\n",
    "        for t, u in tu:\n",
    "            J[r,s,t,u] = Repulsion_electron((zetai[r], zetai[s], zetaj[t], zetaj[u]), l)\n",
    "    return J\n",
    "\n",
    "def K_matrix(zetai, zetaj, l):\n",
    "    K = np.zeros((len(zetai), len(zetai), len(zetaj), len(zetaj)))\n",
    "\n",
    "    rs = list(product(range(len(zetai)),repeat=2))\n",
    "    tu = list(product(range(len(zetaj)),repeat=2))\n",
    "\n",
    "    for r, s in rs:\n",
    "        for t, u in tu:\n",
    "            K[r,s,t,u] = Repulsion_electron((zetai[r], zetaj[u], zetaj[t], zetai[s]), l)\n",
    "    return K\n",
    "\n",
    "# Caculate G Matrix for 1s\n",
    "def Gs_matrix(Cos, Cop, Jss, Kss, Jsp, Ksp):\n",
    "\n",
    "    G = np.zeros((Cos.shape[0], Cos.shape[0]))\n",
    "    Ps = Ps_matrix(Cos)\n",
    "    Pp = Pp_matrix(Cop)\n",
    "    \n",
    "    rs = list(product(range( Cos.shape[0]),repeat=2))\n",
    "    tu = list(product(range( Cos.shape[0]),repeat=2))\n",
    "    ij = list(product(range( Cop.shape[0]),repeat=2))\n",
    "\n",
    "    for r, s in rs:\n",
    "        g = 0\n",
    "        for t, u in tu:\n",
    "            int1 = Jss[r, s, t, u]\n",
    "            int2 = Kss[r, s, t, u]\n",
    "            g+= Ps[t, u] * (int1 - 0.5 * int2)\n",
    "        for i, j in ij:\n",
    "            int1 = Jsp[r, s, i, j]\n",
    "            int2 = Ksp[r, s, i, j]\n",
    "            g+= Pp[i, j] * (int1 - 0.5 * int2)\n",
    "        G[r, s] = g\n",
    "    return G\n",
    "\n",
    "# Returns the Fock matrix\n",
    "def Fs_matrix(fs, Z, Cos, Cop, Jss, Kss, Jsp, Ksp):\n",
    "    return Hs_matrix(fs, Z) + Gs_matrix(Cos, Cop, Jss, Kss, Jsp, Ksp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Caculate G Matrix for p\n",
    "def Gp_matrix(Cos, Cop, Jpp, Kpp, Jps, Kps):\n",
    "\n",
    "    G = np.zeros((Cop.shape[0], Cop.shape[0]))\n",
    "    Ps = Ps_matrix(Cos)\n",
    "    Pp = Pp_matrix(Cop)\n",
    "    \n",
    "    rs = list(product(range( Cop.shape[0]),repeat=2))\n",
    "    tu = list(product(range( Cop.shape[0]),repeat=2))\n",
    "    ij = list(product(range( Cos.shape[0]),repeat=2))\n",
    "\n",
    "    for r, s in rs:\n",
    "        g = 0\n",
    "        for t, u in tu:\n",
    "            int1 = Jpp[r, s, t, u]\n",
    "            int2 = Kpp[r, s, t, u]\n",
    "            g+= Pp[t, u] * 0.5*(int1-int2)\n",
    "        for i, j in ij:\n",
    "            int1 = Jps[r, s, i, j]\n",
    "            int2 = Kps[r, s, i, j]\n",
    "            g+= Ps[i, j] * (int1 - 0.5 * int2)\n",
    "        G[r, s] = g\n",
    "    return G\n",
    "\n",
    "# Returns the Fock matrix\n",
    "def Fp_matrix(fp, Z, Cos, Cop, Jpp, Kpp, Jps, Kps):\n",
    "    return Hp_matrix(fp, Z) + Gp_matrix(Cos, Cop, Jpp, Kpp, Jps, Kps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# slove secular equation, return the energy and improved coeffients\n",
    "# the energy here is orbital energy for 1 electron\n",
    "def secular_eqn(F, S):\n",
    "    ei, C = eig(F, S)\n",
    "    \n",
    "    # sort eigvalue and eigvector from lower to higher\n",
    "    idx = ei.argsort()[::1]   \n",
    "    ei = ei[idx]\n",
    "    C = C[:,idx]\n",
    "\n",
    "    # eigvector from scipy.linalg.eig is not normalized, which is a bug\n",
    "    # this is to fix it\n",
    "    Co = np.zeros((C.shape[0],C.shape[0]))\n",
    "    inte = np.matmul(np.matmul(C.T, S), C)\n",
    "    for i in range(C.shape[0]):\n",
    "        for j in range(C.shape[0]):\n",
    "            Co[j][i]=C[j][i]/np.sqrt(inte[i][i])\n",
    "\n",
    "    return ei, Co"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "# return energy of atom\n",
    "def get_E0(e1, e2, Ps, Pp, Hs, Hp):\n",
    "    \n",
    "    E0 = e1[0].real + e1[1].real + e2[0].real + 0.5*(Ps*Hs).sum() + 0.5*(Pp*Hp).sum()\n",
    "    return E0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------ Initialization ------------------------------\n",
      "------------------------- Ignore repulsion integral ------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 7.522 \\quad \\zeta_2 = 5.123 \\quad \\zeta_3 = 1.831 \\quad \\zeta_4 = 1.153 \\quad \\zeta_5 = 2.730 \\quad \\zeta_6 = 1.257$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1s = c_{11} \\chi_1 + c_{21} \\chi_2 + c_{31} \\chi_3 + c_{41} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2s = c_{12} \\chi_1 + c_{22} \\chi_2 + c_{32} \\chi_3 + c_{42} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2p = c_{52} \\chi_5 + c_{62} \\chi_6$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = -0.349 \\quad c21 = -0.672 \\quad c31 = 0.045 \\quad c41 = -0.026$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = 0.132 \\quad c22 = 0.187 \\quad c32 = -1.559 \\quad c42 = 0.631$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c52 = -1.070 \\quad c62 = 0.105$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -17.990 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_2 = -4.303 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_3 \\; for \\; \\phi_3 = -4.478 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -53.54086 \\ hartree = -1456.90047 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------ Iteration 1 ------------------------------\n",
