Beryllium-HF.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<h2 style=\"margin-bottom:0px;\"><center>Restricted Hartree–Fock for Beryllium</center></h2>\n",
    "\n",
    "<p style=\"text-align: center; margin-top: 10px; margin-bottom: 0px;\">\n",
    "    By <a target=\"_blank\" href=\"https://github.com/yueyericardo\">$Richard\\;Xue$</a>&nbsp;/&nbsp;\n",
    "    <a target=\"_blank\" href=\"https://github.com/yueyericardo/hartree-fock\">$Source\\;code$</a>\n",
    "</p>\n",
    "\n",
    "<p style=\"text-align: center; margin-top: 5px; margin-bottom: 0px;\">\n",
    "    $2018/12/07$\n",
    "</p>\n",
    "\n",
    "<p style=\"text-align: center; margin-top: 5px;\">\n",
    "    <a target=\"_blank\" href=\"https://yyrcd.com/hf/he.html\">$Helium$</a>&nbsp;/&nbsp;\n",
    "    <a target=\"_blank\" href=\"https://yyrcd.com/hf/li.html\">$Lithium$</a>&nbsp;/&nbsp;    \n",
    "    <a target=\"_blank\" href=\"https://yyrcd.com/hf/be.html\">$Beryllium$</a>\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<h2><center>Part 1 Function Definition</center></h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define STO function\n",
    "<p><a href=\"https://en.wikipedia.org/wiki/Slater-type_orbital\">$STO$</a>$ \\; function \\; has \\; format \\; of: \\; Nr^{n-1}e^{-r\\zeta}$</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For example: STO for 1s\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFkAAAAcCAYAAAAKnhNwAAAABHNCSVQICAgIfAhkiAAAA69JREFUaIHt2F+IlFUYx/FP7RjbrhT0D8uw2oqiCKQwCfpjJWWEF7VdVBdKGSWuRIUQGtHeiDdCf6Ei+nOxRahFUhKCmxUIEZGZZaVdiJBrsvTvQtDapovnyE7vvLPz7uzsjtZ84fDOnHOe5/3NOe/7PM8Z2rQ5TvgS5Zx2aSvEXI/3sT+JuKuATb9q8QcmSV+jnIUZuA67cAhPowNOnGIx3diB5eO0+wFnV7QrmqyrUaal60EswGZ8j0vwKEaadaPt8l+Vo21TDbvxPMnfTFjlxDlXaL4Xn+IwFqWxvvT9oTzDUsXn03EHbhdPykwcwU68ntrfGfsT8C42VvRdjHvSGAw28IOy9OCnpOczrMTeJvgdD7PTdQVWYQ9+xdV4Riz++npOloqd2o83sQav4bfUv8HowuVxElaLHS2L2DtnjPlFn+Tb0Cs2fr7YtCGcVsC2mTwhYm1Ppv9zvFTUyU1YqDpOz8A+sSi9NWzPM5phd+HGAvcrushZuvEzHmvANku/sUNdGfPS3PVYl7G/KM25oAlarErOns8Zu1xk+zKeRWdBn40uMmzFizXGevEhhkV42SP0d+TMPUOUWWO1rjR3N5Zl7BeJkDEmpXoTEn+m61+Z/nOwBWfiAbxa0N9E6BQ/fmumvwMDuBs/iifvsAg3q0XGX5yxGU6tHt24UCT5SkqiwugSoaRhSiL5lXFrZmww9fcV9DVdJJDZyW5F+jwrjS8XJVAla3GDeCXn4gP8IUJUJS8kn2v8++GZhm1p7LKCOrNcI8qx7kx/j3hb1on8c2qD/q2VX4otTP0bqyxqM09+3Hsjjfen75W8LZLxEVFhvKN6seaKyue9Gvd9MPm9bxxaK1mqevOPskBUPIfSPZ4br/OHk+F3qrP5pjR2LBwMBoSWt8RGZduGNH7/JOtYIt6ywvQJYd+KCqOSkti53U2RNnEOql8llEUJOFmcIkq5LUUNHhGidopzeZbzjdbCraZTaPmkxTpW4iOxNnV5XIjeLkqcPHrSnG1NEDdRTjb6xh0XPCkEf2HsE1WHKH1GROBvNTuE7jtrjF8rv06eEiqPyYtFlh8Rh47fc+bvNVoJLMEr4scN4itRBWwWiXIquUUk4pKIiV+Lk+tMXCXKuFk1raeQfvUTx8cZm/mihBsSJVZZHACunArBGeaIKuKAODwNi5zyMm5ugZ5JY5lY6P4W6zimaPaf9kPpuq/JftsknsIvonae3mIt/0m6xJF3QCSbNm3atGnTps3/lX8APCT/b5NLtc4AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$2 \\zeta^{1.5} e^{- r \\zeta}$$"
      ],
      "text/plain": [
       "   1.5  -r⋅ζ\n",
       "2⋅ζ   ⋅ℯ    "
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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)\n",
    "\n",
    "print(\"For example: STO for 1s\")\n",
    "STO(zeta, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Overlap Integrate\n",
    "\n",
    "$S = \\int_{0}^\\infty f_1^* f_2 \\; r^2dr$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "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": "markdown",
   "metadata": {},
   "source": [
    "### Hamiltonian core\n",
    "\n",
    "H core = kinetics energy + electron and nuclear potential energy\n",
    "\n",
    "$H = \\int_{0}^\\infty f_1 \\hat{H} f_2 \\; r^2dr$\n",
    "\n",
    "$H = \\int_{0}^\\infty f_1 ((-\\dfrac{1}{2}) \\nabla^2 - \\dfrac{Z_{\\alpha}}{r})f_2 \\; r^2 dr$\n",
    "\n",
    "<p><a href=\"https://en.wikipedia.org/wiki/Laplace_operator\">$Laplace \\; operator: $</a> $\\nabla^2$</p>\n",
    "<p><left><img class = \"none\"style=\"text-align: center; margin-left:0px\" src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/b4a3135d1cc01d19309d36c749aaef4a48dc81da\"></left></p>\n",
