HF_helium_atom.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import lib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hartree Fock computation of the ground state of the Helium atom\n",
    "\n",
    "In this Jupyter Notebook we are going to compare the groundstate energies obtained with the analytical formula for the two body integrals with Montecarlo integration. In both cases, the Self-Consistent Field method is used.\n",
    "\n",
    "### Basis functions\n",
    "First we write the basis we are going to use"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "ALPHA_1 =  0.298073\n",
    "ALPHA_2 =  1.242567\n",
    "ALPHA_3 =  5.782948\n",
    "ALPHA_4 = 38.474970\n",
    "ALPHA = [ALPHA_1, ALPHA_2, ALPHA_3,ALPHA_4]\n",
    "\n",
    "def He_wf(x, y, z, n):\n",
    "    \"\"\"\n",
    "    Evaluates the n^th eigenfunction of the Hydrogen atom with exponential coefficient alpha_i. \n",
    "    The units of x are atomic units. \n",
    "\n",
    "    Parameters\n",
    "    ==========\n",
    "    x, y, z : float or np.ndarray\n",
    "        Position in which to evaluate the wave function\n",
    "    n : int\n",
    "        Number of the wave function\n",
    "\n",
    "    Returns\n",
    "    =======\n",
    "    float or np.ndarray\n",
    "    \"\"\"\n",
    "\n",
    "    if n == 1:\n",
    "        alpha = ALPHA_1\n",
    "    elif n == 2:\n",
    "        alpha = ALPHA_2\n",
    "    elif n == 3:\n",
    "        alpha = ALPHA_3\n",
    "    elif n == 4:\n",
    "        alpha = ALPHA_4\n",
    "    else:\n",
    "        alpha = None\n",
    "\n",
    "    r2 = x**2 + y**2 + z**2\n",
    "\n",
    "    return np.exp(-alpha*r2)\n",
    "\n",
    "def He_wf_basis(R,k):\n",
    "    \"\"\"\n",
    "    Evaluates the k^th eigenfunction of the Hydrogen atom with exponential coefficient alpha_i. \n",
    "    The units of x are atomic units. \n",
    "\n",
    "    Parameters\n",
    "    ==========\n",
    "    R : np.ndarray(3,N)\n",
    "        Position in which to evaluate the wave function\n",
    "    k : int\n",
    "        Number of the wave function\n",
    "\n",
    "    Returns\n",
    "    =======\n",
    "    float or np.ndarray(N)\n",
    "    \"\"\"\n",
    "    return He_wf(R[0],R[1],R[2],k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now write the functions to calculate the integrands of the two-body integrals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def integrand_2(R):\n",
    "    r1 = R[:,0:3]\n",
    "    r2 = R[:,3:6]\n",
    "    r12 = np.sqrt(np.sum((r1 - r2)**2, axis=-1))\n",
    "    return 1/r12\n",
    "\n",
    "def norm_product(p, r, q, s):\n",
    "    a = ALPHA[p-1] + ALPHA[q-1]\n",
    "    b = ALPHA[r-1] + ALPHA[s-1]\n",
    "    PROD = (np.pi/a)**1.5 * (np.pi/b)**1.5\n",
    "    \n",
    "    return PROD\n",
    "\n",
    "def He_two_body_integrand(p, r, q, s):\n",
    "    \"\"\"\n",
    "    Integrand that goes into the monte carlo method in order to compute the \n",
    "    two electron integrals.\n",
    "\n",
    "    Parameters\n",
    "    ==========\n",
    "    indices : int np.ndarray(4)\n",
    "        Indices of the wave function\n",
    "\n",
    "    Returns\n",
    "    =======\n",
    "    function\n",
    "    \"\"\"\n",
    "    \n",
    "    f = lambda R: integrand_2(R)*norm_product(p, r, q, s)\n",
    "    \n",
    "    return f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### One- and two- body integral computations\n",
    "We first initialize some necessary parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_electrons = 2\n",
    "N_basis = 4\n",
    "N_points = 1000000\n",
    "integrals_file_num = \"integrals/integrals_He_num.npy\" # numerical integrals\n",
    "integrals_file_ana = \"integrals/integrals_He_ana.npy\" # numerical integrals\n",
    "\n",
    "normalized_wf = False\n",
    "\n",
    "max_iter_SCF = 500\n",
    "eps_SCF = 1E-5\n",
    "Delta_SCF = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The exact one-body integral function is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def analytical_1(p,q):\n",
    "    I = 3*ALPHA[p-1]*ALPHA[q-1]*np.pi**(1.5)/(ALPHA[p-1] + ALPHA[q-1])**(5/2) - 4*np.pi/(ALPHA[p-1] + ALPHA[q-1])\n",
    "    return I"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The exact two-body integral function is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def analytical_2(p, r, q, s):\n",
    "    I = 2*np.pi**2.5 / ((ALPHA[p-1] + ALPHA[q-1])*(ALPHA[r-1] + ALPHA[s-1])*np.sqrt((ALPHA[p-1] + ALPHA[q-1] + ALPHA[r-1] + ALPHA[s-1])))\n",
    "    return I"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The covariance function for the exponents of the gaussians is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_cov(p, r, q, s):\n",
    "    cov = 0.5*np.diag([1/(ALPHA[p-1] + ALPHA[q-1])]*3 + [1/(ALPHA[r-1] + ALPHA[s-1])]*3)\n",
    "    return cov"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then calculate and store the one- and two-body integrals using lib.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integral file already exists. Not computing the integrals. \n",
      "Integral file already exists. Not computing the integrals. \n"
     ]
    }
   ],
   "source": [
    "# One- and Two-body integrals (numerical)\n",
    "MC_args = {\"f_cov\":f_cov, \"f_integrand\":He_two_body_integrand, \"N_points\":N_points}\n",
    "integrals_num = lib.integral_master(N_basis)\n",
    "integrals_num.calculate(integrals_file_num, analytical_1, analytical_2=None, MC_args=MC_args)\n",
    "\n",
    "# One- and Two-body integrals (analytical)\n",
    "integrals_ana = lib.integral_master(N_basis)\n",
    "integrals_ana.calculate(integrals_file_ana, analytical_1, analytical_2=analytical_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We calculate the overlap matrix S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S = \n",
      " [[1.20975063e+01 2.91187719e+00 3.71330014e-01 2.30637530e-02]\n",
      " [2.91187719e+00 1.42134692e+00 2.99025043e-01 2.22459699e-02]\n",
      " [3.71330014e-01 2.99025043e-01 1.41564997e-01 1.89120383e-02]\n",
      " [2.30637530e-02 2.22459699e-02 1.89120383e-02 8.24921040e-03]]\n"
     ]
    }
   ],
   "source": [
    "S = np.zeros((4,4))\n",
    "for p in range(4):\n",
    "    for q in range(4):\n",
    "        S[p][q] = (np.pi/(ALPHA[p]+ALPHA[q]))**(1.5)\n",
    "SVAL, SVEC = np.linalg.eigh(S) \n",
    "SVAL_minhalf = (np.diag(SVAL**(-0.5))) \n",
    "X = np.dot(SVEC, np.dot(SVAL_minhalf, np.transpose(SVEC)))\n",
    "print('S = \\n',S)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Self-Consistent Field (numerical integration)\n",
    "\n",
    "Finally, we run the Self-Consistent Field for Hartree Fock"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E = -0.6042396 | N(SCF) = 1\n",
      "E = -1.9433821 | N(SCF) = 2\n",
      "E = -1.9110050 | N(SCF) = 3\n",
      "E = -2.8296607 | N(SCF) = 4\n",
      "E = -2.7210994 | N(SCF) = 5\n",
      "E = -2.7427273 | N(SCF) = 6\n",
      "E = -2.8095379 | N(SCF) = 7\n",
      "E = -2.8607228 | N(SCF) = 8\n",
      "E = -2.8511643 | N(SCF) = 9\n",
      "E = -2.8448826 | N(SCF) = 10\n",
      "E = -2.8505860 | N(SCF) = 11\n",
      "E = -2.8611955 | N(SCF) = 12\n",
      "E = -2.8281373 | N(SCF) = 13\n",
      "E = -2.8763011 | N(SCF) = 14\n",
      "E = -2.8276697 | N(SCF) = 15\n",
      "E = -2.8880942 | N(SCF) = 16\n",
      "E = -2.8357733 | N(SCF) = 17\n",
      "E = -2.8392938 | N(SCF) = 18\n",
      "E = -2.8438858 | N(SCF) = 19\n",
      "E = -2.8897208 | N(SCF) = 20\n",
      "E = -2.8051901 | N(SCF) = 21\n",
      "E = -2.8767568 | N(SCF) = 22\n",
      "E = -2.8443954 | N(SCF) = 23\n",
      "E = -2.8741079 | N(SCF) = 24\n",
      "E = -2.8283481 | N(SCF) = 25\n",
      "E = -2.8640777 | N(SCF) = 26\n",
      "E = -2.8362524 | N(SCF) = 27\n",
      "E = -2.8688703 | N(SCF) = 28\n",
      "E = -2.8501253 | N(SCF) = 29\n",
      "E = -2.8475172 | N(SCF) = 30\n",
      "E = -2.8600183 | N(SCF) = 31\n",
      "E = -2.8603063 | N(SCF) = 32\n",
      "E = -2.8393407 | N(SCF) = 33\n",
      "E = -2.8766773 | N(SCF) = 34\n",
      "E = -2.7857504 | N(SCF) = 35\n",
      "E = -2.8404307 | N(SCF) = 36\n",
      "E = -2.9028093 | N(SCF) = 37\n",
      "E = -2.7040214 | N(SCF) = 38\n",
      "E = -2.9358619 | N(SCF) = 39\n",
      "E = -2.6452755 | N(SCF) = 40\n",
      "E = -3.0320962 | N(SCF) = 41\n",
      "E = -2.6080419 | N(SCF) = 42\n",
      "E = -2.7973553 | N(SCF) = 43\n",
      "E = -3.0011213 | N(SCF) = 44\n",
      "E = -2.6784555 | N(SCF) = 45\n",
      "E = -2.7046214 | N(SCF) = 46\n",
      "E = -3.0035379 | N(SCF) = 47\n",
      "E = -2.5166526 | N(SCF) = 48\n",
      "E = -3.2910408 | N(SCF) = 49\n",
      "E = -2.5237214 | N(SCF) = 50\n",
      "E = -2.7024138 | N(SCF) = 51\n",
      "E = -3.1616027 | N(SCF) = 52\n",
      "E = -2.7450742 | N(SCF) = 53\n",
      "E = -2.7695562 | N(SCF) = 54\n",
      "E = -2.8265446 | N(SCF) = 55\n",
      "E = -2.9628568 | N(SCF) = 56\n",
      "E = -2.5342054 | N(SCF) = 57\n",