      "------- Iteration 1 needs more time to caculate Repulsion Integral ------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 7.522 \\quad \\zeta_2 = 5.123 \\quad \\zeta_3 = 1.831 \\quad \\zeta_4 = 1.153 \\quad \\zeta_5 = 2.730 \\quad \\zeta_6 = 1.257$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1s = c_{11} \\chi_1 + c_{21} \\chi_2 + c_{31} \\chi_3 + c_{41} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2s = c_{12} \\chi_1 + c_{22} \\chi_2 + c_{32} \\chi_3 + c_{42} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2p = c_{52} \\chi_5 + c_{62} \\chi_6$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = 0.219 \\quad c21 = 0.785 \\quad c31 = 0.021 \\quad c41 = -0.011$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = 0.008 \\quad c22 = -0.254 \\quad c32 = 0.628 \\quad c42 = 0.439$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c52 = 0.061 \\quad c62 = 0.956$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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3hvY+IiJ9QMhCwTm3GDjYySlXAo87bxmQbmbDunyDUO6l0JpWSxWRGBLOPoURQGGr74san+uaUO6l0JrmKohIDAlnKFg7z7l2TzS72cwKzKygtLTUP9lboZCWBtnZCgURiQnhDIUiILfV9zlAcXsnOucec87lO+fys7Ky/JMVFb3TfAQagSQiMSOcofAC8KXGUUizgTLnXEmX391bNQXQaqkiEjNCOST1KeA94HQzKzKzG83s62b29cZT/gFsA7YA/wPc2q0b9GYojB8Pe/dCeXnv3E9EJEziQ3Vh59znT/C6A2476RuEcn/mtlp3Nk+f3jv3FBEJg8ie0dybfQqgJiQRiXqRHQq9VVMYO9Y/KhREJMpFbij0ZvNRSgpcdRXs39879xMRCZPIDIXaWqiv773mI/A7sL36au/dT0QkDCIzFHprMbzWpk+Hjz/WCCQRiWqRGQq9tZdCa02jjlat6r17ioj0ssgMhd7aS6G1plBYsaL37iki0ssiOxR6s6YwdCjk5CgURCSqKRS6Y/p0KCjo3XuKiPSiyAyFpj6F3mw+Ah8Kmzaps1lEolZkhkK4agr5+f5Rnc0iEqUUCt2hzmYRiXKRGQrhGJIKMGSI72xWv4KIRKnIDIVwDEltkp+vmoKIRK3IDQUzvyZRb1Nns4hEscgMhYoK6NfPB0Nv08xmEYlikRkKvbmXQltNoaB+BRGJQpEbCr3dydxkyBD41Kdgx47w3F9EJIQiMxR6cy+F9qSnw9NP++W0RUSiSGSGQjibjwDmz/cb7qxeHb4yiIiEQHy4C3BSwtl8BHDxxf5x0SKYNi185eiGgwd9N8jatX7w1IYNkJkJb74JU6bA4sW+397Mb0ldVQVZWTBjBiQm+h1JzzoLzjzTv09EopM558Jdhm7Jz893BXV1MGYMPP98+AoyaZJfOXXhwvCVoRP19fDOO/Dee/DUU7Bunc/RI0cgOxsmTvR/4J2D4cN9i5xz/qithT17WnYfXbLEh8SMGbB8uZ+/96lPwfjxcMEFcPbZEIjMOqdILOnScM3IrClUVIS3+Qh8beFXv/J/LcMxX6IDH38Mv/2trwm89JL/4z98OFx7LcyZ4/+Ad/eTvnNQUuKvuWoVrFwJb73l//kAGRkwdy5ceSXMmwejR/f0v0pEektkhkK4m4/A9ys88ID/OD5/fliL4pxv/nngAXjjDZ9Tn/kM/O//wqWXnnp+mvlgGT4cLrqo5fnCQnj7bR8Qb7zhayX79vlK1JVX+mPatPBMJxGRkxPSSr+ZXWpmH5vZFjP7t3Ze/7KZlZrZ6sbjpi5duC+Ewty5vrF90aKwFuO99+DGG30zzrJlcO+9/o/100/D1VeHtkKVmwvXXedrJtu2+Xy8/34YOBB++EO/IsinPw3f/a7vk4+wlkqRmBSyUDCzOOAR4DLgTODzZnZmO6c+45yb0nj8tksXD/foI/ChdM45YetT2LULvvQlX4QVK+CXv4Tt2+Fb3/J9BuEwbhx85zu+1rJnD/zhD/4/0wMPwNSpvinrv/4LtmwJT/lE5MRCWVOYCWxxzm1zztUCTwNXnvJVg0H/kTPcNQXw/QqrVkFpaa/dsqHBB8CZZ8Lu3XDPPfDuu/CNb/Sprg2ysuDLX4YnnvAB8etf++f+z/+BG27wFa0//rFlwVsR6RtC2acwAihs9X0RMKud8z5jZnOBTcC3nXOF7ZzTomnCWF8Ihfnz4T//0zeoX3NNyG9XXOyba4JB/0f1V78KfadufbCe4iPFHKg8QHlNOWU1Zf6xuoyEQAKHaw4TsAABCxBncSTFJZEYn0hGcgbpyemkJ6eTkZLBl746lK99LYXCQj9o7OGH4Stfgdtv9z+6G2+E2bPV/yASbqEMhfZ+vdu2Kv8deMo5V2NmXwf+L3DhcRcyuxm4GWDM8OH+yb4QCtOn+6E3CxeGPBReesl/8q6shIcegq9+tef+gDrn2HZoGxv2b2DtvrVsO7St+dhVtotzc89l8a7Fx73v/JHns2TXkmOey+qXRWnlsTWnEWkj2H1kN4NTBpM7MJeczBwu/EUunzwyiVVLsnny72fwuz+cxhnjE7jjDt9JnpXVM/82EemekM1TMLM5wPedc5c0fn83gHPuxx2cHwccdM4N7Oy6+RMnuoL16+Evf4HPfrani919V1/tB+/v2BGSj7n19fDTn/oKyeTJvgP5jDNO7ZoVtRW8V/geS3YtofhIMf+7/n8pryknLyOPbYe2MSR1CHkZeYxJH0NeRh5jB41lYNJABiYPZEDSgOav+8X3IxAI0BBsIOiCBF2QumAdVXVVHK4+zKHqQxyuPkxZdRlF5UUUlRdRWF7oj7JCxqSPYeWelQDEEU/S0bFUF58OJVOYkzeJ2z49jWsuGUUgoOqDSA8I+zyF5cA4MxsD7AauBb7Q+gQzG+acK2n89lPAhhNetS81H4HvV3j2Wdi82c/m6kEVFX5+wbJlcMcd8JOfQHJy96/jnGNd6Tpe3PQir259leW7l3O07igBC3DRmIv44tlfZGr2VCYNncTEIRPpn3jqnfijGHXCcw5XHWbzwc1s3L/RHwc2snVvCR8d+C+WWgNLP4DrlmRwWr+pLDh7GheOn0P+8HxyB+RiamcSCYmQzmg2s8uB/wbigN87535oZvcCBc65F8zsx/gwqAcOArc45zZ2ds380093BZs2+cHxn/hEyMreZTt2+BrLNdfAXXf12GVLSuCKK/xQzkcega9/vXvvd86xtHApL29+mT+v+TM7y3YCMH3YdK464yryh+czJ3cOA5IG9FiZe0pVXRXLC9fwh5dX8vLqVRxNW0lF4hYsuRxnQYanDWdOzhzm5Mzh/FHnMzV7KglxCeEutkhf16VPUpG3zMXYsa5g61a/kE/T3gbhlp/vm46WL++Ry61bB5dfDgcO+Fayyy/v+ns3H9jMEx89wZ8++hPbD2/nwtEX0j+pP1eMu4LLx13OiAEjeqSMvWntWvjVY7U8/spHHM14jwET3yMx7z32N+xg1MBRlFaWck7uOcwdOZdPjP4EM0fMJDn+JKpUItEtSkMhL88VbN/u11w41cb1nnL//fAv/+KbkMaOPaVLvfkmXHWVH1760ktdW2+vur6ap9c+zfMbn+dvH/8Nw7g472Kun3Q9V024qkeag/qCo0fhmWfg8cfh/fchmFrMnM8tJWvGEjbVvM2avWtwOM4feT7xgXguHHMhF465kBnDZ6gmIRK1oTB6tCvYudPP3srNDXdxvF27YNQoPzPrP/7jpC/zyit+9m9yMvz1rzByZOfnFx8p5tHlj/KbFb+htLKUT0/4NLNHzOYLZ38hImsE3bFqFTz2GPzpT77v5eyz4abbD5I57R22H13DsxueZfWe1Tgc/RP7c9UZVzElewrz8+Zz1pCz1CchsShKQyE31xUUFfm1oDMywl2cFjfe6GsvS5ee1Cik117zK49OmOBXzhg8uONzP9zzIT9792f8Zd1faAg2cMX4K/jmrG9y0ZiLYu6PXUWFXwX2N7/xzW179vgBYTfdBBPzD/D2zrd4Y/sb7K3Yy7MbnwUgu382F+ddzPy8+VycdzHD04aH+V8h0iuiNBRGjHAFxcVQU+PXHuor/vAHP3lg8WI4//xuvXXRIvjkJ+H00+H11zsOhPeL3ue+xffx0uaXmDl8JufknsNtM29j7KBTa7KKFitX+nWY/vxnKC/3y27cdJNfDiQ7G3aV7WLRtkUs3LaQRdsWsb9yP9OGTaO2oZYFeQtYcNoC5o6aS0pCH5oaLtJzojQUhg1zBfv3Q11duItyrKNH/TKiV17pG7276I03/CijsWP91+0ta/3urnf5/tvfZ+G2hQxKGcSds+/kthm3kZ6S3oP/gOhRWelXiP3tb/0ifXl5ft2lL3/Z/6wTEyHogny450OWFS3juY3PsWTnEmoaakiKS2LuqLksOG0Bl5x2iZqaJJpEaSgMHeoKamvh0KFwF+V4t97qA2HHji5tWvD223DZZf6P1ptvHj+Ld/We1dz9+t1U1Faw6cAm7ppzF7fMuCVqOo57w8cf+0rc44/7Yb6DB8MXv+gDYsqUlpa+yrpKFu9czGtbX+PVra+yvnQ9U7OnUlJRwoLTFrAgbwHzT5vPkNQhYf33iJyCKA2FzExXkJwMRUXhLsrx1q716yF961vwr//a6anvvQf/9m9+Lb033/SbuDXZcnAL33vzezy19ikykjP49/P+nVtn3kq/hH4h/gdEr/p6vxrJH//o116aNct/rrjuOvjCF44fs1BUXsSibYt4deurLNy6kANVBwCYmj2VBact4LKxlzErZ5aGvkokidJQGDTIFWRl+Y+AfdH8+X6iwY4dHfZ5rF8P550HQ4b4QBg2zD9/oPIAP3j7B6woWcHqPav59uxvc9c5d5GerGainnTwoA+G3//ejwsAPw/yK1/xfTuDBh17fkOwgVV7VjXXIpbuWsrQ1KEcqj7E3FFzmZ83n/mnzefsIWerqUn6sigNhfR0V5CX53sV+6JXX/UN13/8o2+naGPXLjj3XP/J9d13/VbTNfU1PLL8Ee5bfB/lNeV8e9a3uevcu8juH6aNEWLItm3w5JN+aGt2tg+JBQv88iJXXgkD2pnwXV5TzuKdi1m4dSGvbXuNjfv9JPyhqUO59qxrmTx0MhflXcTIgScYUyzSu6I0FNLSXMHUqX6UT1/knN8Dc8sWP0S1VW1h/34/MKmkxBf/7LMdL256kbteu4tNBzdx6dhLuX/+/UwcMjGM/4DY5Jz/nPHMM/7YtQtmzvTNep/5jB8u3NEI6KLyIhZuXcii7YtYsnMJheV+9ffTMk7jojEXcVHeRcwbPY+sVC39KmEVpaGQmuoK5s6Fl18Od1E69vLLfm2KRx9tXrSoosKvnbd6tZ+TkDlhPXe8cgeLti3i6jOv5sapN3Lp2EvDXHABHxDLlvnhwY895rc3jY+HefN85W/+fD/QrP33+sUHX9/2Oq9vf523drzFkdojAFycdzETsyZywegLmDtqLoNSBrV/EZHQiNJQSElxBf/0T37Kb1/lnN80uV8/+MtfqEtO46ab/IzlX/zqEB/0+z6PLH+EtKQ07pt3H1/P/zrxgVAuWCsnyzm/zNZzz/nFcJOS/HiC/Hxfe/jkJ/2S5h11JdQH6ykoLuCt7W/x+vbXWVq4lKr6KgxjcvZkLh97OdOGTeP8UedrZJOEWpSGQlKSK/j8532bfV+2fDnMmkXwW3fypX338+cnG/jnh57k/1XdyYHKA3xt+te478L7yOx34qGr0jc45wcJ/P3v8MILvjYxaZJvFrz0Un9cfDGkdzIuoKa+huXFy3lrx1u8s+sd3i18t7kmcUbmGVwx7grOHno25+aeS15GnjqupSdFaSjEx7uCr33Nryfdx7mbv8Z3fjuBB3JmMPym26lJ3sX04dP56cU/ZUr2lHAXT07Rvn2+iem55/xw17IyiIuDOXN86+EFF8CMGb7pqSO1DbWsLFnJ4p2LWbxzMXXBOl7b+hrgl+NoWv115oiZTB02VUNg5VREaSgEAq7grrvgZz8Ld1FO6D++v4UfrbkHJj1JTtoI7l/wcz438XP69BeF6ut9zeGVV3yH9Suv+JpFWpof7nrhhXDRRXDWWRAIdHydhmAD60vXs7RwqT92LWVA0gA+3PshiXGJTM2eyuyc2Zw/8nymZE9RbUK6I0pDwcwV/OAH8L3vhbsoHaqsq+T6R/6b54ofIJB8hLvfqeHuuXeT+v0fhbto0ksOHPBzUF5/3R+bN/t+iC1b/ByV88+HuXP90ugnWsKruLyY93e/z7KiZSzbvYzlu5eT2S+TwvJCBqUMYsbwGcwbPY/xg8czffh07UwnHYniULj/fvjOd8JdlOMEXZAn1zzJt1+8m/11ReTuvoPX7vsmZ/zmT3DPPX6theuvD3cxJQx27YIlS/yGgUuWtMy9vOgiqK2F2bNbjo5GNjWpa6hj7b61LC9ezvLdy/lg9wfsPrK7edZ1Vr8srhh3Bdlp2UzJnsKU7CmMHTSWgHVSRZFYEMWh0GqoZ1+xZOcS7nztTgqKC4jfN51zjvyCFx+ZS1oafvG+Sy6B6mr40Y98Y7PEtL17/WJ9a9e2NDnV1vrX/umffO1h+vSWo4nFjfUAABAFSURBVO26WG1V1lXy0d6PWFG8ghUlK6iqr+Kv6/9KfbAegHmj51FZV8mkoZOYNHQSk4dOZkLWBA10iC1RHApPPOEXrekD1peu59Hlj/Lw8ofJTBxB2XM/5vSaL/LWm4Fjl8A+dMg3LpeUwN/+BuecE7YyS99TU+M3Dlq2zM+L+PvffZNTk5wcPwR28GC/odDZZ/uVdTvrxK6pr2HD/g2s3rOawrJC3tjxBh/t/YiDVQc5e8jZrNm3hiGpQzgz60wmZk1k0tBJjB88njMyz2Bo6lA1QUWfKA6F557ze1aG0cf7P+bexffy1JqnyB2Qy4Ksf+bJb9zJqOH9eOstv67RcXbv9iupLlrk51lcdllvF1siSFmZD4qVK2HFCl+TeO45CAb960lJcOaZPiBmz/aL+p1xhl86JS6u/Ws65yipKGHtvrWs27eOdaWNx751jE4fzZp9awAYkDSAMzLP4PTBpzMlewo5A3IYO2gsYweNZUBSO2t/SCSI4lB49VW/QE0rlZV+kbOCAjh82P9SDB3q/+6ec85JbYbWri0Ht3Df4vv400d/Ijk+mdtn3s7s4F08/LNMCgt9m3HTAnft2rsXvvEN/1Hwhz+Eb3+78+EoIq1UVfnVU9asOfYYO9b3VYBveho/3gdFZqZ/rekYNqz9/92ccxSVF7Fx/0Y+PvAxG/dvbP66qq6qub8CYEjqEObkzKF/Yn/yMvIYkz6GMRljGJM+hpwBOcQFOkgkCbcoDoWlS49pflm1Cn7+cz+JKCvL/49fUeEXOysv95+cbrnFj/o4Gc45lhUt46H3H2JZ0TL2HN3DbTNu47vnfpfFLw/hi1/0v3Cvv+4XVTuhigpfY1i6FE47DX71K38BkZN04ABs2gQbN7YcZvDSS364bJOUFD+HoqYGRo/2x5gx/jEnx//+tP0AdbT2KFsPbWXLwS1sObiFzQc2U9tQy1s736KovIig81WXOTlz+GD3B+QMyGFU+ihmjZhFYlwiuQNyyRmQQ+5A/5iRnKGmqfCI4lBYvdqvLYD/u3rjjb4afeutfkZpk6oqeOIJv8lKQoLfnvH++7u+tXNNfQ3PrHuGh95/iBUlKxiQNIC7z7ubGybfQHb/YfzP//j+7nPO8R/8u7VltHO+YH/5i0+1G26Af/mXE/coinRDfb0f+bRlS8tx5IifcL99u//QBH7EU3Gxr2Xk5PimqKbH4cP9B63hw/2RnQ3JjXPoahtqKSwrZNuhbeyt2MuG/RvYWbaTnWU7GZwymBc3vUiDawDgrCFnsXbfWpLjkxmeNpwRaSOYPmw6AMPShpHdP5th/YcxLG0YQ1KHMDhlsGodPSuKQ2HzZhg7llWr/FjvSy6Bhx/u+FN6ZaUf9POTn/jq9MMP+5UvO/qwsm7fOl74+AUeWPYApZWlTMicwO0zb+f6ydfTP7E/R4/CN7/pV9P8/OfhwQf9MkcnpbjYF+jBB30v4uc+5zvRO1tQR6QHOOebWnfsgJ07fQd3YaHfv6qw0I+N2LTp+J1vJ0/2gTJ0qO87GzrUH+PG+VAZPNj/nmVmQsagBmqTSthfW8jeir1sP7yd4iPF7D6ym91HdpOZksmrW1/laN3R5uufl3se7xS+g2Fk9stkSOoQJmROIBAIkJmSyeB+g8nsl3nMkZGcQUZKBgOSBmjobcfCHwpmdinwIBAH/NY595M2rycBjwPTgQPANc65HZ1dM9/MFRQXs7N2GHPm+NEX770HI0acuDyrVvmN3Feu9GvlP/KIf59zjg/3fsgrm1/hybVPsmbfGganDOYToz7BLTNu4aIxFzVXdwsK/EbwGRl+jPk993TcqdctH38MP/2p/21ctAiuvtr3Gi5Y4NdwTkrqgZuIdE8w6Jumiov9wLniYh8kO3f67rG9e/1yH3v3+tnab799/DXi4nxNPSPDb2A0aJAPlvJyv05Uejr0S6+god8e6pNKaEg6wNHAbo7aPiqC+zhcv5eUxEQ+2rea/ZX7OVh1EEfL360x6WPYfng7AAELkJ6czqCUQeQMyCE+EM/ApIGkJ6e3PCYPJCM5g9TEVAYkDSAtMa35MS0pjdTE1GhdoDK8oWBmccAmYD5QBCwHPu+cW9/qnFuBSc65r5vZtcBVzrlrOrtuvpl7bUc5X7srjYULffPRxG5sP1BfDz9/oI7v/XIDo+cuJWncEoaNLuO1Hf8A4JPjP8mC0xbw2TM/y9D+LXtkFhfDQw/5dfgGDYIHHvA1lB534IBvUlq82I9P3LHD19WvuQYGDvQrsI0b5xuChw/voUQSOXV1db52sX//scfBgy3HoUP+MTvbf5g7fNiHw5AhPlhamzUL3n+/5fukJL9syOw5DWwuOkxSxn7iB+wnLvUgKYMPUG0HCSYdoiHhEHUJBwnGl1PpDlBjZVS7MiqDh6lxlQAkWCJ1rvaY+80eNpdlJX6fluT4ZPon9ufMzDM5UHWA1MRUUhNSmx9zB+RSXV9NSkIKKfEp9EvoR2a/TIIuSHJ8MikJ/rmkuCSS45NJivePyfHJJMUlkRSf1PyYGEgk0DuDTcIeCnOA7zvnLmn8/m4A59yPW53zauM575lZPLAHyHKdFOpsS3STPl/NR2sCPPpoS+exc47ahlqq66uprq/mcPVh9lTsYU/FHkoqSig5UkJ1QzVv7XiLDaUbmDR4FitK3yFwdBgZxZ9l1uipXDfrMi6ePZTMxvk8xcXwwQd+M7XFi/2nnblz4d57u9l/cLIOHfIfvRYv9h/Hnn/e9xAGg/6Ii/MNvxdc4H+zBg/2iZWb65ue+veH1FR/9O/v/wGJicce8fH+iIs79ggE/KOZ/zoQ8F+rSUt6WDDo//dtfZSV+bmeBw74cRlHjrQ89uvnm6+OHm05Bgzw/SWVlf6oqfEfFteta3OzQB2nTSxja1E5JB6BpHJIKmfQsCMcPFwHqaWQWAGJFQwfXUHpngQYWIglVmKJR0lKO0p1QyWJlWOoGvQBLq6KYFwVABnl53NowJLmW6UGh3M0UHzM7ZOC6dQEDh/zXE5gOiXBj4gjkXiSiLNExiTMoqR+HXGWQLwlEG+JjEyZyN7a7f77gH8+O3k0ZfX7iLN44gLxJAQS6BeXRtDqiLN44gMtx/+94b6wh8LVwKXOuZsav78emOWc+0arc9Y2nlPU+P3WxnP2d3TdhKwU524NEB/vsIDDOcfMETNZsmvJMedNyJzAhv0bmr9PjEvkk+M/SVV9FWdlnUX+8HymDZtG+c48nnnGeP99HwJZWf5/uro6aGjw/8MOHOiH9113nf+AHjbBoP9t2LzZ19937vS9iElJ/iPVwYP+t2jWrJbxiU3OO89Poe2qpCT/m9Xa3LktO941BYSZ/5hXWtoSGGZ+z9F33235Ho59rsk55/iPjG219/xZZ/kpwK2NHu1rU63NmXP8e+fM8TWv1pKT/V+eJuPH+0b0jr4fN679/Tmlz2lwAaqCiVQHk6hqSKQqmER10D/WBBOaH6uDiVQHE2lwAY4GU6gJJvjDJZAaqGZvXQa1wQRqXTy1wQTS449QVDOEWhdPnYunLhhPjQuQkljOPhKojQtSG1dHfaCekf23s7FuCPWBehri62iIq6PeGsjqV0JJsD8NcXW4+Fpy4g5RFJcAcTUQVwtxtQysi6cs9XDj93UQV8uQylT2DSyFQJ1/LlBHRvkQDg3eCYH6xqMOjmYRSN9J0IKtnm/A/aA+7KHwWeCSNqEw0zl3e6tz1jWe0zoUZjrnDrS51s3AzQCBpITpg0YMOqbVJD4QT9AFCVgAMyNAgPhAPHGBOBLiEkgIJJywjTAY9J84amp8GID/AJ2c7EOiL35ALi0tJau90UrBYEuitT6ca3ls/TUc+9j6/4nWXwcCLT+c1q+ZHXse+FpGQ8Oxz8fHHzs+sqPnWr//RM8FAhAMUlVZSUpTb39X39tW47U6/L6iom/+j9BGXV0dCQkJ4S5GnxAJPwvX2KrjMHD+0bV6rfl1B7R57ZjHxtf9c8eeA7Cpat8659xZJypPKHtTioDcVt/nAMUdnFPU2Hw0EDjY9kLOuceAxwDy8/NdQUFBSAocafLz89HPwtPPooV+Fi30s2hhZtUnPgtC2buxHBhnZmPMLBG4FnihzTkvADc0fn018EZn/QkiIhJaIaspOOfqzewbwKv4Iam/d86tM7N7gQLn3AvA74AnzGwLvoZwbajKIyIiJxbSwbjOuX8A/2jz3PdafV0NfLY717z55pt7pnBRQD+LFvpZtNDPooV+Fsd4rCsnRdyMZiDiCiwi0gd0aZSE5oOLiEiziAoFM7v09NNPZ+zYsfzkJz858Rui1Fe/+lWGDBnCWWedcHRZ1CssLGTevHlMmDCBiRMn8uCDD4a7SGFTXV3NzJkzmTx5MhMnTuSee+4Jd5HCqqGhgalTp3LFFVeEuyhhN3r0aMxsjZmtNrNOh2NFTCg0LpvxyMsvv8z69et56qmnWL9+/QnfF42+/OUv88orr4S7GH1CfHw8P//5z9mwYQPLli3jkUceidn/L5KSknjjjTf48MMPWb16Na+88grL2k7YiyEPPvggEyZMCHcx+pJ5zrkpzrn8zk6KmFAAZgJb8vLySExM5Nprr+Vvf/tbuMsUFnPnzmXQoEHhLkafMGzYMKZNmwZAWloaEyZMYPfu3WEuVXiYGf379wf8pK26urqY3begqKiIl156iZtuuincRYk4EdPR3JVlM2KJmY0GXuzKDMVY0fgzWQyc5ZwrD29pwqOxRr0CGAs84pz71zAXKSzM7K/Aj4E04C7nXEy3IZnZduAQfqDObxonBLcrkmoK7X3kiYxEk5Azs/7As8C3YjUQAJxzDc65KfgVBGaaWcx9aDCzK4B9zrkV4S5LH3Kuc24acBlwm5nN7ejESAqFriybITHIzBLwgfBn59xz4S5PX+CcOwy8BVwa5qKEw7nAp8xsB/A0cKGZ/Sm8RQov51xx4+M+4P/hm+PbFUmh0JVlMyTGmG80/x2wwTn3i3CXJ5zMLMvM0hu/TgEuBjaGt1S9zzl3t3Muxzk3Gv934g3n3HVhLlbYmFmqmaU1fQ0sANZ2dH7EhIJzrh5oWjZjA/AX51zb1dJjgpk9BbwHnG5mRWZ2Y7jLFEbnAtfjPw2ubjwuD3ehwmQY8KaZfYT/ELXQOfdimMsk4TcUeMfMPgQ+AF5yznU4fDFiOppFRCT0IqamICIioadQEBGRZgoFERFpplAQEZFmCgUREWmmUBARkWYKBRERaaZQEBGJUmY2w8w+MrPkxpnN6060HpYmr4mIRDEz+y8gGUgBipxzP+70fIWCiEj0alwrbjlQDZzjnGvo7Hw1H4mIRLdBQH/83hLJJzpZNQURkShmZi/glxAfAww70cZk8b1SKhER6XVm9iWg3jn3ZOOufO+a2YXOuTc6fI9qCiIi0kR9CiIi0kyhICIizRQKIiLSTKEgIiLNFAoiItJMoSAiIs0UCiIi0kyhICIizf5/ySF0AVvAmyYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -9.650 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_2 = -0.247 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_3 \\; for \\; \\phi_3 = -0.149 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -34.73930 \\ hartree = -945.29120 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 12.2 s\n",
      "------------------------------ Iteration 2 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 7.522 \\quad \\zeta_2 = 5.123 \\quad \\zeta_3 = 1.831 \\quad \\zeta_4 = 1.153 \\quad \\zeta_5 = 2.730 \\quad \\zeta_6 = 1.257$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1s = c_{11} \\chi_1 + c_{21} \\chi_2 + c_{31} \\chi_3 + c_{41} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2s = c_{12} \\chi_1 + c_{22} \\chi_2 + c_{32} \\chi_3 + c_{42} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2p = c_{52} \\chi_5 + c_{62} \\chi_6$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = 0.233 \\quad c21 = 0.778 \\quad c31 = -0.006 \\quad c41 = 0.004$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = 0.010 \\quad c22 = -0.272 \\quad c32 = 0.822 \\quad c42 = 0.244$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c52 = -0.305 \\quad c62 = -0.764$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -11.660 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_2 = -0.794 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_3 \\; for \\; \\phi_3 = -0.486 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -38.27665 \\ hartree = -1041.54589 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.3 s\n",
