{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sc\n",
    "from numba import njit\n",
    "import matplotlib.pyplot as plt\n",
    "datatype='float64'\n",
    "np.set_printoptions(suppress=True)\n",
    "\n",
    "# coefficient and exponent arrays\n",
    "sto_coefs=np.zeros((19,7,5,6),dtype=datatype)\n",
    "\"\"\"\n",
    "Coefficient array for Slater-type orbitals:\n",
    "Axis 1: Element (1 for H, 2 for He, ...), currently implemented: H,C,N,O;\n",
    "Axis 2: Number of primitve Gaussians (e.g. STO-3, STO-6), currently implemented: STO-3G;\n",
    "Axis 3: Orbital type: 0: 1s, 1: 2s, 2: 2p, 3: 3s, 4: 3p;\n",
    "Axis 4: Coefficients for selected element, precision and orbital\n",
    "\"\"\"\n",
    "sto_exps=np.zeros((19,7,3,6),dtype=datatype)\n",
    "\"\"\"\n",
    "Exponent array for Slater-type orbitals:\n",
    "Axis 1: Element (1 for H, 2 for He, ...), currently implemented: H,C,N,O;\n",
    "Axis 2: Number of primitve Gaussians (e.g. STO-3, STO-6), currently implemented: STO-3G;\n",
    "Axis 3: Orbital type: 0: 1s, 1: 2s/2p, 2: 3s/3p;\n",
    "Axis 4: Exponents for selected element, precision and orbital\n",
    "\"\"\"\n",
    "sto_norms=np.zeros((19,7,5,6),dtype=datatype)\n",
    "\"\"\"\n",
    "Normalization array for Slater-type orbitals:\n",
    "Axis 1: Element (1 for H, 2 for He, ...), currently implemented: H,C,N,O;\n",
    "Axis 2: Number of primitve Gaussians (e.g. STO-3, STO-6), currently implemented: STO-3G;\n",
    "Axis 3: Orbital type: 0: 1s, 1: 2s, 2: 2p, 3: 3s, 4: 3p;\n",
    "Axis 4: Normalization constants for selected element, precision and orbital\n",
    "\"\"\"\n",
    "# values for coefficients and exponents are included below\n",
    "\n",
    "sto_coefs[1,2,0,:2]=np.array([0.4301284983E+00,0.6789135305E+00],dtype=datatype)\n",
    "sto_exps[1,2,0,:2]=np.array([0.1309756377E+01,0.2331359749E+00],dtype=datatype)\n",
    "sto_norms[1,2,0,:2]=np.array([0.8725754,0.23912063],dtype=datatype)\n",
    "sto_coefs[6,2,:2,:2]=np.array([[0.4301284983E+00,0.6789135305E+00],\n",
    "                              [0.4947176920E-01,0.9637824081E+00]],dtype=datatype) \n",
    "sto_exps[6,2,:2,:2]=np.array([[0.2738503303E+02,0.4874522075E+01],\n",
    "                             [0.1136748198E+01,0.2883093603E+00]],dtype=datatype)\n",
    "sto_norms[6,2,:2,:2]=np.array([[8.531886,2.3380787],\n",
    "                              [0.7846181,0.28041688]],dtype=datatype) \n",
    "sto_coefs[7,2,:2,:2]=np.array([[0.4301284983E+00,0.6789135305E+00],\n",
    "                              [0.4947176920E-01,0.9637824081E+00]],dtype=datatype) \n",
    "sto_exps[7,2,:2,:2]=np.array([[0.3789647534E+02,0.6745553507E+01],\n",
    "                             [0.1461088772E+01,0.3705706944E+00]],dtype=datatype)\n",
    "sto_norms[7,2,:2,:2]=np.array([[10.885772,2.9831378],\n",
    "                              [0.94714737,0.3385037]],dtype=datatype) \n",
    "sto_coefs[8,2,:2,:2]=np.array([[0.4301284983E+00,0.6789135305E+00],\n",
    "                              [0.4947176920E-01,0.5115407076E+00]],dtype=datatype) \n",
    "sto_exps[8,2,:2,:2]=np.array([[0.4998097117E+02,0.8896587673E+01],\n",
    "                             [0.1945236531E+01,0.4933633506E+00]],dtype=datatype)\n",
    "sto_norms[8,2,:2,:2]=np.array([[13.397187,3.671366],\n",
    "                              [1.1739224,0.41955146]],dtype=datatype) \n",
    "\n",
    "\n",
    "\n",
    "sto_coefs[1,3,0,:3]=np.array([0.1543289673E+00,0.5353281423E+00,0.4446345422E+00],dtype=datatype)\n",