    "\n",
    "$\\therefore H = \\int_{0}^\\infty f_1 ((-\\dfrac{1}{2}) \\dfrac{1}{r} \\dfrac{\\partial}{\\partial r} \\dfrac{\\partial}{\\partial r} r f_2 - \\dfrac{Z_{\\alpha}}{r}r^2 f_2 )dr$\n",
    "\n",
    "**reminder:** change the Z of nucleus if you want to run for other atom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "# H core = kinetics energy + electron and nuclear potential energy\n",
    "def H_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": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Returns the core hamiltonian matrix\n",
    "def H_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] =  H_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": "markdown",
   "metadata": {},
   "source": [
    "### Two elecron repulsion integral\n",
    "$(rs|tu) = \\int \\int \\dfrac{f_r^*(1) f_s(1) f_t^*(2) f_u(2)}{r_{12}} \\; dv_1 dv_2 $\n",
    "\n",
    "For 1s 2s orbital\n",
    "\n",
    "$(rs|tu)  = \\int_{0}^\\infty \\int_{0}^\\infty \\dfrac{f_r^*(1) f_s(1) f_t^*(2) f_u(2)}{r_{12}} \\; r_1^2dr_1\\; r_2^2dr_2  $\n",
    "\n",
    "$(rs|tu) = \\int_{0}^\\infty f_r^*(1) f_s(1)  \\; r_1^2dr_1\\int_{0}^\\infty \\frac{ f_t^*(2) f_u(2)}{r_{12}}\\; r_2^2dr_2  $\n",
    "\n",
    "From problem 9.14 in quantum_chemistry by levine\n",
    "\n",
    "$(rs|tu) = \\int_{0}^\\infty f_r^*(1) f_s(1)  \\; r_1^2dr_1\\int_{0}^\\infty \\frac{ f_t^*(2) f_u(2)}{r_{>}}\\; r_2^2dr_2  $\n",
    "\n",
    "$(rs|tu) = \\int_{0}^\\infty f_r^*(1) f_s(1)  \\; r_1^2dr_1(\\int_{0}^{r_1} \\frac{ f_t^*(2) f_u(2)}{r_{1}}\\; r_2^2dr_2 + \\int_{r_1}^\\infty \\frac{ f_t^*(2) f_u(2)}{r_{2}}\\; r_2^2dr_2)  $\n",
    "\n",
    "$Let \\; B= \\int_{0}^{r_1} \\frac{ f_t^*(2) f_u(2)}{r_{1}}\\; r_2^2dr_2 + \\int_{r_1}^\\infty \\frac{ f_t^*(2) f_u(2)}{r_{2}}\\; r_2^2dr_2$\n",
    "\n",
    "$(rs|tu) = \\int_{0}^\\infty f_r^*(1) f_s(1) B \\; r_1^2 dr_1  $\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "def Repulsion_electron(zetas):\n",
    "    \n",
    "    f1=STO(zetas[0][0], zetas[0][1], r1)\n",
    "    f2=STO(zetas[1][0], zetas[1][1], r1)\n",
    "    f3=STO(zetas[2][0], zetas[2][1], r2)\n",
    "    f4=STO(zetas[3][0], zetas[3][1], r2)\n",
    "    fs = [f1, f2, f3, f4]\n",
    "    \n",
    "    B = (1/r1)*sp.integrate(f3*f4*r2*r2 ,(r2, 0, r1)) + sp.integrate((1/r2)*f3*f4*r2*r2 ,(r2, r1, +oo))\n",
    "    A = sp.integrate(f1*f2*r1*r1*B ,(r1, 0, +oo))\n",
    "    return A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Density matrix\n",
    "$ P_{tu} =2 \\sum_{j=1}^{n/2}c_{tj}^* c_{uj} $\n",
    "\n",
    "**Reminder:** P need to be changed if the atom have unpaired electron"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculates Density matrix\n",
    "def P_matrix(Co):\n",
    "\n",
    "    P = np.zeros([Co.shape[0], Co.shape[0]])\n",
    "\n",
    "    for t in range(Co.shape[0]):\n",
    "        for u in range(Co.shape[0]):\n",
    "            for j in range(int(Co.shape[0]/2)):\n",
    "                P[t][u] += 2* Co[t][j]*Co[u][j]\n",
    "    return P            "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fock matrix\n",
    "$ F_{rs} = H_{rs}^{core} + \\sum_{t=1}^{b} \\sum_{t=1}^{b}P_{tu}[(rs|tu)- \\frac{1}2(ru|ts)] $  \n",
    "\n",
    "$G = \\sum_{t=1}^{b} \\sum_{t=1}^{b}P_{tu}[(rs|tu)- \\frac{1}2(ru|ts)]$ \n",
    "\n",
    "$ F_{rs} = H_{rs}^{core} + G $  \n",
    "\n",
    "$In\\;G \\;one\\;is\\;coulombic\\;repulsion,\\;another\\;is\\;exchange\\;energy$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "def R_matrix(zetas):\n",
    "    R = np.zeros((len(zetas), len(zetas), len(zetas), len(zetas)))\n",
    "\n",
    "    rs = list(product(range(len(zetas)),repeat=2))\n",
    "    tu = list(product(range(len(zetas)),repeat=2))\n",
    "\n",
    "    for r, s in rs:\n",
    "        for t, u in tu:\n",
    "            R[r,s,t,u] = Repulsion_electron((zetas[r], zetas[s], zetas[t], zetas[u]))\n",
    "    return R\n",
    "\n",
    "# Caculate G Matrix\n",
    "def G_matrix(zetas, Co, R):\n",