      "------------------------------ Iteration 3 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 7.522 \\quad \\zeta_2 = 5.123 \\quad \\zeta_3 = 1.831 \\quad \\zeta_4 = 1.153 \\quad \\zeta_5 = 2.730 \\quad \\zeta_6 = 1.257$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1s = c_{11} \\chi_1 + c_{21} \\chi_2 + c_{31} \\chi_3 + c_{41} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2s = c_{12} \\chi_1 + c_{22} \\chi_2 + c_{32} \\chi_3 + c_{42} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2p = c_{52} \\chi_5 + c_{62} \\chi_6$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = 0.231 \\quad c21 = 0.779 \\quad c31 = -0.003 \\quad c41 = 0.002$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = 0.011 \\quad c22 = -0.269 \\quad c32 = 0.784 \\quad c42 = 0.283$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c52 = -0.245 \\quad c62 = -0.814$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -11.247 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_2 = -0.683 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_3 \\; for \\; \\phi_3 = -0.398 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -37.51987 \\ hartree = -1020.95331 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.3 s\n",
      "------------------------------ Iteration 4 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 7.522 \\quad \\zeta_2 = 5.123 \\quad \\zeta_3 = 1.831 \\quad \\zeta_4 = 1.153 \\quad \\zeta_5 = 2.730 \\quad \\zeta_6 = 1.257$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1s = c_{11} \\chi_1 + c_{21} \\chi_2 + c_{31} \\chi_3 + c_{41} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2s = c_{12} \\chi_1 + c_{22} \\chi_2 + c_{32} \\chi_3 + c_{42} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2p = c_{52} \\chi_5 + c_{62} \\chi_6$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = 0.231 \\quad c21 = 0.779 \\quad c31 = -0.004 \\quad c41 = 0.003$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = 0.011 \\quad c22 = -0.270 \\quad c32 = 0.796 \\quad c42 = 0.271$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c52 = -0.259 \\quad c62 = -0.803$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -11.347 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_2 = -0.711 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_3 \\; for \\; \\phi_3 = -0.418 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -37.70363 \\ hartree = -1025.95343 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.3 s\n",
      "------------------------------ Iteration 5 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 7.522 \\quad \\zeta_2 = 5.123 \\quad \\zeta_3 = 1.831 \\quad \\zeta_4 = 1.153 \\quad \\zeta_5 = 2.730 \\quad \\zeta_6 = 1.257$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1s = c_{11} \\chi_1 + c_{21} \\chi_2 + c_{31} \\chi_3 + c_{41} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2s = c_{12} \\chi_1 + c_{22} \\chi_2 + c_{32} \\chi_3 + c_{42} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2p = c_{52} \\chi_5 + c_{62} \\chi_6$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = 0.231 \\quad c21 = 0.779 \\quad c31 = -0.003 \\quad c41 = 0.003$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = 0.011 \\quad c22 = -0.270 \\quad c32 = 0.794 \\quad c42 = 0.273$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c52 = -0.255 \\quad c62 = -0.806$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -11.322 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_2 = -0.704 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_3 \\; for \\; \\phi_3 = -0.413 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -37.65881 \\ hartree = -1024.73381 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.4 s\n",
      "------------------------------ Iteration 6 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 7.522 \\quad \\zeta_2 = 5.123 \\quad \\zeta_3 = 1.831 \\quad \\zeta_4 = 1.153 \\quad \\zeta_5 = 2.730 \\quad \\zeta_6 = 1.257$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1s = c_{11} \\chi_1 + c_{21} \\chi_2 + c_{31} \\chi_3 + c_{41} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2s = c_{12} \\chi_1 + c_{22} \\chi_2 + c_{32} \\chi_3 + c_{42} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2p = c_{52} \\chi_5 + c_{62} \\chi_6$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = 0.231 \\quad c21 = 0.779 \\quad c31 = -0.004 \\quad c41 = 0.003$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = 0.011 \\quad c22 = -0.270 \\quad c32 = 0.794 \\quad c42 = 0.272$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c52 = -0.256 \\quad c62 = -0.805$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -11.328 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_2 = -0.706 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_3 \\; for \\; \\phi_3 = -0.414 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -37.66937 \\ hartree = -1025.02127 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.3 s\n",