      "E = -2.6925881 | N(SCF) = 58\n",
      "E = -3.0780366 | N(SCF) = 59\n",
      "E = -2.6562385 | N(SCF) = 60\n",
      "E = -2.7569124 | N(SCF) = 61\n",
      "E = -2.8028974 | N(SCF) = 62\n",
      "E = -2.9755358 | N(SCF) = 63\n",
      "E = -2.5699501 | N(SCF) = 64\n",
      "E = -2.9989767 | N(SCF) = 65\n",
      "E = -2.6755794 | N(SCF) = 66\n",
      "E = -2.7653586 | N(SCF) = 67\n",
      "E = -3.0577296 | N(SCF) = 68\n",
      "E = -2.5076362 | N(SCF) = 69\n",
      "E = -3.2523457 | N(SCF) = 70\n",
      "E = -2.4244018 | N(SCF) = 71\n",
      "E = -3.6183505 | N(SCF) = 72\n",
      "E = -2.2506786 | N(SCF) = 73\n",
      "E = -2.5676412 | N(SCF) = 74\n",
      "E = -2.7924389 | N(SCF) = 75\n",
      "E = -2.8693009 | N(SCF) = 76\n",
      "E = -2.8932838 | N(SCF) = 77\n",
      "E = -2.8736913 | N(SCF) = 78\n",
      "E = -2.8477031 | N(SCF) = 79\n",
      "E = -2.8621225 | N(SCF) = 80\n",
      "E = -2.8438859 | N(SCF) = 81\n",
      "E = -2.8657578 | N(SCF) = 82\n",
      "E = -2.8432535 | N(SCF) = 83\n",
      "E = -2.8565005 | N(SCF) = 84\n",
      "E = -2.8721570 | N(SCF) = 85\n",
      "E = -2.8029121 | N(SCF) = 86\n",
      "E = -2.9139720 | N(SCF) = 87\n",
      "E = -2.6504133 | N(SCF) = 88\n",
      "E = -2.9163889 | N(SCF) = 89\n",
      "E = -2.7807842 | N(SCF) = 90\n",
      "E = -2.7959936 | N(SCF) = 91\n",
      "E = -2.8362770 | N(SCF) = 92\n",
      "E = -2.9090553 | N(SCF) = 93\n",
      "E = -2.7657237 | N(SCF) = 94\n",
      "E = -2.9976389 | N(SCF) = 95\n",
      "E = -2.4765052 | N(SCF) = 96\n",
      "E = -2.7607637 | N(SCF) = 97\n",
      "E = -2.7567091 | N(SCF) = 98\n",
      "E = -2.8164510 | N(SCF) = 99\n",
      "E = -2.9050551 | N(SCF) = 100\n",
      "E = -2.8359293 | N(SCF) = 101\n",
      "E = -2.8408829 | N(SCF) = 102\n",
      "E = -2.8856715 | N(SCF) = 103\n",
      "E = -2.8542915 | N(SCF) = 104\n",
      "E = -2.8580364 | N(SCF) = 105\n",
      "E = -2.8473413 | N(SCF) = 106\n",
      "E = -2.8548754 | N(SCF) = 107\n",
      "E = -2.8630274 | N(SCF) = 108\n",
      "E = -2.8448287 | N(SCF) = 109\n",
      "E = -2.8541666 | N(SCF) = 110\n",
      "E = -2.8738711 | N(SCF) = 111\n",
      "E = -2.8014336 | N(SCF) = 112\n",
      "E = -2.8773979 | N(SCF) = 113\n",
      "E = -2.8067359 | N(SCF) = 114\n",
      "E = -2.9211601 | N(SCF) = 115\n",
      "E = -2.5806603 | N(SCF) = 116\n",
      "E = -2.9710139 | N(SCF) = 117\n",
      "E = -2.6949851 | N(SCF) = 118\n",
      "E = -3.0850965 | N(SCF) = 119\n",
      "E = -2.5071485 | N(SCF) = 120\n",
      "E = -2.6968600 | N(SCF) = 121\n",
      "E = -3.0695866 | N(SCF) = 122\n",
      "E = -2.6252957 | N(SCF) = 123\n",
      "E = -2.7642499 | N(SCF) = 124\n",
      "E = -2.8659700 | N(SCF) = 125\n",
      "E = -2.8701426 | N(SCF) = 126\n",
      "E = -2.8297805 | N(SCF) = 127\n",
      "E = -2.8616267 | N(SCF) = 128\n",
      "E = -2.8602772 | N(SCF) = 129\n",
      "E = -2.8953976 | N(SCF) = 130\n",
      "E = -2.6936118 | N(SCF) = 131\n",
      "E = -2.9180748 | N(SCF) = 132\n",
      "E = -2.6890842 | N(SCF) = 133\n",
      "E = -2.8216367 | N(SCF) = 134\n",
      "E = -2.9569353 | N(SCF) = 135\n",
      "E = -2.6372758 | N(SCF) = 136\n",
      "E = -3.0253335 | N(SCF) = 137\n",
      "E = -2.5362900 | N(SCF) = 138\n",
      "E = -2.8102444 | N(SCF) = 139\n",
      "E = -2.8250086 | N(SCF) = 140\n",
      "E = -2.9658427 | N(SCF) = 141\n",
      "E = -2.8507359 | N(SCF) = 142\n",
      "E = -2.8527032 | N(SCF) = 143\n",
      "E = -2.8623036 | N(SCF) = 144\n",
      "E = -2.8561697 | N(SCF) = 145\n",
      "E = -2.8539903 | N(SCF) = 146\n",
      "E = -2.8552320 | N(SCF) = 147\n",
      "E = -2.8550102 | N(SCF) = 148\n",
      "E = -2.8544705 | N(SCF) = 149\n",
      "E = -2.8554476 | N(SCF) = 150\n",
      "E = -2.8546330 | N(SCF) = 151\n",
      "E = -2.8545693 | N(SCF) = 152\n",
      "E = -2.8550857 | N(SCF) = 153\n",
      "E = -2.8539432 | N(SCF) = 154\n",
      "E = -2.8555124 | N(SCF) = 155\n",
      "E = -2.8544144 | N(SCF) = 156\n",
      "E = -2.8566031 | N(SCF) = 157\n",
      "E = -2.8521264 | N(SCF) = 158\n",
      "E = -2.8610299 | N(SCF) = 159\n",
      "E = -2.8489378 | N(SCF) = 160\n",
      "E = -2.8555953 | N(SCF) = 161\n",
      "E = -2.8545386 | N(SCF) = 162\n",
      "E = -2.8545854 | N(SCF) = 163\n",
      "E = -2.8553266 | N(SCF) = 164\n",
      "E = -2.8529837 | N(SCF) = 165\n",
      "E = -2.8615608 | N(SCF) = 166\n",
      "E = -2.8374690 | N(SCF) = 167\n",
      "E = -2.8702979 | N(SCF) = 168\n",
      "E = -2.8202853 | N(SCF) = 169\n",
      "E = -2.9049281 | N(SCF) = 170\n",
      "E = -2.5780296 | N(SCF) = 171\n",
      "E = -2.7304736 | N(SCF) = 172\n",
      "E = -3.1426722 | N(SCF) = 173\n",
      "E = -2.3754750 | N(SCF) = 174\n",
      "E = -2.4709568 | N(SCF) = 175\n",
      "E = -2.6026245 | N(SCF) = 176\n",
      "E = -2.6205673 | N(SCF) = 177\n",
      "E = -3.0648387 | N(SCF) = 178\n",
      "E = -2.6849842 | N(SCF) = 179\n",
      "E = -2.7622222 | N(SCF) = 180\n",
      "E = -2.8543301 | N(SCF) = 181\n",
      "E = -2.9565745 | N(SCF) = 182\n",
      "E = -2.8546049 | N(SCF) = 183\n",
      "E = -2.8544132 | N(SCF) = 184\n",
      "E = -2.8626798 | N(SCF) = 185\n",
      "E = -2.8284980 | N(SCF) = 186\n",
      "E = -2.9313105 | N(SCF) = 187\n",
      "E = -2.5711500 | N(SCF) = 188\n",
      "E = -3.0200353 | N(SCF) = 189\n",
      "E = -2.6861341 | N(SCF) = 190\n",
      "E = -2.7237770 | N(SCF) = 191\n",
      "E = -2.8363604 | N(SCF) = 192\n",
      "E = -2.8992472 | N(SCF) = 193\n",
      "E = -2.8430937 | N(SCF) = 194\n",
      "E = -2.8910488 | N(SCF) = 195\n",
      "E = -2.8154648 | N(SCF) = 196\n",
      "E = -2.8880936 | N(SCF) = 197\n",
      "E = -2.7812756 | N(SCF) = 198\n",
      "E = -2.9021392 | N(SCF) = 199\n",
      "E = -2.6948328 | N(SCF) = 200\n",
      "E = -2.8510130 | N(SCF) = 201\n",
      "E = -2.8180606 | N(SCF) = 202\n",
      "E = -2.8266059 | N(SCF) = 203\n",
      "E = -2.8177248 | N(SCF) = 204\n",
      "E = -2.8363395 | N(SCF) = 205\n",
      "E = -2.8315205 | N(SCF) = 206\n",
      "E = -2.8407443 | N(SCF) = 207\n",
      "E = -2.8898940 | N(SCF) = 208\n",
      "E = -2.8587435 | N(SCF) = 209\n",
      "E = -2.8548298 | N(SCF) = 210\n",
      "E = -2.8552711 | N(SCF) = 211\n",
      "E = -2.8544458 | N(SCF) = 212\n",
      "E = -2.8551496 | N(SCF) = 213\n",
      "E = -2.8545427 | N(SCF) = 214\n",
      "E = -2.8549338 | N(SCF) = 215\n",
      "E = -2.8543924 | N(SCF) = 216\n",
      "E = -2.8550525 | N(SCF) = 217\n",
      "E = -2.8549557 | N(SCF) = 218\n",
      "E = -2.8545287 | N(SCF) = 219\n",
      "E = -2.8550207 | N(SCF) = 220\n",
      "E = -2.8546936 | N(SCF) = 221\n",
      "E = -2.8548082 | N(SCF) = 222\n",
      "E = -2.8548691 | N(SCF) = 223\n",
      "E = -2.8546814 | N(SCF) = 224\n",
      "E = -2.8551561 | N(SCF) = 225\n",
      "E = -2.8545262 | N(SCF) = 226\n",
      "E = -2.8547370 | N(SCF) = 227\n",
      "E = -2.8549187 | N(SCF) = 228\n",
      "E = -2.8544675 | N(SCF) = 229\n",
      "E = -2.8556474 | N(SCF) = 230\n",
      "E = -2.8528750 | N(SCF) = 231\n",
      "E = -2.8620566 | N(SCF) = 232\n",
      "E = -2.8318861 | N(SCF) = 233\n",
      "E = -2.9163447 | N(SCF) = 234\n",
      "E = -2.4214907 | N(SCF) = 235\n",
      "E = -2.9293292 | N(SCF) = 236\n",
      "E = -2.8841520 | N(SCF) = 237\n",
      "E = -2.9557816 | N(SCF) = 238\n",
      "E = -2.7393702 | N(SCF) = 239\n",
      "E = -2.8014808 | N(SCF) = 240\n",
      "E = -2.8875911 | N(SCF) = 241\n",
      "E = -2.8143912 | N(SCF) = 242\n",
      "E = -2.9362872 | N(SCF) = 243\n",
      "E = -2.6004251 | N(SCF) = 244\n",
      "E = -2.7108774 | N(SCF) = 245\n",
      "E = -2.8966648 | N(SCF) = 246\n",
      "E = -2.7851038 | N(SCF) = 247\n",
      "E = -2.8554927 | N(SCF) = 248\n",
      "E = -2.8919947 | N(SCF) = 249\n",
      "E = -2.8604815 | N(SCF) = 250\n",
      "E = -2.8635913 | N(SCF) = 251\n",
      "E = -2.8353583 | N(SCF) = 252\n",
      "E = -2.8825135 | N(SCF) = 253\n",
      "E = -2.7657647 | N(SCF) = 254\n",
      "E = -2.9709317 | N(SCF) = 255\n",
      "E = -2.4064436 | N(SCF) = 256\n",
      "E = -2.6121672 | N(SCF) = 257\n",
      "E = -2.8803376 | N(SCF) = 258\n",
      "E = -2.8279105 | N(SCF) = 259\n",
      "E = -2.8514797 | N(SCF) = 260\n",
      "E = -2.9195515 | N(SCF) = 261\n",
      "E = -2.8563989 | N(SCF) = 262\n",
      "E = -2.8552280 | N(SCF) = 263\n",
      "E = -2.8560974 | N(SCF) = 264\n",
      "E = -2.8612865 | N(SCF) = 265\n",
      "E = -2.8219151 | N(SCF) = 266\n",
      "E = -2.9114805 | N(SCF) = 267\n",
      "E = -2.4954427 | N(SCF) = 268\n",
      "E = -3.1651347 | N(SCF) = 269\n",
      "E = -2.5533000 | N(SCF) = 270\n",
      "E = -2.7400066 | N(SCF) = 271\n",
      "E = -2.8996225 | N(SCF) = 272\n",
      "E = -2.8885351 | N(SCF) = 273\n",
      "E = -2.9579765 | N(SCF) = 274\n",
      "E = -2.4728464 | N(SCF) = 275\n",
      "E = -3.0778177 | N(SCF) = 276\n",
      "E = -2.6490358 | N(SCF) = 277\n",
      "E = -3.2005349 | N(SCF) = 278\n",
      "E = -2.4146943 | N(SCF) = 279\n",
      "E = -2.4462515 | N(SCF) = 280\n",