    "\n",
    "    G = np.zeros((Co.shape[0], Co.shape[0]))\n",
    "\n",
    "    P = P_matrix(Co)\n",
    "    \n",
    "    rs = list(product(range( Co.shape[0]),repeat=2))\n",
    "    tu = list(product(range( Co.shape[0]),repeat=2))\n",
    "\n",
    "    for r, s in rs:\n",
    "        g = 0\n",
    "        for t, u in tu:\n",
    "            int1 = R[r, s, t, u]\n",
    "            int2 = R[r, u, t, s]\n",
    "#             print('({0}{1}|{2}{3}): {4}'.format(r, s, t, u, int1))\n",
    "            g+= P[t, u] * (int1 - 0.5 * int2)\n",
    "        G[r, s] = g\n",
    "    return G\n",
    "\n",
    "# Returns the Fock matrix\n",
    "def F_matrix(fs, Z, zetas, Co, R):\n",
    "    return H_matrix(fs, Z) + G_matrix(zetas, Co, R)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solve Hartree-Fork equation\n",
    "\n",
    "$det(F_{rs}-\\epsilon_i S_{rs} = 0)$  \n",
    "\n",
    "$The\\;energy\\;returned\\;is\\;the\\;orbital\\;energy\\;for\\;1\\;electron$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "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": "markdown",
   "metadata": {},
   "source": [
    "### Return atom energy\n",
    "$ E_{HF} = \\sum_{i=1}^{2/n}\\epsilon  +\\frac{1}2 \\sum_{r=1}^{b} \\sum_{s=1}^{b}P_{rs}H_{rs}+V_{NN} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "# return energy of atom\n",
    "def get_E0(e, P, H):\n",
    "    \n",
    "    E0 = 0\n",
    "    for i in range(int(e.shape[0]/2)):\n",
    "        E0 += e[i].real \n",
    "    E0 = E0 + 0.5*(P*H).sum()\n",
    "    return E0 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<h2><center>Part 2 Hartree Fork Iteration (Main Process)</center></h2>\n",
    "\n",
    "- Initialization\n",
    "    1. initializing Co (coefficients) without considering electron repulsion\n",
    "    1. Solve Hartree-Fork equation with H_matrix and S_matrix to get initial Co\n",
    "\n",
    "\n",
    "- Iteration\n",
    "\t1. Using Co, we can get P_matrix (electron density)\n",
    "\t2. Using P_matrix, H_matrix, G_matrix => F_matrix\n",
    "\t3. Solve Hartree-Fork equation with F_matrix and S_matrix to get improved orbital energy and Co, which also means improved orbital functions.\n",
    "\t4. Using improved Co, return to step 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------ Initialization ------------------------------\n",
      "------------------------- Ignore repulsion integral ------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 5.591 \\quad \\zeta_2 = 3.355 \\quad \\zeta_3 = 1.011 \\quad \\zeta_4 = 0.610$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = 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_2 = 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 c11 = -0.275 \\quad c21 = -0.751 \\quad c31 = 0.052 \\quad c41 = -0.031$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = 0.127 \\quad c22 = 0.113 \\quad c32 = -1.542 \\quad c42 = 0.683$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -7.985 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = -1.774 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -19.51846 \\ hartree = -531.11686 \\ 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 = 5.591 \\quad \\zeta_2 = 3.355 \\quad \\zeta_3 = 1.011 \\quad \\zeta_4 = 0.610$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = 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_2 = 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 c11 = 0.156 \\quad c21 = 0.856 \\quad c31 = 0.003 \\quad c41 = -0.001$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = -0.004 \\quad c22 = 0.252 \\quad c32 = -1.173 \\quad c42 = 0.166$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -4.422 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = -0.245 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -14.28744 \\ hartree = -388.77544 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 58.7 s\n",