      "------------------------------ Iteration 7 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 7.522 \\quad \\zeta_2 = 5.123 \\quad \\zeta_3 = 1.831 \\quad \\zeta_4 = 1.153 \\quad \\zeta_5 = 2.730 \\quad \\zeta_6 = 1.257$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1s = c_{11} \\chi_1 + c_{21} \\chi_2 + c_{31} \\chi_3 + c_{41} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2s = c_{12} \\chi_1 + c_{22} \\chi_2 + c_{32} \\chi_3 + c_{42} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2p = c_{52} \\chi_5 + c_{62} \\chi_6$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = 0.231 \\quad c21 = 0.779 \\quad c31 = -0.004 \\quad c41 = 0.003$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = 0.011 \\quad c22 = -0.270 \\quad c32 = 0.794 \\quad c42 = 0.273$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c52 = -0.256 \\quad c62 = -0.806$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -11.327 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_2 = -0.705 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_3 \\; for \\; \\phi_3 = -0.413 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -37.66677 \\ hartree = -1024.95055 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.7 s\n",
      "------------------------------ Iteration 8 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 7.522 \\quad \\zeta_2 = 5.123 \\quad \\zeta_3 = 1.831 \\quad \\zeta_4 = 1.153 \\quad \\zeta_5 = 2.730 \\quad \\zeta_6 = 1.257$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1s = c_{11} \\chi_1 + c_{21} \\chi_2 + c_{31} \\chi_3 + c_{41} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2s = c_{12} \\chi_1 + c_{22} \\chi_2 + c_{32} \\chi_3 + c_{42} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2p = c_{52} \\chi_5 + c_{62} \\chi_6$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = 0.231 \\quad c21 = 0.779 \\quad c31 = -0.004 \\quad c41 = 0.003$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = 0.011 \\quad c22 = -0.270 \\quad c32 = 0.794 \\quad c42 = 0.273$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c52 = -0.256 \\quad c62 = -0.806$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -11.327 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_2 = -0.706 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_3 \\; for \\; \\phi_3 = -0.414 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -37.66738 \\ hartree = -1024.96711 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.3 s\n",
      "------------------------------ Iteration 9 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 7.522 \\quad \\zeta_2 = 5.123 \\quad \\zeta_3 = 1.831 \\quad \\zeta_4 = 1.153 \\quad \\zeta_5 = 2.730 \\quad \\zeta_6 = 1.257$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1s = c_{11} \\chi_1 + c_{21} \\chi_2 + c_{31} \\chi_3 + c_{41} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2s = c_{12} \\chi_1 + c_{22} \\chi_2 + c_{32} \\chi_3 + c_{42} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2p = c_{52} \\chi_5 + c_{62} \\chi_6$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = 0.231 \\quad c21 = 0.779 \\quad c31 = -0.004 \\quad c41 = 0.003$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = 0.011 \\quad c22 = -0.270 \\quad c32 = 0.794 \\quad c42 = 0.273$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c52 = -0.256 \\quad c62 = -0.806$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -11.327 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_2 = -0.706 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_3 \\; for \\; \\phi_3 = -0.414 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -37.66723 \\ hartree = -1024.96301 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.4 s\n",
      "------------------------------ Iteration 10 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 7.522 \\quad \\zeta_2 = 5.123 \\quad \\zeta_3 = 1.831 \\quad \\zeta_4 = 1.153 \\quad \\zeta_5 = 2.730 \\quad \\zeta_6 = 1.257$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1s = c_{11} \\chi_1 + c_{21} \\chi_2 + c_{31} \\chi_3 + c_{41} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2s = c_{12} \\chi_1 + c_{22} \\chi_2 + c_{32} \\chi_3 + c_{42} \\chi_4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_2p = c_{52} \\chi_5 + c_{62} \\chi_6$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c11 = 0.231 \\quad c21 = 0.779 \\quad c31 = -0.004 \\quad c41 = 0.003$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = 0.011 \\quad c22 = -0.270 \\quad c32 = 0.794 \\quad c42 = 0.273$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c52 = -0.256 \\quad c62 = -0.806$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -11.327 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_2 = -0.706 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_3 \\; for \\; \\phi_3 = -0.414 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -37.66727 \\ hartree = -1024.96396 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.3 s\n"
     ]
    }
   ],
   "source": [
    "# input \n",
    "# zeta obtained from https://www.scm.com/zorabasis/periodic.dzae.html\n",
    "zetas = [[7.52232, 1], [5.12306, 1], [1.83068, 2], [1.15282, 2]]\n",
    "zetap = [[2.73045, 2], [1.25656, 2]]\n",
    "# input nuclear charge (element number)\n",
    "Z = 6\n",
    "\n",
    "# build basis function\n",