      "E = -2.8205003 | N(SCF) = 281\n",
      "E = -2.8199340 | N(SCF) = 282\n",
      "E = -2.8943484 | N(SCF) = 283\n",
      "E = -2.9191046 | N(SCF) = 284\n",
      "E = -2.8519211 | N(SCF) = 285\n",
      "E = -2.8675452 | N(SCF) = 286\n",
      "E = -2.8484983 | N(SCF) = 287\n",
      "E = -2.8289764 | N(SCF) = 288\n",
      "E = -2.9083351 | N(SCF) = 289\n",
      "E = -2.5816784 | N(SCF) = 290\n",
      "E = -3.1371406 | N(SCF) = 291\n",
      "E = -2.4320381 | N(SCF) = 292\n",
      "E = -2.7562455 | N(SCF) = 293\n",
      "E = -2.7770195 | N(SCF) = 294\n",
      "E = -2.7689524 | N(SCF) = 295\n",
      "E = -2.9921794 | N(SCF) = 296\n",
      "E = -2.8439921 | N(SCF) = 297\n",
      "E = -2.8520585 | N(SCF) = 298\n",
      "E = -2.8583418 | N(SCF) = 299\n",
      "E = -2.8647095 | N(SCF) = 300\n",
      "E = -2.8525360 | N(SCF) = 301\n",
      "E = -2.8505057 | N(SCF) = 302\n",
      "E = -2.8549954 | N(SCF) = 303\n",
      "E = -2.8572333 | N(SCF) = 304\n",
      "E = -2.8457846 | N(SCF) = 305\n",
      "E = -2.8821259 | N(SCF) = 306\n",
      "E = -2.7124705 | N(SCF) = 307\n",
      "E = -2.9723070 | N(SCF) = 308\n",
      "E = -2.4819191 | N(SCF) = 309\n",
      "E = -3.3661876 | N(SCF) = 310\n",
      "E = -2.4223412 | N(SCF) = 311\n",
      "E = -2.7372249 | N(SCF) = 312\n",
      "E = -2.9232508 | N(SCF) = 313\n",
      "E = -2.8206375 | N(SCF) = 314\n",
      "E = -2.8703225 | N(SCF) = 315\n",
      "E = -2.8582507 | N(SCF) = 316\n",
      "E = -2.9428823 | N(SCF) = 317\n",
      "E = -2.6981094 | N(SCF) = 318\n",
      "E = -2.7406743 | N(SCF) = 319\n",
      "E = -2.8348115 | N(SCF) = 320\n",
      "E = -2.8902971 | N(SCF) = 321\n",
      "E = -2.7868029 | N(SCF) = 322\n",
      "E = -2.9601716 | N(SCF) = 323\n",
      "E = -2.4151426 | N(SCF) = 324\n",
      "E = -2.4527645 | N(SCF) = 325\n",
      "E = -2.9323121 | N(SCF) = 326\n",
      "E = -2.9681070 | N(SCF) = 327\n",
      "E = -2.9816428 | N(SCF) = 328\n",
      "E = -2.4183798 | N(SCF) = 329\n",
      "E = -2.9183306 | N(SCF) = 330\n",
      "E = -2.9604550 | N(SCF) = 331\n",
      "E = -2.6109675 | N(SCF) = 332\n",
      "E = -2.7849212 | N(SCF) = 333\n",
      "E = -2.9848844 | N(SCF) = 334\n",
      "E = -2.7309747 | N(SCF) = 335\n",
      "E = -2.9411466 | N(SCF) = 336\n",
      "E = -2.5154386 | N(SCF) = 337\n",
      "E = -3.0167259 | N(SCF) = 338\n",
      "E = -2.6309803 | N(SCF) = 339\n",
      "E = -2.7375042 | N(SCF) = 340\n",
      "E = -2.9283374 | N(SCF) = 341\n",
      "E = -2.8037311 | N(SCF) = 342\n",
      "E = -2.8262293 | N(SCF) = 343\n",
      "E = -2.8269691 | N(SCF) = 344\n",
      "E = -2.8339359 | N(SCF) = 345\n",
      "E = -2.8543404 | N(SCF) = 346\n",
      "E = -2.8864130 | N(SCF) = 347\n",
      "E = -2.8511950 | N(SCF) = 348\n",
      "E = -2.8691112 | N(SCF) = 349\n",
      "E = -2.7971120 | N(SCF) = 350\n",
      "E = -2.8913688 | N(SCF) = 351\n",
      "E = -2.6834282 | N(SCF) = 352\n",
      "E = -2.8194166 | N(SCF) = 353\n",
      "E = -2.8923506 | N(SCF) = 354\n",
      "E = -2.8421851 | N(SCF) = 355\n",
      "E = -2.9571692 | N(SCF) = 356\n",
      "E = -2.4582830 | N(SCF) = 357\n",
      "E = -2.6205488 | N(SCF) = 358\n",
      "E = -2.8975789 | N(SCF) = 359\n",
      "E = -2.8805392 | N(SCF) = 360\n",
      "E = -2.8696360 | N(SCF) = 361\n",
      "E = -2.8444227 | N(SCF) = 362\n",
      "E = -2.8676235 | N(SCF) = 363\n",
      "E = -2.8433871 | N(SCF) = 364\n",
      "E = -2.8420941 | N(SCF) = 365\n",
      "E = -2.9226249 | N(SCF) = 366\n",
      "E = -2.4462171 | N(SCF) = 367\n",
      "E = -3.3584271 | N(SCF) = 368\n",
      "E = -2.2465033 | N(SCF) = 369\n",
      "E = -2.8642118 | N(SCF) = 370\n",
      "E = -2.7560904 | N(SCF) = 371\n",
      "E = -3.0392854 | N(SCF) = 372\n",
      "E = -2.5688399 | N(SCF) = 373\n",
      "E = -2.8464047 | N(SCF) = 374\n",
      "E = -2.8851773 | N(SCF) = 375\n",
      "E = -2.8723968 | N(SCF) = 376\n",
      "E = -2.8753157 | N(SCF) = 377\n",
      "E = -2.8502338 | N(SCF) = 378\n",
      "E = -2.8776712 | N(SCF) = 379\n",
      "E = -2.8360513 | N(SCF) = 380\n",
      "E = -2.8562893 | N(SCF) = 381\n",
      "E = -2.8553357 | N(SCF) = 382\n",
      "E = -2.8652550 | N(SCF) = 383\n",
      "E = -2.8193108 | N(SCF) = 384\n",
      "E = -2.8980534 | N(SCF) = 385\n",
      "E = -2.6580512 | N(SCF) = 386\n",
      "E = -3.0896813 | N(SCF) = 387\n",
      "E = -2.4479954 | N(SCF) = 388\n",
      "E = -2.8273128 | N(SCF) = 389\n",
      "E = -2.9242114 | N(SCF) = 390\n",
      "E = -2.9255469 | N(SCF) = 391\n",
      "E = -2.9177065 | N(SCF) = 392\n",
      "E = -2.6937108 | N(SCF) = 393\n",
      "E = -3.0310536 | N(SCF) = 394\n",
      "E = -2.4950933 | N(SCF) = 395\n",
      "E = -2.9162285 | N(SCF) = 396\n",
      "E = -2.8833115 | N(SCF) = 397\n",
      "E = -2.9289165 | N(SCF) = 398\n",
      "E = -2.5250311 | N(SCF) = 399\n",
      "E = -2.8614238 | N(SCF) = 400\n",
      "E = -2.7380108 | N(SCF) = 401\n",
      "E = -2.8339896 | N(SCF) = 402\n",
      "E = -2.9480376 | N(SCF) = 403\n",
      "E = -2.8264726 | N(SCF) = 404\n",
      "E = -2.8932883 | N(SCF) = 405\n",
      "E = -2.7313412 | N(SCF) = 406\n",
      "E = -2.9203108 | N(SCF) = 407\n",
      "E = -2.6718178 | N(SCF) = 408\n",
      "E = -3.0747994 | N(SCF) = 409\n",
      "E = -2.4867510 | N(SCF) = 410\n",
      "E = -2.8941328 | N(SCF) = 411\n",
      "E = -2.7334831 | N(SCF) = 412\n",
      "E = -2.8631013 | N(SCF) = 413\n",
      "E = -2.9548149 | N(SCF) = 414\n",
      "E = -2.5818998 | N(SCF) = 415\n",
      "E = -2.9251092 | N(SCF) = 416\n",
      "E = -2.7680464 | N(SCF) = 417\n",
      "E = -2.7499188 | N(SCF) = 418\n",
      "E = -2.9796220 | N(SCF) = 419\n",
      "E = -2.7323206 | N(SCF) = 420\n",
      "E = -2.6781744 | N(SCF) = 421\n",
      "E = -2.7214691 | N(SCF) = 422\n",
      "E = -2.8251276 | N(SCF) = 423\n",
      "E = -2.8382622 | N(SCF) = 424\n",
      "E = -2.8478582 | N(SCF) = 425\n",
      "E = -2.8851156 | N(SCF) = 426\n",
      "E = -2.8492705 | N(SCF) = 427\n",
      "E = -2.8632127 | N(SCF) = 428\n",
      "E = -2.8556163 | N(SCF) = 429\n",
      "E = -2.8558112 | N(SCF) = 430\n",
      "E = -2.8541964 | N(SCF) = 431\n",
      "E = -2.8553359 | N(SCF) = 432\n",
      "E = -2.8589386 | N(SCF) = 433\n",
      "E = -2.8396629 | N(SCF) = 434\n",
      "E = -2.8563496 | N(SCF) = 435\n",
      "E = -2.8771035 | N(SCF) = 436\n",
      "E = -2.8460743 | N(SCF) = 437\n",
      "E = -2.8376329 | N(SCF) = 438\n",
      "E = -2.8544234 | N(SCF) = 439\n",
      "E = -2.8541644 | N(SCF) = 440\n",
      "E = -2.8568760 | N(SCF) = 441\n",
      "E = -2.8539389 | N(SCF) = 442\n",
      "E = -2.8541983 | N(SCF) = 443\n",
      "E = -2.8570977 | N(SCF) = 444\n",
      "E = -2.8543551 | N(SCF) = 445\n",
      "E = -2.8527105 | N(SCF) = 446\n",
      "E = -2.8558124 | N(SCF) = 447\n",
      "E = -2.8553256 | N(SCF) = 448\n",
      "E = -2.8535830 | N(SCF) = 449\n",
      "E = -2.8583226 | N(SCF) = 450\n",
      "E = -2.8448952 | N(SCF) = 451\n",
      "E = -2.8614000 | N(SCF) = 452\n",
      "E = -2.8526385 | N(SCF) = 453\n",
      "E = -2.8559082 | N(SCF) = 454\n",
      "E = -2.8550175 | N(SCF) = 455\n",
      "E = -2.8547542 | N(SCF) = 456\n",
      "E = -2.8555340 | N(SCF) = 457\n",
      "E = -2.8546985 | N(SCF) = 458\n",
      "E = -2.8525826 | N(SCF) = 459\n",
      "E = -2.8574144 | N(SCF) = 460\n",
      "E = -2.8497758 | N(SCF) = 461\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E = -2.8560997 | N(SCF) = 462\n",
      "E = -2.8564930 | N(SCF) = 463\n",
      "E = -2.8557096 | N(SCF) = 464\n",
      "E = -2.8537531 | N(SCF) = 465\n",
      "E = -2.8559317 | N(SCF) = 466\n",
      "E = -2.8544696 | N(SCF) = 467\n",
      "E = -2.8551191 | N(SCF) = 468\n",
      "E = -2.8539290 | N(SCF) = 469\n",
      "E = -2.8562939 | N(SCF) = 470\n",
      "E = -2.8529945 | N(SCF) = 471\n",
      "E = -2.8549742 | N(SCF) = 472\n",
      "E = -2.8572131 | N(SCF) = 473\n",
      "E = -2.8484411 | N(SCF) = 474\n",
      "E = -2.8633646 | N(SCF) = 475\n",
      "E = -2.8528375 | N(SCF) = 476\n",
      "E = -2.8452359 | N(SCF) = 477\n",
      "E = -2.8770347 | N(SCF) = 478\n",
      "E = -2.7919115 | N(SCF) = 479\n",
      "E = -2.8858811 | N(SCF) = 480\n",
      "E = -2.7764887 | N(SCF) = 481\n",
      "E = -2.8347614 | N(SCF) = 482\n",
      "E = -2.9635726 | N(SCF) = 483\n",
      "E = -2.6004218 | N(SCF) = 484\n",
      "E = -2.8485174 | N(SCF) = 485\n",
      "E = -2.9601180 | N(SCF) = 486\n",
      "E = -2.8371099 | N(SCF) = 487\n",
      "E = -2.8881615 | N(SCF) = 488\n",
      "E = -2.8422356 | N(SCF) = 489\n",
      "E = -2.8039077 | N(SCF) = 490\n",
      "E = -2.8900528 | N(SCF) = 491\n",
      "E = -2.8205756 | N(SCF) = 492\n",
      "E = -2.8437067 | N(SCF) = 493\n",
      "E = -2.8540136 | N(SCF) = 494\n",
      "E = -2.8838715 | N(SCF) = 495\n",
      "E = -2.8200695 | N(SCF) = 496\n",
      "E = -2.8639253 | N(SCF) = 497\n",
      "E = -2.8549441 | N(SCF) = 498\n",
      "E = -2.8543326 | N(SCF) = 499\n",
      "E = -2.8572209 | N(SCF) = 500\n",