      "------------------------------ Iteration 2 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 5.591 \\quad \\zeta_2 = 3.355 \\quad \\zeta_3 = 1.011 \\quad \\zeta_4 = 0.610$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = 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_2 = 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 c11 = 0.155 \\quad c21 = 0.858 \\quad c31 = -0.002 \\quad c41 = 0.001$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c12 = -0.005 \\quad c22 = 0.230 \\quad c32 = -1.013 \\quad c42 = -0.020$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -4.654 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = -0.290 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -14.50425 \\ hartree = -394.67518 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.5 s\n",
      "------------------------------ Iteration 3 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 5.591 \\quad \\zeta_2 = 3.355 \\quad \\zeta_3 = 1.011 \\quad \\zeta_4 = 0.610$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = 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_2 = 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 c11 = 0.155 \\quad c21 = 0.858 \\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 = -0.004 \\quad c22 = 0.223 \\quad c32 = -0.963 \\quad c42 = -0.076$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -4.708 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = -0.304 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -14.55105 \\ hartree = -395.94867 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.2 s\n",
      "------------------------------ Iteration 4 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 5.591 \\quad \\zeta_2 = 3.355 \\quad \\zeta_3 = 1.011 \\quad \\zeta_4 = 0.610$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = 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_2 = 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 c11 = 0.155 \\quad c21 = 0.858 \\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 = -0.003 \\quad c22 = 0.221 \\quad c32 = -0.948 \\quad c42 = -0.093$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -4.726 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = -0.308 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -14.56616 \\ hartree = -396.35976 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.2 s\n",
      "------------------------------ Iteration 5 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 5.591 \\quad \\zeta_2 = 3.355 \\quad \\zeta_3 = 1.011 \\quad \\zeta_4 = 0.610$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = 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_2 = 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 c11 = 0.155 \\quad c21 = 0.858 \\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 = -0.003 \\quad c22 = 0.220 \\quad c32 = -0.944 \\quad c42 = -0.097$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -4.731 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = -0.309 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -14.57061 \\ hartree = -396.48075 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.2 s\n",
      "------------------------------ Iteration 6 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 5.591 \\quad \\zeta_2 = 3.355 \\quad \\zeta_3 = 1.011 \\quad \\zeta_4 = 0.610$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = 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_2 = 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 c11 = 0.155 \\quad c21 = 0.858 \\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 = -0.003 \\quad c22 = 0.220 \\quad c32 = -0.942 \\quad c42 = -0.099$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -4.732 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = -0.309 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -14.57187 \\ hartree = -396.51521 \\ 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 = 5.591 \\quad \\zeta_2 = 3.355 \\quad \\zeta_3 = 1.011 \\quad \\zeta_4 = 0.610$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = 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_2 = 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 c11 = 0.155 \\quad c21 = 0.858 \\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 = -0.003 \\quad c22 = 0.220 \\quad c32 = -0.942 \\quad c42 = -0.099$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -4.733 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = -0.309 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -14.57223 \\ hartree = -396.52493 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.2 s\n",