    "fs1=STO(zetas[0][0], zetas[0][1])\n",
    "fs2=STO(zetas[1][0], zetas[1][1])\n",
    "fs3=STO(zetas[2][0], zetas[2][1])\n",
    "fs4=STO(zetas[3][0], zetas[3][1])\n",
    "fs = [fs1, fs2, fs3, fs4]\n",
    "\n",
    "fp1=STO(zetap[0][0], zetap[0][1])\n",
    "fp2=STO(zetap[1][0], zetap[1][1])\n",
    "fp = [fp1, fp2]\n",
    "\n",
    "# initialization\n",
    "#Jss = np.zeros((len(zetas), len(zetas), len(zetas), len(zetas)))\n",
    "#Kss = np.zeros((len(zetas), len(zetas), len(zetas), len(zetas)))\n",
    "#Jsp = np.zeros((len(zetas), len(zetas), len(zetap), len(zetap)))\n",
    "#Ksp = np.zeros((len(zetas), len(zetas), len(zetap), len(zetap)))\n",
    "#Jps = np.zeros((len(zetap), len(zetap), len(zetas), len(zetas)))\n",
    "#Kps = np.zeros((len(zetap), len(zetap), len(zetas), len(zetas)))\n",
    "Jpp = np.zeros((len(zetas), len(zetas), len(zetap), len(zetap)))\n",
    "Kpp = np.zeros((len(zetas), len(zetas), len(zetap), len(zetap)))\n",
    "Hs = Hs_matrix(fs, Z)\n",
    "Hp = Hp_matrix(fp, Z)\n",
    "Ss = S_matrix(fs)\n",
    "Sp = S_matrix(fp)\n",
    "es, Cos = secular_eqn(Hs, Ss)\n",
    "ep, Cop = secular_eqn(Hp, Sp)\n",
    "Ps = Ps_matrix(Cos)\n",
    "Pp = Pp_matrix(Cop)\n",
    "scf_H = get_E0(es, ep, Ps, Pp, Hs, Hp)\n",
    "\n",
    "##############################################print information below#################################################\n",
    "print('-'*30, \"Initialization\", '-'*30)\n",
    "print('-'*25, \"Ignore repulsion integral\", '-'*24)\n",
    "display(Math('\\zeta_1 = {0} \\quad \\zeta_2 = {1} \\quad \\zeta_3 = {2} \\quad \\zeta_4 = {3} \\quad \\zeta_5 = {4} \\quad \\zeta_6 = {5}'.format(format(zetas[0][0], '0.3f'), format(zetas[1][0], '0.3f'), format(zetas[2][0], '0.3f'),format(zetas[3][0], '0.3f'), format(zetap[0][0], '0.3f'),format(zetap[1][0], '0.3f')))) \n",
    "display(Math('Orbitals:'))\n",
    "display(Math(' \\phi_1s = c_{11} \\chi_1 + c_{21} \\chi_2 + c_{31} \\chi_3 + c_{41} \\chi_4'))\n",
    "display(Math(' \\phi_2s = c_{12} \\chi_1 + c_{22} \\chi_2 + c_{32} \\chi_3 + c_{42} \\chi_4'))    \n",
    "display(Math(' \\phi_2p = c_{52} \\chi_5 + c_{62} \\chi_6')) \n",
    "display(Math('c11 = {0} \\quad c21 = {1} \\quad c31 = {2} \\quad c41 = {3}'.format(format(Cos[0][0], '0.3f'), format(Cos[1][0], '0.3f'), format(Cos[2][0], '0.3f'), format(Cos[3][0], '0.3f')))) \n",
    "display(Math('c12 = {0} \\quad c22 = {1} \\quad c32 = {2} \\quad c42 = {3}'.format(format(Cos[0][1], '0.3f'), format(Cos[1][1], '0.3f'), format(Cos[2][1], '0.3f'), format(Cos[3][1], '0.3f'))))     \n",
    "display(Math('c52 = {0} \\quad c62 = {1}'.format(format(Cop[0][0], '0.3f'), format(Cop[1][0], '0.3f'))))     \n",
    "\n",
    "# plot density graph\n",
    "colorlist = ['red', 'orange', 'yellow', 'green', 'blue', 'purple', 'black', 'red', 'orange', 'yellow', 'green', 'blue', 'purple', 'black']\n",
    "phi1 = Cos[0,0]*fs1+Cos[1,0]*fs2+Cos[2,0]*fs3+Cos[3,0]*fs4\n",
    "phi2 = Cos[0,1]*fs1+Cos[1,1]*fs2+Cos[2,1]*fs3+Cos[3,1]*fs4\n",
    "phi3 = Cop[0,0]*fp1+Cop[1,0]*fp2\n",
    "density_1 = phi1*phi1*r*r\n",
    "density_2 = phi2*phi2*r*r    \n",
    "density_3 = phi3*phi3*r*r   \n",
    "p = plot((density_1, (r, 0, 5)), (density_2, (r, 0, 5)), (density_3, (r, 0, 5)), show = False, legend = True)\n",
    "p[0].label = 'electron density $r^2 \\phi_1^2$ '\n",
    "p[1].label = 'electron density $r^2 \\phi_2^2$ '    \n",
    "p[2].label = 'electron density $r^2 \\phi_2^2$ ' \n",
    "p[0].line_color = colorlist[0]\n",
    "p[1].line_color = 'blue'\n",
    "p[2].line_color = 'green'\n",
    "p.show()\n",
    "# print energy result\n",
    "display(Math(' \\epsilon_1 \\; for \\; \\phi_1  = {0} '.format(format(es[0].real, '0.3f'))))    \n",
    "display(Math(' \\epsilon_2 \\; for \\; \\phi_2 = {0} '.format(format(es[1].real, '0.3f'))))      \n",
    "display(Math(' \\epsilon_3 \\; for \\; \\phi_3 = {0} '.format(format(ep[0].real, '0.3f'))))   \n",
    "display(Math(' Hartree \\ Fork \\; atom \\; energy = {0} \\ hartree = {1} \\ eV'.format(format(scf_H, '0.5f'), format(scf_H*27.211, '0.5f'))))    \n",
    "\n",
    "##############################################print information above#################################################\n",
    "\n",
    "for i in range(10):\n",
    "    print('-'*30, \"Iteration\", i + 1, '-'*30)\n",
    "    if(i==0):\n",
    "        print('-'*7, \"Iteration 1 needs more time to caculate Repulsion Integral\", '-'*6)\n",
    "        start = time.time()\n",
    "        #Jss = J_matrix(zetas, zetas, 0)\n",
    "        #Kss = K_matrix(zetas, zetas, 0)\n",
    "        #Jsp = J_matrix(zetas, zetap, 0)\n",
    "        #Ksp = 1/3 * K_matrix(zetas, zetap, 1)\n",
    "        #Jps = J_matrix(zetap, zetas, 0)\n",
    "        #Kps = 1/3 * K_matrix(zetap, zetas, 1)\n",
    "        Jpp = J_matrix(zetap, zetap, 0) + 2/25 * J_matrix(zetap, zetap, 2) # 1/25 for minimum\n",
    "        Kpp = 1/5 * K_matrix(zetap, zetap, 2) # 6/25 for minimum\n",