      "SCF not converged!\n",
      "Restarting again...\n",
      "E = -2.3475587 | N(SCF) = 1\n",
      "E = -2.7310765 | N(SCF) = 2\n",
      "E = -2.7555608 | N(SCF) = 3\n",
      "E = -2.7774524 | N(SCF) = 4\n",
      "E = -2.7902235 | N(SCF) = 5\n",
      "E = -2.8710345 | N(SCF) = 6\n",
      "E = -2.8569881 | N(SCF) = 7\n",
      "E = -2.8510243 | N(SCF) = 8\n",
      "E = -2.8555002 | N(SCF) = 9\n",
      "E = -2.8570032 | N(SCF) = 10\n",
      "E = -2.8482089 | N(SCF) = 11\n",
      "E = -2.8574438 | N(SCF) = 12\n",
      "E = -2.8581041 | N(SCF) = 13\n",
      "E = -2.8457424 | N(SCF) = 14\n",
      "E = -2.8869935 | N(SCF) = 15\n",
      "E = -2.6662651 | N(SCF) = 16\n",
      "E = -2.7975544 | N(SCF) = 17\n",
      "E = -2.9123726 | N(SCF) = 18\n",
      "E = -2.7628258 | N(SCF) = 19\n",
      "E = -2.9200767 | N(SCF) = 20\n",
      "E = -2.6204700 | N(SCF) = 21\n",
      "E = -2.7880906 | N(SCF) = 22\n",
      "E = -3.0730407 | N(SCF) = 23\n",
      "E = -2.7124084 | N(SCF) = 24\n",
      "E = -2.8752491 | N(SCF) = 25\n",
      "E = -2.8309717 | N(SCF) = 26\n",
      "E = -2.8615694 | N(SCF) = 27\n",
      "E = -2.8697198 | N(SCF) = 28\n",
      "E = -2.8375724 | N(SCF) = 29\n",
      "E = -2.9011720 | N(SCF) = 30\n",
      "E = -2.7383406 | N(SCF) = 31\n",
      "E = -2.8800809 | N(SCF) = 32\n",
      "E = -2.8281501 | N(SCF) = 33\n",
      "E = -2.8470162 | N(SCF) = 34\n",
      "E = -2.8581821 | N(SCF) = 35\n",
      "E = -2.8598883 | N(SCF) = 36\n",
      "E = -2.8513167 | N(SCF) = 37\n",
      "E = -2.8562120 | N(SCF) = 38\n",
      "E = -2.8536570 | N(SCF) = 39\n",
      "E = -2.8530709 | N(SCF) = 40\n",
      "SCF CONVERGED! E = -2.8530709022\n"
     ]
    }
   ],
   "source": [
    "_ = lib.SCF(N_electrons, integrals_num, S, max_iter_SCF, eps_SCF)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Self-Consistent Field (analytical integration)\n",
    "\n",
    "Finally, we run the Self-Consistent Field for Hartree Fock"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E = -2.8439921 | N(SCF) = 1\n",
      "E = -2.7399774 | N(SCF) = 2\n",
      "E = -2.7165229 | N(SCF) = 3\n",
      "E = -2.8433812 | N(SCF) = 4\n",
      "E = -2.7805373 | N(SCF) = 5\n",
      "E = -2.8603455 | N(SCF) = 6\n",
      "E = -2.8568954 | N(SCF) = 7\n",
      "E = -2.8490452 | N(SCF) = 8\n",
      "E = -2.8615266 | N(SCF) = 9\n",
      "E = -2.8349428 | N(SCF) = 10\n",
      "E = -2.9001743 | N(SCF) = 11\n",
      "E = -2.6772109 | N(SCF) = 12\n",
      "E = -3.0143114 | N(SCF) = 13\n",
      "E = -2.5532448 | N(SCF) = 14\n",
      "E = -2.7370146 | N(SCF) = 15\n",
      "E = -2.9705445 | N(SCF) = 16\n",
      "E = -2.6461280 | N(SCF) = 17\n",
      "E = -3.0055466 | N(SCF) = 18\n",
      "E = -2.6611203 | N(SCF) = 19\n",
      "E = -2.7587670 | N(SCF) = 20\n",
      "E = -2.9931236 | N(SCF) = 21\n",
      "E = -2.6495647 | N(SCF) = 22\n",
      "E = -2.8115719 | N(SCF) = 23\n",
      "E = -3.0447424 | N(SCF) = 24\n",
      "E = -2.7270375 | N(SCF) = 25\n",
      "E = -2.8272550 | N(SCF) = 26\n",
      "E = -2.8885693 | N(SCF) = 27\n",
      "E = -2.9126861 | N(SCF) = 28\n",
      "E = -2.7212346 | N(SCF) = 29\n",
      "E = -2.8766014 | N(SCF) = 30\n",
      "E = -2.8363893 | N(SCF) = 31\n",
      "E = -2.9618906 | N(SCF) = 32\n",
      "E = -2.4714217 | N(SCF) = 33\n",
      "E = -3.0894006 | N(SCF) = 34\n",
      "E = -2.6643960 | N(SCF) = 35\n",
      "E = -2.7667411 | N(SCF) = 36\n",
      "E = -2.7597423 | N(SCF) = 37\n",
      "E = -3.0552977 | N(SCF) = 38\n",
      "E = -2.5310622 | N(SCF) = 39\n",
      "E = -2.6745318 | N(SCF) = 40\n",
      "E = -3.0351185 | N(SCF) = 41\n",
      "E = -2.5648041 | N(SCF) = 42\n",
      "E = -2.4602342 | N(SCF) = 43\n",
      "E = -3.0495387 | N(SCF) = 44\n",
      "E = -2.6645906 | N(SCF) = 45\n",
      "E = -2.8987420 | N(SCF) = 46\n",
      "E = -2.8175992 | N(SCF) = 47\n",
      "E = -2.9233009 | N(SCF) = 48\n",
      "E = -2.8269859 | N(SCF) = 49\n",
      "E = -2.9061285 | N(SCF) = 50\n",
      "E = -2.7304085 | N(SCF) = 51\n",
      "E = -2.8208232 | N(SCF) = 52\n",
      "E = -2.8321608 | N(SCF) = 53\n",
      "E = -2.8778730 | N(SCF) = 54\n",
      "E = -2.8320261 | N(SCF) = 55\n",
      "E = -2.9335847 | N(SCF) = 56\n",
      "E = -2.4755136 | N(SCF) = 57\n",
      "E = -3.1620556 | N(SCF) = 58\n",
      "E = -2.4795904 | N(SCF) = 59\n",
      "E = -2.5088903 | N(SCF) = 60\n",
      "E = -2.6665242 | N(SCF) = 61\n",
      "E = -3.2016269 | N(SCF) = 62\n",
      "E = -2.4278466 | N(SCF) = 63\n",
      "E = -2.6026906 | N(SCF) = 64\n",
      "E = -2.9938703 | N(SCF) = 65\n",
      "E = -2.7279534 | N(SCF) = 66\n",
      "E = -2.8373422 | N(SCF) = 67\n",
      "E = -2.8847961 | N(SCF) = 68\n",
      "E = -2.8466009 | N(SCF) = 69\n",
      "E = -2.8668501 | N(SCF) = 70\n",
      "E = -2.8500288 | N(SCF) = 71\n",
      "E = -2.8828534 | N(SCF) = 72\n",
      "E = -2.8360346 | N(SCF) = 73\n",
      "E = -2.8334357 | N(SCF) = 74\n",
      "E = -2.8720754 | N(SCF) = 75\n",
      "E = -2.8064345 | N(SCF) = 76\n",
      "E = -2.8800010 | N(SCF) = 77\n",
      "E = -2.8290608 | N(SCF) = 78\n",
      "E = -2.7832377 | N(SCF) = 79\n",
      "E = -2.9419159 | N(SCF) = 80\n",
      "E = -2.4628939 | N(SCF) = 81\n",
      "E = -2.3114495 | N(SCF) = 82\n",
      "E = -3.2428410 | N(SCF) = 83\n",
      "E = -2.5356897 | N(SCF) = 84\n",
      "E = -2.7984273 | N(SCF) = 85\n",
      "E = -2.9902056 | N(SCF) = 86\n",
      "E = -2.8683505 | N(SCF) = 87\n",
      "E = -2.8591314 | N(SCF) = 88\n",
      "E = -2.8526281 | N(SCF) = 89\n",
      "E = -2.8557340 | N(SCF) = 90\n",
      "E = -2.8558198 | N(SCF) = 91\n",
      "E = -2.8537644 | N(SCF) = 92\n",
      "E = -2.8605686 | N(SCF) = 93\n",
      "E = -2.8471337 | N(SCF) = 94\n",
      "E = -2.8718129 | N(SCF) = 95\n",
      "E = -2.8244020 | N(SCF) = 96\n",
      "E = -2.9082197 | N(SCF) = 97\n",
      "E = -2.6367702 | N(SCF) = 98\n",
      "E = -3.0071424 | N(SCF) = 99\n",
      "E = -2.5146159 | N(SCF) = 100\n",
      "E = -2.7933717 | N(SCF) = 101\n",
      "E = -2.7492580 | N(SCF) = 102\n",
      "E = -2.8014935 | N(SCF) = 103\n",
      "E = -2.7669100 | N(SCF) = 104\n",
      "E = -2.8329573 | N(SCF) = 105\n",
      "E = -2.8026934 | N(SCF) = 106\n",
      "E = -2.8381732 | N(SCF) = 107\n",
      "E = -2.8653947 | N(SCF) = 108\n",
      "E = -2.8455880 | N(SCF) = 109\n",
      "E = -2.8484272 | N(SCF) = 110\n",
      "E = -2.8649194 | N(SCF) = 111\n",
      "E = -2.8625015 | N(SCF) = 112\n",
      "E = -2.8561636 | N(SCF) = 113\n",
      "E = -2.8555371 | N(SCF) = 114\n",
      "E = -2.8552357 | N(SCF) = 115\n",
      "E = -2.8550572 | N(SCF) = 116\n",
      "E = -2.8553631 | N(SCF) = 117\n",
      "E = -2.8546501 | N(SCF) = 118\n",
      "E = -2.8563081 | N(SCF) = 119\n",
      "E = -2.8527568 | N(SCF) = 120\n",
      "E = -2.8558086 | N(SCF) = 121\n",
      "E = -2.8592639 | N(SCF) = 122\n",
      "E = -2.8441610 | N(SCF) = 123\n",
      "E = -2.8711554 | N(SCF) = 124\n",
      "E = -2.8352417 | N(SCF) = 125\n",
      "E = -2.8653325 | N(SCF) = 126\n",
      "E = -2.8379194 | N(SCF) = 127\n",
      "E = -2.8816319 | N(SCF) = 128\n",
      "E = -2.7537152 | N(SCF) = 129\n",
      "E = -2.8496425 | N(SCF) = 130\n",
      "E = -2.8389054 | N(SCF) = 131\n",
      "E = -2.8736461 | N(SCF) = 132\n",
      "E = -2.8448074 | N(SCF) = 133\n",
      "E = -2.8603953 | N(SCF) = 134\n",
      "E = -2.8527153 | N(SCF) = 135\n",
      "E = -2.8597309 | N(SCF) = 136\n",
      "E = -2.8566447 | N(SCF) = 137\n",
      "E = -2.8543434 | N(SCF) = 138\n",
      "E = -2.8560941 | N(SCF) = 139\n",
      "E = -2.8546913 | N(SCF) = 140\n",
      "E = -2.8562758 | N(SCF) = 141\n",
      "E = -2.8542268 | N(SCF) = 142\n",
      "E = -2.8559109 | N(SCF) = 143\n",
      "E = -2.8551958 | N(SCF) = 144\n",
      "E = -2.8550899 | N(SCF) = 145\n",
      "E = -2.8553590 | N(SCF) = 146\n",
      "E = -2.8545610 | N(SCF) = 147\n",
      "E = -2.8553108 | N(SCF) = 148\n",
      "E = -2.8561279 | N(SCF) = 149\n",
      "E = -2.8545052 | N(SCF) = 150\n",
      "E = -2.8551409 | N(SCF) = 151\n",
      "E = -2.8551716 | N(SCF) = 152\n",
      "E = -2.8551464 | N(SCF) = 153\n",
      "E = -2.8551978 | N(SCF) = 154\n",
      "E = -2.8550052 | N(SCF) = 155\n",
      "E = -2.8558718 | N(SCF) = 156\n",
      "E = -2.8540311 | N(SCF) = 157\n",
      "E = -2.8566292 | N(SCF) = 158\n",
      "E = -2.8537589 | N(SCF) = 159\n",
      "E = -2.8553939 | N(SCF) = 160\n",
      "E = -2.8554182 | N(SCF) = 161\n",
      "E = -2.8550002 | N(SCF) = 162\n",
      "E = -2.8552088 | N(SCF) = 163\n",
      "E = -2.8552007 | N(SCF) = 164\n",
      "E = -2.8551495 | N(SCF) = 165\n",
      "E = -2.8551345 | N(SCF) = 166\n",
      "E = -2.8552088 | N(SCF) = 167\n",
      "E = -2.8550551 | N(SCF) = 168\n",
      "E = -2.8554675 | N(SCF) = 169\n",
      "E = -2.8541117 | N(SCF) = 170\n",
      "E = -2.8597161 | N(SCF) = 171\n",
      "E = -2.8539870 | N(SCF) = 172\n",
      "E = -2.8386536 | N(SCF) = 173\n",
      "E = -2.9115335 | N(SCF) = 174\n",
      "E = -2.7477012 | N(SCF) = 175\n",