      "------------------------------ Iteration 8 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 5.591 \\quad \\zeta_2 = 3.355 \\quad \\zeta_3 = 1.011 \\quad \\zeta_4 = 0.610$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = 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_2 = 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 c11 = 0.155 \\quad c21 = 0.858 \\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 = -0.003 \\quad c22 = 0.220 \\quad c32 = -0.942 \\quad c42 = -0.099$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -4.733 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = -0.309 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -14.57233 \\ hartree = -396.52766 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.2 s\n",
      "------------------------------ Iteration 9 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 5.591 \\quad \\zeta_2 = 3.355 \\quad \\zeta_3 = 1.011 \\quad \\zeta_4 = 0.610$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = 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_2 = 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 c11 = 0.155 \\quad c21 = 0.858 \\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 = -0.003 \\quad c22 = 0.220 \\quad c32 = -0.942 \\quad c42 = -0.099$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -4.733 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = -0.309 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -14.57236 \\ hartree = -396.52843 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.2 s\n",
      "------------------------------ Iteration 10 ------------------------------\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\zeta_1 = 5.591 \\quad \\zeta_2 = 3.355 \\quad \\zeta_3 = 1.011 \\quad \\zeta_4 = 0.610$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Orbitals:$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\phi_1 = 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_2 = 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 c11 = 0.155 \\quad c21 = 0.858 \\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 = -0.003 \\quad c22 = 0.220 \\quad c32 = -0.942 \\quad c42 = -0.099$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_1 \\; for \\; \\phi_1  = -4.733 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  \\epsilon_2 \\; for \\; \\phi_1 = -0.309 $"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle  Hartree \\ Fork \\; atom \\; energy = -14.57237 \\ hartree = -396.52865 \\ eV$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time used: 1.2 s\n"
     ]
    }
   ],
   "source": [
    "# input \n",
    "# input for zeta\n",
    "zetas = [[5.59108, 1], [3.35538, 1], [1.01122, 2], [0.61000, 2]]\n",
    "# input nuclear charge (element number)\n",
    "Z = 4\n",
    "\n",
    "# build basis function\n",
    "f1=STO(zetas[0][0], zetas[0][1])\n",
    "f2=STO(zetas[1][0], zetas[1][1])\n",
    "f3=STO(zetas[2][0], zetas[2][1])\n",
    "f4=STO(zetas[3][0], zetas[3][1])\n",
    "fs = [f1, f2, f3, f4]\n",
    "\n",
    "# initialization\n",
    "R = np.zeros((len(zetas), len(zetas), len(zetas), len(zetas)))\n",
    "H = H_matrix(fs, Z)\n",
    "S = S_matrix(fs)\n",
    "e, Co = secular_eqn(H, S)\n",
    "P = P_matrix(Co)\n",
    "scf_H = get_E0(e, P, H)\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}'.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')))) \n",
    "display(Math('Orbitals:'))\n",
    "display(Math(' \\phi_1 = c_{11} \\chi_1 + c_{21} \\chi_2 + c_{31} \\chi_3 + c_{41} \\chi_4'))\n",