    "    else:\n",
    "        start = time.time()\n",
    "    Fs = Fs_matrix(fs, Z, Cos, Cop, Jss, Kss, Jsp, Ksp)\n",
    "    Fp = Fp_matrix(fp, Z, Cos, Cop, Jpp, Kpp, Jps, Kps)\n",
    "    S = S_matrix(fs)\n",
    "    es, Cos = secular_eqn(Fs, Ss)\n",
    "    ep, Cop = secular_eqn(Fp, Sp)\n",
    "    Ps = Ps_matrix(Cos)\n",
    "    Pp = Pp_matrix(Cop)\n",
    "    scf_H = get_E0(es, ep, Ps, Pp, Hs, Hp)\n",
    "    ##########################################print information below#################################################\n",
    "    # print information\n",
    "    display(Math('\\zeta_1 = {0} \\quad \\zeta_2 = {1} \\quad \\zeta_3 = {2} \\quad \\zeta_4 = {3} \\quad \\zeta_5 = {4} \\quad \\zeta_6 = {5}'.format(format(zetas[0][0], '0.3f'), format(zetas[1][0], '0.3f'), format(zetas[2][0], '0.3f'),format(zetas[3][0], '0.3f'), format(zetap[0][0], '0.3f'),format(zetap[1][0], '0.3f')))) \n",
    "    display(Math('Orbitals:'))\n",
    "    display(Math(' \\phi_1s = c_{11} \\chi_1 + c_{21} \\chi_2 + c_{31} \\chi_3 + c_{41} \\chi_4'))\n",
    "    display(Math(' \\phi_2s = c_{12} \\chi_1 + c_{22} \\chi_2 + c_{32} \\chi_3 + c_{42} \\chi_4'))    \n",
    "    display(Math(' \\phi_2p = c_{52} \\chi_5 + c_{62} \\chi_6')) \n",
    "    display(Math('c11 = {0} \\quad c21 = {1} \\quad c31 = {2} \\quad c41 = {3}'.format(format(Cos[0][0], '0.3f'), format(Cos[1][0], '0.3f'), format(Cos[2][0], '0.3f'), format(Cos[3][0], '0.3f')))) \n",
    "    display(Math('c12 = {0} \\quad c22 = {1} \\quad c32 = {2} \\quad c42 = {3}'.format(format(Cos[0][1], '0.3f'), format(Cos[1][1], '0.3f'), format(Cos[2][1], '0.3f'), format(Cos[3][1], '0.3f'))))     \n",
    "    display(Math('c52 = {0} \\quad c62 = {1}'.format(format(Cop[0][0], '0.3f'), format(Cop[1][0], '0.3f'))))     \n",
    "    # plot density graph\n",
    "    phi1 = Cos[0,0]*fs1+Cos[1,0]*fs2+Cos[2,0]*fs3+Cos[3,0]*fs4\n",
    "    phi2 = Cos[0,1]*fs1+Cos[1,1]*fs2+Cos[2,1]*fs3+Cos[3,1]*fs4\n",
    "    phi3 = Cop[0,0]*fp1+Cop[1,0]*fp2\n",
    "    density_1 = phi1*phi1*r*r\n",
    "    density_2 = phi2*phi2*r*r    \n",
    "    density_3 = phi3*phi3*r*r    \n",
    "    p = plot((density_1, (r, 0, 5)), (density_2, (r, 0, 5)), (density_3, (r, 0, 5)), show = False)\n",
    "    p[0].label = 'electron density $r^2 \\phi_1^2$ '\n",
    "    p[1].label = 'electron density $r^2 \\phi_2^2$ '    \n",
    "    p[2].label = 'electron density $r^2 \\phi_2^2$ ' \n",
    "    p[0].line_color = colorlist[0]\n",
    "    p[1].line_color = 'blue'\n",
    "    p[2].line_color = 'green'\n",
    "    p.show()\n",
    "    # print energy result\n",
    "    display(Math(' \\epsilon_1 \\; for \\; \\phi_1  = {0} '.format(format(es[0].real, '0.3f'))))    \n",
    "    display(Math(' \\epsilon_2 \\; for \\; \\phi_2 = {0} '.format(format(es[1].real, '0.3f'))))      \n",
    "    display(Math(' \\epsilon_3 \\; for \\; \\phi_3 = {0} '.format(format(ep[0].real, '0.3f'))))   \n",
    "    display(Math(' Hartree \\ Fork \\; atom \\; energy = {0} \\ hartree = {1} \\ eV'.format(format(scf_H, '0.5f'), format(scf_H*27.211, '0.5f'))))   \n",
    "    stop = time.time()\n",
    "    print('Time used:',format(stop-start, '0.1f'),'s')\n",
    "    ##########################################print information above#################################################\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.00000000000000\n",
      "5.66383156062133\n",
      "0.268560991814453\n",
      "0.0973592535392598\n",
      "1.00000000000000\n",
      "0.897672408309650\n",
      "1.58921926506433\n",
      "3.05206253542544\n",
      "1.00000000000000\n",
      "1.62769766349268\n",
      "0.781768015725644\n",
      "1.70919321502870\n",
      "3.68729969875941\n"
     ]
    }
   ],
   "source": [
    "print(sp.integrate(density_1 ,(r, 0, +oo)))\n",
    "print(sp.integrate(density_1/r ,(r, 0, +oo)))\n",
    "print(sp.integrate(density_1*r ,(r, 0, +oo)))\n",
    "print(sp.integrate(density_1*r*r ,(r, 0, +oo)))\n",
    "\n",
    "print(sp.integrate(density_2 ,(r, 0, +oo)))\n",
    "print(sp.integrate(density_2/r ,(r, 0, +oo)))\n",
    "print(sp.integrate(density_2*r ,(r, 0, +oo)))\n",
    "print(sp.integrate(density_2*r*r ,(r, 0, +oo)))\n",
    "\n",
    "print(sp.integrate(density_3 ,(r, 0, +oo)))\n",
    "print(sp.integrate(density_3/r/r/r ,(r, 0, +oo)))\n",
    "print(sp.integrate(density_3/r ,(r, 0, +oo)))\n",
    "print(sp.integrate(density_3*r ,(r, 0, +oo)))\n",
    "print(sp.integrate(density_3*r*r ,(r, 0, +oo)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reference:\n",
    "1. Larsen, A. and R. S. Poulsen (2015). Applied Hartree-Fock methods: Atomic and diatomic energy computations. Department of Physics. Denmark, Aalborg University. Master: 68.\n",
    "2. Bransden, B. H. (2003). Physics of atoms and molecules. Harlow, England\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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