      "E = -2.8580877 | N(SCF) = 176\n",
      "E = -2.8968635 | N(SCF) = 177\n",
      "E = -2.7097513 | N(SCF) = 178\n",
      "E = -2.7663186 | N(SCF) = 179\n",
      "E = -2.9551990 | N(SCF) = 180\n",
      "E = -2.5595221 | N(SCF) = 181\n",
      "E = -2.9209311 | N(SCF) = 182\n",
      "E = -2.9451380 | N(SCF) = 183\n",
      "E = -2.6520174 | N(SCF) = 184\n",
      "E = -2.7985177 | N(SCF) = 185\n",
      "E = -2.9079581 | N(SCF) = 186\n",
      "E = -2.8032025 | N(SCF) = 187\n",
      "E = -2.9772908 | N(SCF) = 188\n",
      "E = -2.4470319 | N(SCF) = 189\n",
      "E = -2.9421312 | N(SCF) = 190\n",
      "E = -2.8058771 | N(SCF) = 191\n",
      "E = -2.8235444 | N(SCF) = 192\n",
      "E = -2.8220918 | N(SCF) = 193\n",
      "E = -2.9212449 | N(SCF) = 194\n",
      "E = -2.8449655 | N(SCF) = 195\n",
      "E = -2.8772767 | N(SCF) = 196\n",
      "E = -2.8035278 | N(SCF) = 197\n",
      "E = -2.9423150 | N(SCF) = 198\n",
      "E = -2.5443807 | N(SCF) = 199\n",
      "E = -3.0433201 | N(SCF) = 200\n",
      "E = -2.6518178 | N(SCF) = 201\n",
      "E = -3.0101722 | N(SCF) = 202\n",
      "E = -2.5550309 | N(SCF) = 203\n",
      "E = -3.0875979 | N(SCF) = 204\n",
      "E = -2.5480715 | N(SCF) = 205\n",
      "E = -2.9878855 | N(SCF) = 206\n",
      "E = -2.8266748 | N(SCF) = 207\n",
      "E = -2.8388171 | N(SCF) = 208\n",
      "E = -2.9259645 | N(SCF) = 209\n",
      "E = -2.7865124 | N(SCF) = 210\n",
      "E = -2.7966269 | N(SCF) = 211\n",
      "E = -2.8441336 | N(SCF) = 212\n",
      "E = -2.8878877 | N(SCF) = 213\n",
      "E = -2.7704688 | N(SCF) = 214\n",
      "E = -2.9180621 | N(SCF) = 215\n",
      "E = -2.5330082 | N(SCF) = 216\n",
      "E = -2.8532864 | N(SCF) = 217\n",
      "E = -2.8667676 | N(SCF) = 218\n",
      "E = -2.9183235 | N(SCF) = 219\n",
      "E = -2.8501727 | N(SCF) = 220\n",
      "E = -2.9187571 | N(SCF) = 221\n",
      "E = -2.6101329 | N(SCF) = 222\n",
      "E = -2.8623423 | N(SCF) = 223\n",
      "E = -2.8507554 | N(SCF) = 224\n",
      "E = -2.9458432 | N(SCF) = 225\n",
      "E = -2.6935622 | N(SCF) = 226\n",
      "E = -2.9904997 | N(SCF) = 227\n",
      "E = -2.4971376 | N(SCF) = 228\n",
      "E = -2.6569826 | N(SCF) = 229\n",
      "E = -2.9244537 | N(SCF) = 230\n",
      "E = -2.8395059 | N(SCF) = 231\n",
      "E = -2.8982867 | N(SCF) = 232\n",
      "E = -2.7970498 | N(SCF) = 233\n",
      "E = -2.9746924 | N(SCF) = 234\n",
      "E = -2.5870384 | N(SCF) = 235\n",
      "E = -3.1234312 | N(SCF) = 236\n",
      "E = -2.3815151 | N(SCF) = 237\n",
      "E = -3.2777099 | N(SCF) = 238\n",
      "E = -2.6225583 | N(SCF) = 239\n",
      "E = -2.6877616 | N(SCF) = 240\n",
      "E = -2.7581947 | N(SCF) = 241\n",
      "E = -2.9549883 | N(SCF) = 242\n",
      "E = -2.7944064 | N(SCF) = 243\n",
      "E = -2.8431634 | N(SCF) = 244\n",
      "E = -2.8513432 | N(SCF) = 245\n",
      "E = -2.8486462 | N(SCF) = 246\n",
      "E = -2.8495751 | N(SCF) = 247\n",
      "E = -2.8733063 | N(SCF) = 248\n",
      "E = -2.8564560 | N(SCF) = 249\n",
      "E = -2.8544394 | N(SCF) = 250\n",
      "E = -2.8555366 | N(SCF) = 251\n",
      "E = -2.8557881 | N(SCF) = 252\n",
      "E = -2.8537508 | N(SCF) = 253\n",
      "E = -2.8579113 | N(SCF) = 254\n",
      "E = -2.8502269 | N(SCF) = 255\n",
      "E = -2.8550159 | N(SCF) = 256\n",
      "E = -2.8680556 | N(SCF) = 257\n",
      "E = -2.8147757 | N(SCF) = 258\n",
      "E = -2.8474536 | N(SCF) = 259\n",
      "E = -2.8698899 | N(SCF) = 260\n",
      "E = -2.8439650 | N(SCF) = 261\n",
      "E = -2.8729474 | N(SCF) = 262\n",
      "E = -2.8348491 | N(SCF) = 263\n",
      "E = -2.8767728 | N(SCF) = 264\n",
      "E = -2.7751093 | N(SCF) = 265\n",
      "E = -2.8275660 | N(SCF) = 266\n",
      "E = -2.9734595 | N(SCF) = 267\n",
      "E = -2.3975941 | N(SCF) = 268\n",
      "E = -3.1253375 | N(SCF) = 269\n",
      "E = -2.6589869 | N(SCF) = 270\n",
      "E = -2.8746180 | N(SCF) = 271\n",
      "E = -2.8898377 | N(SCF) = 272\n",
      "E = -2.8424197 | N(SCF) = 273\n",
      "E = -2.8803260 | N(SCF) = 274\n",
      "E = -2.8401900 | N(SCF) = 275\n",
      "E = -2.8374827 | N(SCF) = 276\n",
      "E = -2.8653083 | N(SCF) = 277\n",
      "E = -2.8484421 | N(SCF) = 278\n",
      "E = -2.8495708 | N(SCF) = 279\n",
      "E = -2.8521421 | N(SCF) = 280\n",
      "E = -2.8692833 | N(SCF) = 281\n",
      "E = -2.8436053 | N(SCF) = 282\n",
      "E = -2.8592762 | N(SCF) = 283\n",
      "E = -2.8532221 | N(SCF) = 284\n",
      "E = -2.8598474 | N(SCF) = 285\n",
      "E = -2.8395091 | N(SCF) = 286\n",
      "E = -2.9068355 | N(SCF) = 287\n",
      "E = -2.5110858 | N(SCF) = 288\n",
      "E = -2.7210041 | N(SCF) = 289\n",
      "E = -2.9926276 | N(SCF) = 290\n",
      "E = -2.7357069 | N(SCF) = 291\n",
      "E = -2.9524461 | N(SCF) = 292\n",
      "E = -2.8142331 | N(SCF) = 293\n",
      "E = -2.8512261 | N(SCF) = 294\n",
      "E = -2.8539447 | N(SCF) = 295\n",
      "E = -2.8897729 | N(SCF) = 296\n",
      "E = -2.7320845 | N(SCF) = 297\n",
      "E = -2.9818228 | N(SCF) = 298\n",
      "E = -2.4568296 | N(SCF) = 299\n",
      "E = -2.8025160 | N(SCF) = 300\n",
      "E = -2.7931716 | N(SCF) = 301\n",
      "E = -2.9551687 | N(SCF) = 302\n",
      "E = -2.8328655 | N(SCF) = 303\n",
      "E = -2.8781703 | N(SCF) = 304\n",
      "E = -2.8826033 | N(SCF) = 305\n",
      "E = -2.8391614 | N(SCF) = 306\n",
      "E = -2.8476961 | N(SCF) = 307\n",
      "E = -2.8297168 | N(SCF) = 308\n",
      "E = -2.8593346 | N(SCF) = 309\n",
      "E = -2.8601012 | N(SCF) = 310\n",
      "E = -2.8629233 | N(SCF) = 311\n",
      "E = -2.8345650 | N(SCF) = 312\n",
      "E = -2.8567669 | N(SCF) = 313\n",
      "E = -2.8595008 | N(SCF) = 314\n",
      "E = -2.8590051 | N(SCF) = 315\n",
      "E = -2.8508117 | N(SCF) = 316\n",
      "E = -2.8711414 | N(SCF) = 317\n",
      "E = -2.8288101 | N(SCF) = 318\n",
      "E = -2.8696359 | N(SCF) = 319\n",
      "E = -2.8235278 | N(SCF) = 320\n",
      "E = -2.9275763 | N(SCF) = 321\n",
      "E = -2.5746895 | N(SCF) = 322\n",
      "E = -2.9302656 | N(SCF) = 323\n",
      "E = -2.7530559 | N(SCF) = 324\n",
      "E = -2.8031019 | N(SCF) = 325\n",
      "E = -2.8361037 | N(SCF) = 326\n",
      "E = -2.8447751 | N(SCF) = 327\n",
      "E = -2.8307770 | N(SCF) = 328\n",
      "E = -2.8597580 | N(SCF) = 329\n",
      "E = -2.8774004 | N(SCF) = 330\n",
      "E = -2.8588088 | N(SCF) = 331\n",
      "E = -2.8549349 | N(SCF) = 332\n",
      "E = -2.8548349 | N(SCF) = 333\n",
      "E = -2.8551114 | N(SCF) = 334\n",
      "E = -2.8553075 | N(SCF) = 335\n",
      "E = -2.8553609 | N(SCF) = 336\n",
      "E = -2.8550151 | N(SCF) = 337\n",
      "E = -2.8554767 | N(SCF) = 338\n",
      "E = -2.8545219 | N(SCF) = 339\n",
      "E = -2.8567576 | N(SCF) = 340\n",
      "E = -2.8507055 | N(SCF) = 341\n",
      "E = -2.8712394 | N(SCF) = 342\n",
      "E = -2.8102792 | N(SCF) = 343\n",
      "E = -2.8734766 | N(SCF) = 344\n",
      "E = -2.8443905 | N(SCF) = 345\n",
      "E = -2.8463835 | N(SCF) = 346\n",
      "E = -2.8500159 | N(SCF) = 347\n",
      "E = -2.8636534 | N(SCF) = 348\n",
      "E = -2.8524081 | N(SCF) = 349\n",
      "E = -2.8582869 | N(SCF) = 350\n",
      "E = -2.8508815 | N(SCF) = 351\n",
      "E = -2.8725060 | N(SCF) = 352\n",
      "E = -2.7624849 | N(SCF) = 353\n",
      "E = -2.9335504 | N(SCF) = 354\n",
      "E = -2.6257432 | N(SCF) = 355\n",
      "E = -2.6852808 | N(SCF) = 356\n",
      "E = -3.0011221 | N(SCF) = 357\n",
      "E = -2.7279744 | N(SCF) = 358\n",
      "E = -2.9113582 | N(SCF) = 359\n",
      "E = -2.8417050 | N(SCF) = 360\n",
      "E = -2.8515486 | N(SCF) = 361\n",
      "E = -2.8523622 | N(SCF) = 362\n",
      "E = -2.8816012 | N(SCF) = 363\n",
      "E = -2.7673797 | N(SCF) = 364\n",
      "E = -2.9018366 | N(SCF) = 365\n",
      "E = -2.7014586 | N(SCF) = 366\n",
      "E = -2.9198893 | N(SCF) = 367\n",
      "E = -2.8099941 | N(SCF) = 368\n",
      "E = -2.8780007 | N(SCF) = 369\n",
      "E = -2.8285108 | N(SCF) = 370\n",
      "E = -2.8408008 | N(SCF) = 371\n",
      "E = -2.9260127 | N(SCF) = 372\n",
      "E = -2.7285127 | N(SCF) = 373\n",
      "E = -2.8607047 | N(SCF) = 374\n",
      "E = -2.8917986 | N(SCF) = 375\n",
      "E = -2.8477608 | N(SCF) = 376\n",
      "E = -2.8403013 | N(SCF) = 377\n",
      "E = -2.8661497 | N(SCF) = 378\n",
      "E = -2.8482042 | N(SCF) = 379\n",
      "E = -2.8566524 | N(SCF) = 380\n",
      "E = -2.8544679 | N(SCF) = 381\n",
      "E = -2.8631247 | N(SCF) = 382\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E = -2.8374174 | N(SCF) = 383\n",
      "E = -2.8796070 | N(SCF) = 384\n",
      "E = -2.7706529 | N(SCF) = 385\n",
      "E = -2.8995287 | N(SCF) = 386\n",
      "E = -2.6260269 | N(SCF) = 387\n",
      "E = -2.8437059 | N(SCF) = 388\n",
      "E = -2.8429238 | N(SCF) = 389\n",
      "E = -2.8372436 | N(SCF) = 390\n",
      "E = -2.8263186 | N(SCF) = 391\n",
      "E = -2.8724998 | N(SCF) = 392\n",
      "E = -2.8633818 | N(SCF) = 393\n",
      "E = -2.8547407 | N(SCF) = 394\n",
      "E = -2.8502370 | N(SCF) = 395\n",