    "sto_exps[1,3,0,:3]=np.array([0.3425250914E+01,0.6239137298E+00,0.1688554040E+00],dtype=datatype)\n",
    "sto_norms[1,3,0,:3]=np.array([1.7944418,0.50032645,0.18773545],dtype=datatype)\n",
    "sto_coefs[6,3,:2,:3]=np.array([[0.1543289673E+00,0.5353281423E+00,0.4446345422E+00],\n",
    "                              [-0.9996722919E-01,0.3995128261E+00,0.7001154689E+00]],dtype=datatype) \n",
    "sto_exps[6,3,:2,:3]=np.array([[0.7161683735E+02,0.1304509632E+02,0.3530512160E+01],\n",
    "                             [0.2941249355E+01,0.6834830964E+00,0.2222899159E+00]],dtype=datatype)\n",
    "sto_norms[6,3,:2,:3]=np.array([[17.54573,4.8921027,1.8356436],\n",
    "                              [1.6006964,0.5357423,0.23072779]],dtype=datatype) \n",
    "sto_coefs[7,3,:2,:3]=np.array([[0.1543289673E+00,0.5353281423E+00,0.4446345422E+00],\n",
    "                              [-0.9996722919E-01,0.3995128261E+00,0.7001154689E+00]],dtype=datatype) \n",
    "sto_exps[7,3,:2,:3]=np.array([[0.9910616896E+02,0.1805231239E+02,0.4885660238E+01],\n",
    "                             [0.3780455879E+01,0.8784966449E+00,0.2857143744E+00]],dtype=datatype)\n",
    "sto_norms[7,3,:2,:3]=np.array([[22.386469,6.2417984,2.3420842],\n",
    "                              [1.9322718,0.6467183,0.27852178]],dtype=datatype) \n",
    "sto_coefs[8,3,:2,:3]=np.array([[0.1543289673E+00,0.5353281423E+00,0.4446345422E+00],\n",
    "                              [-0.9996722919E-01,0.3995128261E+00,0.7001154689E+00]],dtype=datatype) \n",
    "sto_exps[8,3,:2,:3]=np.array([[0.1307093214E+03,0.2380886605E+02,0.6443608313E+01],\n",
    "                             [0.5033151319E+01,0.1169596125E+01,0.3803889600E+00]],dtype=datatype)\n",
    "sto_norms[8,3,:2,:3]=np.array([[27.551168,7.68182,2.882418],\n",
    "                              [2.3949149,0.80156183,0.3452081]],dtype=datatype) \n",
    "\n",
    "sto_coefs[15,3,:2,:3]=np.array([[0.1543289673E+00,0.5353281423E+00,0.4446345422E+00],\n",
    "                                [-0.9996722919E-01,0.3995128261E+00,0.7001154689E+00]],dtype=datatype) \n",
    "sto_coefs[15,3,3,:3]=np.array([-0.2196203690E+00,0.2255954336E+00,0.9003984260E+00],dtype=datatype)\n",
    "sto_exps[15,3,:2,:3]=np.array([[0.4683656378E+03,0.8531338559E+02,0.2308913156E+02],\n",
    "                               [0.2803263958E+02,0.6514182577E+01,0.2118614352E+01]],dtype=datatype)\n",
    "sto_exps[15,3,2,:3]=np.array([0.1743103231E+01,0.4863213771E+00,0.1903428909E+00],dtype=datatype)\n",
    "sto_norms[15,3,:2,:3]=np.array([[71.75445349,20.00658552,7.5069892],\n",
    "                                [8.6827658,2.90606308,1.25155236]],dtype=datatype)\n",
    "sto_norms[15,3,3,:3]=np.array([1.081191,0.4150521,0.2053821],dtype=datatype)\n",
    "sto_coefs[16,3,:2,:3]=np.array([[0.1543289673E+00,0.5353281423E+00,0.4446345422E+00],\n",
    "                                [-0.9996722919E-01,0.3995128261E+00,0.7001154689E+00]],dtype=datatype) \n",
    "sto_coefs[16,3,3,:3]=np.array([-0.2196203690E+00,0.2255954336E+00,0.9003984260E+00],dtype=datatype)\n",
    "sto_exps[16,3,:2,:3]=np.array([[0.5331257359E+03,0.9710951830E+02,0.2628162542E+02],\n",
    "                               [0.3332975173E+02,0.7745117521E+01,0.2518952599E+01]],dtype=datatype)\n",
    "sto_exps[16,3,2,:3]=np.array([0.2029194274E+01,0.5661400518E+00,0.2215833792E+00],dtype=datatype)\n",
    "sto_norms[16,3,:2,:3]=np.array([[79.07374871,22.04735231,8.27273777],\n",