    "display(Math(' \\phi_2 = c_{12} \\chi_1 + c_{22} \\chi_2 + c_{32} \\chi_3 + c_{42} \\chi_4'))    \n",
    "display(Math('c11 = {0} \\quad c21 = {1} \\quad c31 = {2} \\quad c41 = {3}'.format(format(Co[0][0], '0.3f'), format(Co[1][0], '0.3f'), format(Co[2][0], '0.3f'), format(Co[3][0], '0.3f')))) \n",
    "display(Math('c12 = {0} \\quad c22 = {1} \\quad c32 = {2} \\quad c42 = {3}'.format(format(Co[0][1], '0.3f'), format(Co[1][1], '0.3f'), format(Co[2][1], '0.3f'), format(Co[3][1], '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 = Co[0,0]*f1+Co[1,0]*f2+Co[2,0]*f3+Co[3,0]*f4\n",
    "phi2 = Co[0,1]*f1+Co[1,1]*f2+Co[2,1]*f3+Co[3,1]*f4\n",
    "density_1 = phi1*phi1*r*r\n",
    "density_2 = phi2*phi2*r*r    \n",
    "p = plot((density_1, (r, 0, 5)), (density_2, (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[0].line_color = colorlist[0]\n",
    "p[1].line_color = 'blue'\n",
    "p.show()\n",
    "# print energy result\n",
    "display(Math(' \\epsilon_1 \\; for \\; \\phi_1  = {0} '.format(format(e[0].real, '0.3f'))))    \n",
    "display(Math(' \\epsilon_2 \\; for \\; \\phi_1 = {0} '.format(format(e[1].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",
    "##############################################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",
    "        R = R_matrix(zetas)\n",
    "    else:\n",
    "        start = time.time()\n",
    "    F = F_matrix(fs, Z, zetas, Co, R)\n",
    "    S = S_matrix(fs)\n",
    "    e, Co = secular_eqn(F, S)\n",
    "    P = P_matrix(Co)\n",
    "    scf_H = get_E0(e, P, H)\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}'.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')))) \n",
    "    display(Math('Orbitals:'))\n",
    "    display(Math(' \\phi_1 = c_{11} \\chi_1 + c_{21} \\chi_2 + c_{31} \\chi_3 + c_{41} \\chi_4'))\n",
    "    display(Math(' \\phi_2 = c_{12} \\chi_1 + c_{22} \\chi_2 + c_{32} \\chi_3 + c_{42} \\chi_4'))    \n",
    "    display(Math('c11 = {0} \\quad c21 = {1} \\quad c31 = {2} \\quad c41 = {3}'.format(format(Co[0][0], '0.3f'), format(Co[1][0], '0.3f'), format(Co[2][0], '0.3f'), format(Co[3][0], '0.3f')))) \n",
    "    display(Math('c12 = {0} \\quad c22 = {1} \\quad c32 = {2} \\quad c42 = {3}'.format(format(Co[0][1], '0.3f'), format(Co[1][1], '0.3f'), format(Co[2][1], '0.3f'), format(Co[3][1], '0.3f'))))     \n",
    "    # plot density graph\n",
    "    phi1 = Co[0,0]*f1+Co[1,0]*f2+Co[2,0]*f3+Co[3,0]*f4\n",
    "    phi2 = Co[0,1]*f1+Co[1,1]*f2+Co[2,1]*f3+Co[3,1]*f4\n",
    "    density_1 = phi1*phi1*r*r\n",
    "    density_2 = phi2*phi2*r*r    \n",
    "    p1 = plot((density_1, (r, 0, 5)), (density_2, (r, 0, 5)), show = False, legend = True)\n",
    "    p1[0].label = None \n",
    "    p1[1].label = None     \n",
    "    p1[0].line_color = colorlist[i+1]\n",
    "    p1[1].line_color = colorlist[i+1]\n",
    "    p.extend(p1)\n",
    "    p.show() \n",
    "    # print energy result\n",
    "    display(Math(' \\epsilon_1 \\; for \\; \\phi_1  = {0} '.format(format(e[0].real, '0.3f'))))    \n",
    "    display(Math(' \\epsilon_2 \\; for \\; \\phi_1 = {0} '.format(format(e[1].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#################################################    "
   ]
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    "Reference\n",
    "\n",
    "[1] Levine, Quantum Chemistry, 7th Edition, chapter 14  \n",
    "[2] C. Roetti and E. Clementi, J. Chem. Phys., 60, 4725 (1974)  \n",
    "[3] Acosta C R. Restricted closed shell Hartree Fock Roothaan matrix method applied to Helium atom using   Mathematica[J]. European Journal of Physics Education, 2017, 5(1): 1-14.  \n",
    "[4] [Simple Quantum Chemistry: Hartree-Fock in Python, 2018](http://nznano.blogspot.com/2018/03/simple-quantum-chemistry-hartree-fock.html)  \n",
    "[5] [Helium hartree fork, prtkm, 2015](https://github.com/prtkm/helium-hartree-fock/)"
   ]
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