      "E = -2.8542702 | N(SCF) = 396\n",
      "E = -2.8560227 | N(SCF) = 397\n",
      "E = -2.8571426 | N(SCF) = 398\n",
      "E = -2.8563731 | N(SCF) = 399\n",
      "E = -2.8560278 | N(SCF) = 400\n",
      "E = -2.8540435 | N(SCF) = 401\n",
      "E = -2.8557732 | N(SCF) = 402\n",
      "E = -2.8548680 | N(SCF) = 403\n",
      "E = -2.8555996 | N(SCF) = 404\n",
      "E = -2.8543108 | N(SCF) = 405\n",
      "E = -2.8589367 | N(SCF) = 406\n",
      "E = -2.8419196 | N(SCF) = 407\n",
      "E = -2.8965759 | N(SCF) = 408\n",
      "E = -2.6351280 | N(SCF) = 409\n",
      "E = -2.9006970 | N(SCF) = 410\n",
      "E = -2.7539204 | N(SCF) = 411\n",
      "E = -2.8489862 | N(SCF) = 412\n",
      "E = -2.8717011 | N(SCF) = 413\n",
      "E = -2.8555406 | N(SCF) = 414\n",
      "E = -2.8841659 | N(SCF) = 415\n",
      "E = -2.8148784 | N(SCF) = 416\n",
      "E = -2.8504001 | N(SCF) = 417\n",
      "E = -2.9046538 | N(SCF) = 418\n",
      "E = -2.6876699 | N(SCF) = 419\n",
      "E = -2.9161761 | N(SCF) = 420\n",
      "E = -2.7016257 | N(SCF) = 421\n",
      "E = -3.1064829 | N(SCF) = 422\n",
      "E = -2.4323135 | N(SCF) = 423\n",
      "E = -2.5674551 | N(SCF) = 424\n",
      "E = -2.7806050 | N(SCF) = 425\n",
      "E = -2.9917918 | N(SCF) = 426\n",
      "E = -2.8090041 | N(SCF) = 427\n",
      "E = -2.8544203 | N(SCF) = 428\n",
      "E = -2.8331174 | N(SCF) = 429\n",
      "E = -2.8412237 | N(SCF) = 430\n",
      "E = -2.8646511 | N(SCF) = 431\n",
      "E = -2.8615663 | N(SCF) = 432\n",
      "E = -2.8580056 | N(SCF) = 433\n",
      "E = -2.8547451 | N(SCF) = 434\n",
      "E = -2.8573118 | N(SCF) = 435\n",
      "E = -2.8523326 | N(SCF) = 436\n",
      "E = -2.8638303 | N(SCF) = 437\n",
      "E = -2.8292823 | N(SCF) = 438\n",
      "E = -2.9041395 | N(SCF) = 439\n",
      "E = -2.6873570 | N(SCF) = 440\n",
      "E = -2.9664867 | N(SCF) = 441\n",
      "E = -2.6859355 | N(SCF) = 442\n",
      "E = -2.7755756 | N(SCF) = 443\n",
      "E = -2.9110311 | N(SCF) = 444\n",
      "E = -2.8972304 | N(SCF) = 445\n",
      "E = -2.7658781 | N(SCF) = 446\n",
      "E = -2.9744770 | N(SCF) = 447\n",
      "E = -2.4473226 | N(SCF) = 448\n",
      "E = -3.3044066 | N(SCF) = 449\n",
      "E = -2.4027790 | N(SCF) = 450\n",
      "E = -2.3509127 | N(SCF) = 451\n",
      "E = -2.9103208 | N(SCF) = 452\n",
      "E = -2.8332072 | N(SCF) = 453\n",
      "E = -2.8288285 | N(SCF) = 454\n",
      "E = -2.8541491 | N(SCF) = 455\n",
      "E = -2.8253389 | N(SCF) = 456\n",
      "E = -2.8767408 | N(SCF) = 457\n",
      "E = -2.8588187 | N(SCF) = 458\n",
      "E = -2.8603958 | N(SCF) = 459\n",
      "E = -2.8545776 | N(SCF) = 460\n",
      "E = -2.8546769 | N(SCF) = 461\n",
      "E = -2.8551037 | N(SCF) = 462\n",
      "E = -2.8551516 | N(SCF) = 463\n",
      "E = -2.8550490 | N(SCF) = 464\n",
      "E = -2.8556306 | N(SCF) = 465\n",
      "E = -2.8549476 | N(SCF) = 466\n",
      "E = -2.8549750 | N(SCF) = 467\n",
      "E = -2.8550681 | N(SCF) = 468\n",
      "E = -2.8552118 | N(SCF) = 469\n",
      "E = -2.8552004 | N(SCF) = 470\n",
      "E = -2.8553141 | N(SCF) = 471\n",
      "E = -2.8551504 | N(SCF) = 472\n",
      "E = -2.8548118 | N(SCF) = 473\n",
      "E = -2.8567397 | N(SCF) = 474\n",
      "E = -2.8491010 | N(SCF) = 475\n",
      "E = -2.8582501 | N(SCF) = 476\n",
      "E = -2.8582943 | N(SCF) = 477\n",
      "E = -2.8459351 | N(SCF) = 478\n",
      "E = -2.8788142 | N(SCF) = 479\n",
      "E = -2.7189947 | N(SCF) = 480\n",
      "E = -3.0102909 | N(SCF) = 481\n",
      "E = -2.3542541 | N(SCF) = 482\n",
      "E = -2.7168578 | N(SCF) = 483\n",
      "E = -2.8441125 | N(SCF) = 484\n",
      "E = -2.8904500 | N(SCF) = 485\n",
      "E = -2.8339000 | N(SCF) = 486\n",
      "E = -2.8762751 | N(SCF) = 487\n",
      "E = -2.8746285 | N(SCF) = 488\n",
      "E = -2.8461247 | N(SCF) = 489\n",
      "E = -2.8418291 | N(SCF) = 490\n",
      "E = -2.8949946 | N(SCF) = 491\n",
      "E = -2.6876811 | N(SCF) = 492\n",
      "E = -2.9299575 | N(SCF) = 493\n",
      "E = -2.7023524 | N(SCF) = 494\n",
      "E = -2.7796305 | N(SCF) = 495\n",
      "E = -2.9800217 | N(SCF) = 496\n",
      "E = -2.5390289 | N(SCF) = 497\n",
      "E = -2.9381020 | N(SCF) = 498\n",
      "E = -2.9082497 | N(SCF) = 499\n",
      "E = -2.9444479 | N(SCF) = 500\n",
      "SCF not converged!\n",
      "Restarting again...\n",
      "E = -1.0279178 | N(SCF) = 1\n",
      "E = -2.6730304 | N(SCF) = 2\n",
      "E = -2.5238303 | N(SCF) = 3\n",
      "E = -2.5493535 | N(SCF) = 4\n",
      "E = -2.7815870 | N(SCF) = 5\n",
      "E = -2.7322891 | N(SCF) = 6\n",
      "E = -2.8840992 | N(SCF) = 7\n",
      "E = -2.8595887 | N(SCF) = 8\n",
      "E = -2.8452392 | N(SCF) = 9\n",
      "E = -2.8566607 | N(SCF) = 10\n",
      "E = -2.8481610 | N(SCF) = 11\n",
      "E = -2.8603583 | N(SCF) = 12\n",
      "E = -2.8389465 | N(SCF) = 13\n",
      "E = -2.8911097 | N(SCF) = 14\n",
      "E = -2.8102027 | N(SCF) = 15\n",
      "E = -2.8443153 | N(SCF) = 16\n",
      "E = -2.8529008 | N(SCF) = 17\n",
      "E = -2.8863123 | N(SCF) = 18\n",
      "E = -2.8192516 | N(SCF) = 19\n",
      "E = -2.8524528 | N(SCF) = 20\n",
      "E = -2.8616484 | N(SCF) = 21\n",
      "E = -2.8564945 | N(SCF) = 22\n",
      "E = -2.8556377 | N(SCF) = 23\n",
      "E = -2.8552819 | N(SCF) = 24\n",
      "E = -2.8549787 | N(SCF) = 25\n",
      "E = -2.8556142 | N(SCF) = 26\n",
      "E = -2.8543677 | N(SCF) = 27\n",
      "E = -2.8556631 | N(SCF) = 28\n",
      "E = -2.8550378 | N(SCF) = 29\n",
      "E = -2.8553539 | N(SCF) = 30\n",
      "E = -2.8545199 | N(SCF) = 31\n",
      "E = -2.8555316 | N(SCF) = 32\n",
      "E = -2.8558389 | N(SCF) = 33\n",
      "E = -2.8524126 | N(SCF) = 34\n",
      "E = -2.8612766 | N(SCF) = 35\n",
      "E = -2.8407821 | N(SCF) = 36\n",
      "E = -2.8745201 | N(SCF) = 37\n",
      "E = -2.8254703 | N(SCF) = 38\n",
      "E = -2.8830582 | N(SCF) = 39\n",
      "E = -2.7917796 | N(SCF) = 40\n",
      "E = -2.9240649 | N(SCF) = 41\n",
      "E = -2.5397776 | N(SCF) = 42\n",
      "E = -2.6452617 | N(SCF) = 43\n",
      "E = -2.9865164 | N(SCF) = 44\n",
      "E = -2.6947579 | N(SCF) = 45\n",
      "E = -2.8633075 | N(SCF) = 46\n",
      "E = -2.8467430 | N(SCF) = 47\n",
      "E = -2.8429050 | N(SCF) = 48\n",
      "E = -2.8759232 | N(SCF) = 49\n",
      "E = -2.8509761 | N(SCF) = 50\n",
      "E = -2.8688975 | N(SCF) = 51\n",
      "E = -2.8547566 | N(SCF) = 52\n",
      "E = -2.8554686 | N(SCF) = 53\n",
      "E = -2.8563368 | N(SCF) = 54\n",
      "E = -2.8510290 | N(SCF) = 55\n",
      "E = -2.8598390 | N(SCF) = 56\n",
      "E = -2.8539503 | N(SCF) = 57\n",
      "E = -2.8549424 | N(SCF) = 58\n",
      "E = -2.8527806 | N(SCF) = 59\n",
      "E = -2.8626230 | N(SCF) = 60\n",
      "E = -2.8253520 | N(SCF) = 61\n",
      "E = -2.9296460 | N(SCF) = 62\n",
      "E = -2.4880170 | N(SCF) = 63\n",
      "E = -3.1264617 | N(SCF) = 64\n",
      "E = -2.5531149 | N(SCF) = 65\n",
      "E = -2.8901934 | N(SCF) = 66\n",
      "E = -2.8994464 | N(SCF) = 67\n",
      "E = -2.9298595 | N(SCF) = 68\n",
      "E = -2.6510729 | N(SCF) = 69\n",
      "E = -2.9799524 | N(SCF) = 70\n",
      "E = -2.5959224 | N(SCF) = 71\n",
      "E = -2.8787936 | N(SCF) = 72\n",
      "E = -2.7624746 | N(SCF) = 73\n",
      "E = -2.9137962 | N(SCF) = 74\n",
      "E = -2.8673832 | N(SCF) = 75\n",
      "E = -2.8440744 | N(SCF) = 76\n",
      "E = -2.8686880 | N(SCF) = 77\n",
      "E = -2.8383694 | N(SCF) = 78\n",
      "E = -2.8821035 | N(SCF) = 79\n",
      "E = -2.7705318 | N(SCF) = 80\n",
      "E = -2.9233999 | N(SCF) = 81\n",
      "E = -2.5233615 | N(SCF) = 82\n",
      "E = -3.0431141 | N(SCF) = 83\n",
      "E = -2.7118820 | N(SCF) = 84\n",
      "E = -2.6320713 | N(SCF) = 85\n",
      "E = -3.0530295 | N(SCF) = 86\n",
      "E = -2.5869802 | N(SCF) = 87\n",
      "E = -2.8218813 | N(SCF) = 88\n",
      "E = -2.9149496 | N(SCF) = 89\n",
      "E = -2.8692065 | N(SCF) = 90\n",
      "E = -2.9651732 | N(SCF) = 91\n",
      "E = -2.6377225 | N(SCF) = 92\n",
      "E = -2.6435725 | N(SCF) = 93\n",
      "E = -2.7441076 | N(SCF) = 94\n",
      "E = -2.7770434 | N(SCF) = 95\n",
      "E = -3.0930288 | N(SCF) = 96\n",
      "E = -2.4818632 | N(SCF) = 97\n",
      "E = -3.1207684 | N(SCF) = 98\n",
      "E = -2.5687746 | N(SCF) = 99\n",
      "E = -3.0308895 | N(SCF) = 100\n",
      "E = -2.7114146 | N(SCF) = 101\n",
      "E = -2.8619375 | N(SCF) = 102\n",
      "E = -2.9057517 | N(SCF) = 103\n",
      "E = -2.9087202 | N(SCF) = 104\n",
      "E = -2.5545931 | N(SCF) = 105\n",
      "E = -3.1695942 | N(SCF) = 106\n",
      "E = -2.4064774 | N(SCF) = 107\n",
      "E = -2.6495926 | N(SCF) = 108\n",
      "E = -2.8514649 | N(SCF) = 109\n",
      "E = -2.8024318 | N(SCF) = 110\n",
      "E = -2.9319138 | N(SCF) = 111\n",
      "E = -2.8809741 | N(SCF) = 112\n",
      "E = -2.8472854 | N(SCF) = 113\n",
      "E = -2.8559216 | N(SCF) = 114\n",
      "E = -2.8541236 | N(SCF) = 115\n",
      "E = -2.8540065 | N(SCF) = 116\n",
      "E = -2.8584320 | N(SCF) = 117\n",
      "E = -2.8540966 | N(SCF) = 118\n",