    "                                [9.88630834,3.30888064,1.42503355]],dtype=datatype)\n",
    "sto_norms[16,3,3,:3]=np.array([1.2117215,0.46516069,0.23017756],dtype=datatype)\n",
    "\n",
    "\n",
    "sto_coefs[1,6,0,:]=np.array([0.9163596281E-02,0.4936149294E-01,0.1685383049E+00,0.3705627997E+00,0.4164915298E+00,0.1303340841E+00],dtype=datatype)\n",
    "sto_exps[1,6,0,:]=np.array([0.3552322122E+02,0.6513143725E+01,0.1822142904E+01,0.6259552659E+00,0.2430767471E+00,0.1001124280E+00],dtype=datatype)\n",
    "sto_norms[1,6,0,:]=np.array([10.370372,2.9057155,1.1177558,0.50155383,0.24672756,0.12684579],dtype=datatype)\n",
    "sto_coefs[6,6,:3,:]=np.array([[0.9163596281E-02,0.4936149294E-01,0.1685383049E+00,0.3705627997E+00,0.4164915298E+00,0.1303340841E+00],\n",
    "                              [-0.1325278809E-01,-0.4699171014E-01,-0.3378537151E-01,0.2502417861E+00,0.5951172526E+00,0.2407061763E+00],\n",
    "                              [0.3759696623E-02,0.3767936984E-01,0.1738967435E+00,0.4180364347E+00,0.4258595477E+00,0.1017082955E+00]],dtype=datatype) \n",
    "sto_exps[6,6,:2,:]=np.array([[0.7427370491E+03,0.1361800249E+03,0.3809826352E+02,0.1308778177E+02,0.5082368648E+01,0.2093200076E+01],\n",
    "                             [0.3049723950E+02,0.6036199601E+01,0.1876046337E+01,0.7217826470E+00,0.3134706954E+00,0.1436865550E+00]],dtype=datatype)\n",
    "sto_norms[6,6,:3,:]=np.array([[101.399635,28.411564,10.929215,4.9041033,2.412458,1.2402754],\n",
    "                              [9.2492285,2.7446237,1.1424646,0.5581037,0.298578,0.1663306],\n",
    "                              [102.15645,13.486355,3.129641,0.9483052,0.3343384,0.12609859]],dtype=datatype) \n",
    "sto_coefs[7,6,:3,:]=np.array([[0.9163596281E-02,0.4936149294E-01,0.1685383049E+00,0.3705627997E+00,0.4164915298E+00,0.1303340841E+00],\n",
    "                              [-0.1325278809E-01,-0.4699171014E-01,-0.3378537151E-01,0.2502417861E+00,0.5951172526E+00,0.2407061763E+00],\n",
    "                              [0.3759696623E-02,0.3767936984E-01,0.1738967435E+00,0.4180364347E+00,0.4258595477E+00,0.1017082955E+00]],dtype=datatype) \n",
    "sto_exps[7,6,:2,:]=np.array([[0.1027828458E+04,0.1884512226E+03,0.5272186097E+02,0.1811138217E+02,0.7033179691E+01,0.2896651794E+01],\n",
    "                             [0.3919880787E+02,0.7758467071E+01,0.2411325783E+01,0.9277239437E+00,0.4029111410E+00,0.1846836552E+00]],dtype=datatype)\n",
    "sto_norms[7,6,:3,:]=np.array([[129.37506,36.25011,13.944506,6.2571096,3.0780375,1.5824584],\n",
    "                              [11.165154,3.3131573,1.3791199,0.67371184,0.36042675,0.20078509],\n",
    "                              [139.80771,18.456953,4.283117,1.2978172,0.45756382,0.17257412]],dtype=datatype) \n",
    "sto_coefs[8,6,:3,:]=np.array([[0.9163596281E-02,0.4936149294E-01,0.1685383049E+00,0.3705627997E+00,0.4164915298E+00,0.1303340841E+00],\n",
    "                              [-0.1325278809E-01,-0.4699171014E-01,-0.3378537151E-01,0.2502417861E+00,0.5951172526E+00,0.2407061763E+00],\n",
    "                              [0.3759696623E-02,0.3767936984E-01,0.1738967435E+00,0.4180364347E+00,0.4258595477E+00,0.1017082955E+00]],dtype=datatype) \n",
    "sto_exps[8,6,:2,:]=np.array([[0.1355584234E+04,0.2485448855E+03,0.6953390229E+02,0.2388677211E+02,0.9275932609E+01,0.3820341298E+01],\n",
    "                             [0.5218776196E+02,0.1032932006E+02,0.3210344977E+01,0.1235135428E+01,0.5364201581E+00,0.2458806060E+00]],dtype=datatype)\n",