      "E = -2.8525060 | N(SCF) = 119\n",
      "E = -2.8619532 | N(SCF) = 120\n",
      "E = -2.8427013 | N(SCF) = 121\n",
      "E = -2.8553358 | N(SCF) = 122\n",
      "E = -2.8599473 | N(SCF) = 123\n",
      "E = -2.8548387 | N(SCF) = 124\n",
      "E = -2.8571499 | N(SCF) = 125\n",
      "E = -2.8516118 | N(SCF) = 126\n",
      "E = -2.8555493 | N(SCF) = 127\n",
      "E = -2.8551523 | N(SCF) = 128\n",
      "E = -2.8579442 | N(SCF) = 129\n",
      "E = -2.8494559 | N(SCF) = 130\n",
      "E = -2.8633174 | N(SCF) = 131\n",
      "E = -2.8298305 | N(SCF) = 132\n",
      "E = -2.8573163 | N(SCF) = 133\n",
      "E = -2.8820163 | N(SCF) = 134\n",
      "E = -2.7940686 | N(SCF) = 135\n",
      "E = -2.8821032 | N(SCF) = 136\n",
      "E = -2.8281057 | N(SCF) = 137\n",
      "E = -2.8464181 | N(SCF) = 138\n",
      "E = -2.9068162 | N(SCF) = 139\n",
      "E = -2.6136785 | N(SCF) = 140\n",
      "E = -2.9797228 | N(SCF) = 141\n",
      "E = -2.5939821 | N(SCF) = 142\n",
      "E = -2.8934399 | N(SCF) = 143\n",
      "E = -2.8977157 | N(SCF) = 144\n",
      "E = -2.8108532 | N(SCF) = 145\n",
      "E = -2.8428321 | N(SCF) = 146\n",
      "E = -2.8360326 | N(SCF) = 147\n",
      "E = -2.8498279 | N(SCF) = 148\n",
      "E = -2.8790487 | N(SCF) = 149\n",
      "E = -2.8573870 | N(SCF) = 150\n",
      "E = -2.8521468 | N(SCF) = 151\n",
      "E = -2.8617457 | N(SCF) = 152\n",
      "E = -2.8312410 | N(SCF) = 153\n",
      "E = -2.9082722 | N(SCF) = 154\n",
      "E = -2.6849414 | N(SCF) = 155\n",
      "E = -2.8985578 | N(SCF) = 156\n",
      "E = -2.7836721 | N(SCF) = 157\n",
      "E = -2.8051188 | N(SCF) = 158\n",
      "E = -2.9460698 | N(SCF) = 159\n",
      "E = -2.5435985 | N(SCF) = 160\n",
      "E = -2.8697153 | N(SCF) = 161\n",
      "E = -2.7892790 | N(SCF) = 162\n",
      "E = -2.8997698 | N(SCF) = 163\n",
      "E = -2.8500974 | N(SCF) = 164\n",
      "E = -2.8571145 | N(SCF) = 165\n",
      "E = -2.8714813 | N(SCF) = 166\n",
      "E = -2.8536111 | N(SCF) = 167\n",
      "E = -2.8555620 | N(SCF) = 168\n",
      "E = -2.8579282 | N(SCF) = 169\n",
      "E = -2.8562298 | N(SCF) = 170\n",
      "E = -2.8542246 | N(SCF) = 171\n",
      "E = -2.8554890 | N(SCF) = 172\n",
      "E = -2.8549261 | N(SCF) = 173\n",
      "E = -2.8561602 | N(SCF) = 174\n",
      "E = -2.8507765 | N(SCF) = 175\n",
      "E = -2.8706239 | N(SCF) = 176\n",
      "E = -2.8475068 | N(SCF) = 177\n",
      "E = -2.8255140 | N(SCF) = 178\n",
      "E = -2.9242342 | N(SCF) = 179\n",
      "E = -2.7452995 | N(SCF) = 180\n",
      "E = -2.7535585 | N(SCF) = 181\n",
      "E = -2.9968585 | N(SCF) = 182\n",
      "E = -2.6093000 | N(SCF) = 183\n",
      "E = -2.5499822 | N(SCF) = 184\n",
      "E = -3.1688661 | N(SCF) = 185\n",
      "E = -2.4455743 | N(SCF) = 186\n",
      "E = -2.5347166 | N(SCF) = 187\n",
      "E = -2.8146549 | N(SCF) = 188\n",
      "E = -2.8952812 | N(SCF) = 189\n",
      "E = -2.8453032 | N(SCF) = 190\n",
      "E = -2.8520292 | N(SCF) = 191\n",
      "E = -2.8738225 | N(SCF) = 192\n",
      "E = -2.8615862 | N(SCF) = 193\n",
      "E = -2.8520339 | N(SCF) = 194\n",
      "E = -2.8541521 | N(SCF) = 195\n",
      "E = -2.8570193 | N(SCF) = 196\n",
      "E = -2.8535625 | N(SCF) = 197\n",
      "E = -2.8566186 | N(SCF) = 198\n",
      "E = -2.8543301 | N(SCF) = 199\n",
      "E = -2.8561323 | N(SCF) = 200\n",
      "E = -2.8538613 | N(SCF) = 201\n",
      "E = -2.8567307 | N(SCF) = 202\n",
      "E = -2.8538604 | N(SCF) = 203\n",
      "E = -2.8575855 | N(SCF) = 204\n",
      "E = -2.8463139 | N(SCF) = 205\n",
      "E = -2.8691447 | N(SCF) = 206\n",
      "E = -2.8472680 | N(SCF) = 207\n",
      "E = -2.8448186 | N(SCF) = 208\n",
      "E = -2.8760700 | N(SCF) = 209\n",
      "E = -2.8433780 | N(SCF) = 210\n",
      "E = -2.8266690 | N(SCF) = 211\n",
      "E = -2.9152449 | N(SCF) = 212\n",
      "E = -2.6014153 | N(SCF) = 213\n",
      "E = -2.9412961 | N(SCF) = 214\n",
      "E = -2.7132336 | N(SCF) = 215\n",
      "E = -3.0527600 | N(SCF) = 216\n",
      "E = -2.4438927 | N(SCF) = 217\n",
      "E = -3.4822864 | N(SCF) = 218\n",
      "E = -2.1978790 | N(SCF) = 219\n",
      "E = -2.5733876 | N(SCF) = 220\n",
      "E = -2.4323865 | N(SCF) = 221\n",
      "E = -2.5841228 | N(SCF) = 222\n",
      "E = -2.9029273 | N(SCF) = 223\n",
      "E = -2.8832156 | N(SCF) = 224\n",
      "E = -2.9537948 | N(SCF) = 225\n",
      "E = -2.7567463 | N(SCF) = 226\n",
      "E = -2.8507308 | N(SCF) = 227\n",
      "E = -2.8707294 | N(SCF) = 228\n",
      "E = -2.8503762 | N(SCF) = 229\n",
      "E = -2.9070376 | N(SCF) = 230\n",
      "E = -2.6230025 | N(SCF) = 231\n",
      "E = -2.7850939 | N(SCF) = 232\n",
      "E = -2.8264721 | N(SCF) = 233\n",
      "E = -2.8651130 | N(SCF) = 234\n",
      "E = -2.8192741 | N(SCF) = 235\n",
      "E = -2.8493302 | N(SCF) = 236\n",
      "E = -2.8562482 | N(SCF) = 237\n",
      "E = -2.8736910 | N(SCF) = 238\n",
      "E = -2.8692141 | N(SCF) = 239\n",
      "E = -2.8213267 | N(SCF) = 240\n",
      "E = -2.8657614 | N(SCF) = 241\n",
      "E = -2.8538997 | N(SCF) = 242\n",
      "E = -2.8521019 | N(SCF) = 243\n",
      "E = -2.8539989 | N(SCF) = 244\n",
      "E = -2.8584966 | N(SCF) = 245\n",
      "E = -2.8558161 | N(SCF) = 246\n",
      "E = -2.8550666 | N(SCF) = 247\n",
      "E = -2.8552277 | N(SCF) = 248\n",
      "E = -2.8552682 | N(SCF) = 249\n",
      "E = -2.8552109 | N(SCF) = 250\n",
      "E = -2.8551836 | N(SCF) = 251\n",
      "E = -2.8551606 | N(SCF) = 252\n",
      "E = -2.8551635 | N(SCF) = 253\n",
      "E = -2.8551847 | N(SCF) = 254\n",
      "E = -2.8551174 | N(SCF) = 255\n",
      "E = -2.8553273 | N(SCF) = 256\n",
      "E = -2.8546083 | N(SCF) = 257\n",
      "E = -2.8553047 | N(SCF) = 258\n",
      "E = -2.8558973 | N(SCF) = 259\n",
      "E = -2.8540891 | N(SCF) = 260\n",
      "E = -2.8553849 | N(SCF) = 261\n",
      "E = -2.8567043 | N(SCF) = 262\n",
      "E = -2.8517583 | N(SCF) = 263\n",
      "E = -2.8604333 | N(SCF) = 264\n",
      "E = -2.8495377 | N(SCF) = 265\n",
      "E = -2.8622836 | N(SCF) = 266\n",
      "E = -2.8389204 | N(SCF) = 267\n",
      "E = -2.8824355 | N(SCF) = 268\n",
      "E = -2.7067213 | N(SCF) = 269\n",
      "E = -2.9621150 | N(SCF) = 270\n",
      "E = -2.5289828 | N(SCF) = 271\n",
      "E = -2.7589800 | N(SCF) = 272\n",
      "E = -2.9760994 | N(SCF) = 273\n",
      "E = -2.9040708 | N(SCF) = 274\n",
      "E = -2.8056203 | N(SCF) = 275\n",
      "E = -2.9032616 | N(SCF) = 276\n",
      "E = -2.7679086 | N(SCF) = 277\n",
      "E = -2.9365712 | N(SCF) = 278\n",
      "E = -2.7158640 | N(SCF) = 279\n",
      "E = -2.9298707 | N(SCF) = 280\n",
      "E = -2.6679056 | N(SCF) = 281\n",
      "E = -2.8834426 | N(SCF) = 282\n",
      "E = -2.8195239 | N(SCF) = 283\n",
      "E = -2.8202196 | N(SCF) = 284\n",
      "E = -2.9151912 | N(SCF) = 285\n",
      "E = -2.8460522 | N(SCF) = 286\n",
      "E = -2.8395317 | N(SCF) = 287\n",
      "E = -2.9101457 | N(SCF) = 288\n",
      "E = -2.8071599 | N(SCF) = 289\n",
      "E = -2.6197461 | N(SCF) = 290\n",
      "E = -2.7337174 | N(SCF) = 291\n",
      "E = -2.8040334 | N(SCF) = 292\n",
      "E = -2.8025529 | N(SCF) = 293\n",
      "E = -3.0267616 | N(SCF) = 294\n",
      "E = -2.4390882 | N(SCF) = 295\n",
      "E = -3.0171649 | N(SCF) = 296\n",
      "E = -2.7558614 | N(SCF) = 297\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E = -2.9626039 | N(SCF) = 298\n",
      "E = -2.6934824 | N(SCF) = 299\n",
      "E = -2.7526002 | N(SCF) = 300\n",
      "E = -2.7818040 | N(SCF) = 301\n",
      "E = -2.8239892 | N(SCF) = 302\n",
      "E = -2.9264031 | N(SCF) = 303\n",
      "E = -2.7885843 | N(SCF) = 304\n",
      "E = -2.8998850 | N(SCF) = 305\n",
      "E = -2.6816560 | N(SCF) = 306\n",
      "E = -2.9422116 | N(SCF) = 307\n",
      "E = -2.7273191 | N(SCF) = 308\n",
      "E = -2.7820677 | N(SCF) = 309\n",
      "E = -2.9153950 | N(SCF) = 310\n",
      "E = -2.8162643 | N(SCF) = 311\n",
      "E = -2.8361617 | N(SCF) = 312\n",
      "E = -2.9036986 | N(SCF) = 313\n",
      "E = -2.6826745 | N(SCF) = 314\n",
      "E = -2.7681761 | N(SCF) = 315\n",
      "E = -2.8483723 | N(SCF) = 316\n",
      "E = -2.9062625 | N(SCF) = 317\n",
      "E = -2.8374131 | N(SCF) = 318\n",
      "E = -2.8470275 | N(SCF) = 319\n",
      "E = -2.8629612 | N(SCF) = 320\n",
      "E = -2.8529194 | N(SCF) = 321\n",
      "E = -2.8610532 | N(SCF) = 322\n",
      "E = -2.8549305 | N(SCF) = 323\n",
      "E = -2.8555168 | N(SCF) = 324\n",
      "E = -2.8557285 | N(SCF) = 325\n",
      "E = -2.8550773 | N(SCF) = 326\n",
      "E = -2.8551542 | N(SCF) = 327\n",
      "E = -2.8555147 | N(SCF) = 328\n",
      "E = -2.8548852 | N(SCF) = 329\n",
      "E = -2.8553850 | N(SCF) = 330\n",
      "E = -2.8546130 | N(SCF) = 331\n",
      "E = -2.8561030 | N(SCF) = 332\n",
      "E = -2.8541924 | N(SCF) = 333\n",
      "E = -2.8564407 | N(SCF) = 334\n",
      "E = -2.8541278 | N(SCF) = 335\n",
      "E = -2.8552152 | N(SCF) = 336\n",
      "E = -2.8553239 | N(SCF) = 337\n",
      "E = -2.8550612 | N(SCF) = 338\n",
      "E = -2.8551605 | N(SCF) = 339\n",
      "E = -2.8552410 | N(SCF) = 340\n",
      "E = -2.8550780 | N(SCF) = 341\n",
      "E = -2.8552242 | N(SCF) = 342\n",
      "E = -2.8549455 | N(SCF) = 343\n",
      "E = -2.8554981 | N(SCF) = 344\n",
      "E = -2.8547299 | N(SCF) = 345\n",
      "E = -2.8565998 | N(SCF) = 346\n",
      "E = -2.8532211 | N(SCF) = 347\n",
      "E = -2.8560437 | N(SCF) = 348\n",
      "E = -2.8546049 | N(SCF) = 349\n",
      "E = -2.8573374 | N(SCF) = 350\n",
      "E = -2.8548123 | N(SCF) = 351\n",
      "E = -2.8527020 | N(SCF) = 352\n",
      "E = -2.8580920 | N(SCF) = 353\n",
      "E = -2.8492969 | N(SCF) = 354\n",
      "E = -2.8566720 | N(SCF) = 355\n",
      "E = -2.8628356 | N(SCF) = 356\n",
      "E = -2.8301085 | N(SCF) = 357\n",
      "E = -2.8954285 | N(SCF) = 358\n",
      "E = -2.7418775 | N(SCF) = 359\n",
      "E = -2.9491656 | N(SCF) = 360\n",
      "E = -2.6125011 | N(SCF) = 361\n",
      "E = -3.1098166 | N(SCF) = 362\n",
      "E = -2.4367527 | N(SCF) = 363\n",
      "E = -3.0440363 | N(SCF) = 364\n",
      "E = -2.7433023 | N(SCF) = 365\n",
      "E = -2.9878842 | N(SCF) = 366\n",
      "E = -2.6332279 | N(SCF) = 367\n",
      "E = -2.7981043 | N(SCF) = 368\n",
      "E = -2.9996941 | N(SCF) = 369\n",
      "E = -2.8445114 | N(SCF) = 370\n",
      "E = -2.8396117 | N(SCF) = 371\n",
      "E = -2.8183218 | N(SCF) = 372\n",
      "E = -2.9462171 | N(SCF) = 373\n",
      "E = -2.7177648 | N(SCF) = 374\n",
      "E = -2.7016253 | N(SCF) = 375\n",
      "E = -2.6482239 | N(SCF) = 376\n",
      "E = -2.9669171 | N(SCF) = 377\n",
      "E = -2.6557875 | N(SCF) = 378\n",
      "E = -2.7651954 | N(SCF) = 379\n",
      "E = -2.9639870 | N(SCF) = 380\n",
      "E = -2.7641147 | N(SCF) = 381\n",
      "E = -2.8690983 | N(SCF) = 382\n",
      "E = -2.8496566 | N(SCF) = 383\n",
      "E = -2.8458252 | N(SCF) = 384\n",
      "E = -2.8979311 | N(SCF) = 385\n",
      "E = -2.8506848 | N(SCF) = 386\n",
      "E = -2.8293858 | N(SCF) = 387\n",
      "E = -2.8537750 | N(SCF) = 388\n",
      "E = -2.8709462 | N(SCF) = 389\n",
      "E = -2.8277926 | N(SCF) = 390\n",
      "E = -2.8602673 | N(SCF) = 391\n",
      "E = -2.8766608 | N(SCF) = 392\n",
      "E = -2.8239803 | N(SCF) = 393\n",
      "E = -2.8572414 | N(SCF) = 394\n",
      "E = -2.8636777 | N(SCF) = 395\n",
      "E = -2.8479951 | N(SCF) = 396\n",
      "E = -2.8561796 | N(SCF) = 397\n",
      "E = -2.8538416 | N(SCF) = 398\n",
      "E = -2.8553140 | N(SCF) = 399\n",
      "E = -2.8563100 | N(SCF) = 400\n",
      "E = -2.8544440 | N(SCF) = 401\n",
      "E = -2.8563355 | N(SCF) = 402\n",
      "E = -2.8530004 | N(SCF) = 403\n",
      "E = -2.8594256 | N(SCF) = 404\n",
      "E = -2.8449504 | N(SCF) = 405\n",
      "E = -2.8701716 | N(SCF) = 406\n",
      "E = -2.8450549 | N(SCF) = 407\n",
      "E = -2.8516817 | N(SCF) = 408\n",
      "E = -2.8584003 | N(SCF) = 409\n",
      "E = -2.8528970 | N(SCF) = 410\n",
      "E = -2.8551784 | N(SCF) = 411\n",
      "E = -2.8557431 | N(SCF) = 412\n",
      "E = -2.8545111 | N(SCF) = 413\n",
      "E = -2.8583208 | N(SCF) = 414\n",
      "E = -2.8515791 | N(SCF) = 415\n",
      "E = -2.8580646 | N(SCF) = 416\n",
      "E = -2.8524895 | N(SCF) = 417\n",
      "E = -2.8559028 | N(SCF) = 418\n",
      "E = -2.8545856 | N(SCF) = 419\n",
      "E = -2.8559073 | N(SCF) = 420\n",
      "E = -2.8549497 | N(SCF) = 421\n",
      "E = -2.8546843 | N(SCF) = 422\n",
      "E = -2.8557402 | N(SCF) = 423\n",
      "E = -2.8538920 | N(SCF) = 424\n",
      "E = -2.8583892 | N(SCF) = 425\n",
      "E = -2.8531558 | N(SCF) = 426\n",
      "E = -2.8547548 | N(SCF) = 427\n",
      "E = -2.8551713 | N(SCF) = 428\n",
      "E = -2.8552245 | N(SCF) = 429\n",
      "E = -2.8551727 | N(SCF) = 430\n",
      "E = -2.8551515 | N(SCF) = 431\n",
      "E = -2.8551728 | N(SCF) = 432\n",
      "E = -2.8551591 | N(SCF) = 433\n",
      "SCF CONVERGED! E = -2.8551590708\n"
     ]
    }
   ],
   "source": [
    "_ = lib.SCF(N_electrons, integrals_ana, S, max_iter_SCF, eps_SCF)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Assessment of the errors\n",
    "\n",
    "In this final section, we are going to get an approximate order of the errors done in the Monte Carlo integration and the SCF\n",
    "\n",
    "#### Monte Carlo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative error of MC integration: 0.07346 %\n",
      "Standard deviation of MC integration error: 0.04121 %\n"
     ]
    }
   ],
   "source": [
    "# Average relative error\n",
    "ERRORS = []\n",
    "MC_integrals = integrals_num.integral_dict_2\n",
    "ana_integrals = integrals_ana.integral_dict_2\n",
    "for pqrs in MC_integrals:\n",
    "    ERRORS += [[pqrs, np.abs(MC_integrals[pqrs] - ana_integrals[pqrs]), np.abs(MC_integrals[pqrs] - ana_integrals[pqrs])/ana_integrals[pqrs]]]\n",
    "\n",
    "print(\"Relative error of MC integration: {:0.5f} %\".format(np.average([i[2] for i in ERRORS])*100))\n",
    "print(\"Standard deviation of MC integration error: {:0.5f} %\".format(np.std([i[2] for i in ERRORS])*100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Distribution of relative errors\n",
    "ERRORS_REL = [i[2]*100 for i in ERRORS]\n",
    "plt.hist(ERRORS_REL, bins=40)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pqrs = 3 3 3 1 | absolute error = 0.0001922\n",
      "pqrs = 3 1 3 3 | absolute error = 0.0001922\n",
      "pqrs = 3 3 1 3 | absolute error = 0.0001922\n",
      "pqrs = 1 3 3 3 | absolute error = 0.0001922\n",
      "pqrs = 3 3 3 3 | absolute error = 0.0000918\n",
      "pqrs = 4 3 2 3 | absolute error = 0.0000175\n",
      "pqrs = 2 3 4 3 | absolute error = 0.0000175\n",
      "pqrs = 3 4 3 2 | absolute error = 0.0000175\n",
      "pqrs = 3 2 3 4 | absolute error = 0.0000175\n",
      "pqrs = 4 4 4 2 | absolute error = 0.0000016\n",
      "pqrs = 4 2 4 4 | absolute error = 0.0000016\n",
      "pqrs = 4 4 2 4 | absolute error = 0.0000016\n",
      "pqrs = 2 4 4 4 | absolute error = 0.0000016\n"
     ]
    }
   ],
   "source": [
    "# Maximum relative errors\n",
    "TOP_ERR = sorted(ERRORS_REL, reverse=True)[:10]\n",
    "for data in ERRORS:\n",
    "    if data[2]*100 in TOP_ERR:\n",
    "        print(\"pqrs =\", *data[0], \"| absolute error = {:0.7f}\".format(data[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pqrs = 1 1 1 1 | absolute error = 0.0921757 | relative error = 0.1022371\n",
      "pqrs = 2 1 1 1 | absolute error = 0.0251999 | relative error = 0.0967003\n",
      "pqrs = 1 1 2 1 | absolute error = 0.0251999 | relative error = 0.0967003\n",
      "pqrs = 1 2 1 1 | absolute error = 0.0251999 | relative error = 0.0967003\n",
      "pqrs = 1 1 1 2 | absolute error = 0.0251999 | relative error = 0.0967003\n",
      "pqrs = 2 1 2 1 | absolute error = 0.0166859 | relative error = 0.1240263\n",
      "pqrs = 1 2 1 2 | absolute error = 0.0166859 | relative error = 0.1240263\n",
      "pqrs = 2 2 2 1 | absolute error = 0.0059375 | relative error = 0.1303701\n",
      "pqrs = 2 1 2 2 | absolute error = 0.0059375 | relative error = 0.1303701\n",
      "pqrs = 2 2 1 2 | absolute error = 0.0059375 | relative error = 0.1303701\n",
      "pqrs = 1 2 2 2 | absolute error = 0.0059375 | relative error = 0.1303701\n"
     ]
    }
   ],
   "source": [
    "# Maximum absolute errors\n",
    "ERRORS_ABS = [i[1] for i in ERRORS]\n",
    "TOP_ERR = sorted(ERRORS_ABS, reverse=True)[:10]\n",
    "for data in ERRORS:\n",
    "    if data[1] in TOP_ERR:\n",
    "        print(\"pqrs =\", *data[0], \"| absolute error = {:0.7f}\".format(data[1]), \"| relative error = {:0.7f}\".format(data[2]*100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Self-Consisten Field"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100/100"
     ]
    }
   ],
   "source": [
    "N = 100 # repetitions of the SCF field\n",
    "total_energies_num = []\n",
    "total_energies_ana = []\n",
    "\n",
    "for i in range(N):\n",
    "    print(\"\\r{}/{}\".format(i+1, N), end=\"\")\n",
    "    E_num = lib.SCF(N_electrons, integrals_num, S, max_iter_SCF, eps_SCF, print_E=False)\n",
    "    total_energies_num += [E_num]\n",
    "    E_ana = lib.SCF(N_electrons, integrals_num, S, max_iter_SCF, eps_SCF, print_E=False)\n",
    "    total_energies_ana += [E_ana]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E(SCF numerical)  = -2.8540255 +- 0.0030729\n",
      "E(SCF analytical) = -2.8542953 +- 0.0043931\n"
     ]
    }
   ],
   "source": [
    "print(\"E(SCF numerical)  = {:0.7f} +- {:0.7f}\".format(np.average(total_energies_num), np.std(total_energies_num)))\n",
    "print(\"E(SCF analytical) = {:0.7f} +- {:0.7f}\".format(np.average(total_energies_ana), np.std(total_energies_ana)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=[10,5])\n",
    "ax1 = fig.add_subplot(121)\n",
    "ax1.hist(total_energies_num)\n",
    "ax1.set_title(\"E(SCF numerical)\")\n",
    "ax2 = fig.add_subplot(122)\n",
    "ax2.hist(total_energies_ana)\n",
    "ax2.set_title(\"E(SCF analytical)\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}