    "sto_norms[8,6,:3,:]=np.array([[159.22269,44.613235,17.16159,7.700664,3.7881596,1.9475415],\n",
    "                              [13.838423,4.106425,1.709322,0.83501834,0.4467236,0.24885897],\n",
    "                              [199.94058,26.395493,6.1253333,1.8560228,0.6543671,0.24680015]],dtype=datatype) \n",
    "\n",
    "sto_coefs[15,6,:5,:]=np.array([[0.9163596281E-02,0.4936149294E-01,0.1685383049E+00,0.3705627997E+00,0.4164915298E+00,0.1303340841E+00],\n",
    "                               [-0.1325278809E-01,-0.4699171014E-01,-0.3378537151E-01,0.2502417861E+00,0.5951172526E+00,0.2407061763E+00],\n",
    "                               [0.3759696623E-02,0.3767936984E-01,0.1738967435E+00,0.4180364347E+00,0.4258595477E+00,0.1017082955E+00],\n",
    "                               [-0.7943126362E-02,-0.7100264172E-01,-0.1785026925E+00,0.1510635058E+00,0.7354914767E+00,0.2760593123E+00],\n",
    "                               [-0.7139358907E-02,-0.1829277070E-01,0.7621621429E-01,0.4145098597E+00,0.4889621471E+00,0.1058816521E+00]],dtype=datatype)\n",
    "sto_exps[15,6,:2,:]=np.array([[0.4857412371E+04,0.8906012410E+03,0.2491581331E+03,0.8559254335E+02,0.3323808927E+02,0.1368928069E+02],\n",
    "                              [0.2906649590E+03,0.5753018103E+02,0.1788033738E+02,0.6879210280E+01,0.2987645712E+01,0.1369456623E+01]],dtype=datatype)\n",
    "sto_exps[15,6,2,:]=np.array([0.1111939652E+02,0.2977874272E+01,0.1116734493E+01,0.4998708868E+00,0.2473606277E+00,0.1274811462E+00],dtype=datatype)\n",
    "sto_norms[15,6,:2,:]=np.array([[414.68070016,116.19101999,44.69576689,20.0556638,9.86590955,5.07219059],\n",
    "                               [50.17121301,14.88784702,6.19714809,3.02735974,1.61959681,0.90223839]],dtype=datatype)\n",
    "sto_norms[15,6,3,:]=np.array([4.33981289,1.61562238,0.77423454,0.42369513,0.24998159,0.15205285],dtype=datatype)\n",
    "sto_coefs[16,6,:5,:]=np.array([[0.9163596281E-02,0.4936149294E-01,0.1685383049E+00,0.3705627997E+00,0.4164915298E+00,0.1303340841E+00],\n",
    "                               [-0.1325278809E-01,-0.4699171014E-01,-0.3378537151E-01,0.2502417861E+00,0.5951172526E+00,0.2407061763E+00],\n",
    "                               [0.3759696623E-02,0.3767936984E-01,0.1738967435E+00,0.4180364347E+00,0.4258595477E+00,0.1017082955E+00],\n",
    "                               [-0.7943126362E-02,-0.7100264172E-01,-0.1785026925E+00,0.1510635058E+00,0.7354914767E+00,0.2760593123E+00],\n",
    "                               [-0.7139358907E-02,-0.1829277070E-01,0.7621621429E-01,0.4145098597E+00,0.4889621471E+00,0.1058816521E+00]],dtype=datatype)\n",
    "sto_exps[16,6,:2,:]=np.array([[0.5529038289E+04,0.1013743118E+04,0.2836087927E+03,0.9742727471E+02,0.3783386178E+02,0.1558207360E+02],\n",
    "                              [0.3455896791E+03,0.6840121655E+02,0.2125904712E+02,0.8179121699E+01,0.3552198128E+01,0.1628232301E+01]],dtype=datatype)\n",
    "sto_exps[16,6,2,:]=np.array([0.1294439442E+02,0.3466625105E+01,0.1300021248E+01,0.5819134077E+00,0.2879592903E+00,0.1484042983E+00],dtype=datatype)\n",
    "sto_norms[16,6,:2,:]=np.array([[456.98010207,128.04305616,49.25494751,22.10143681,10.87227921,5.58957813],\n",
    "                               [57.12558561,16.95149327,7.05615217,3.44699057,1.84409367,1.02730019]],dtype=datatype)\n",
    "sto_norms[16,6,3,:]=np.array([4.8637517,1.81067394,0.86770666,0.47484718,0.28016147,0.17040995],dtype=datatype)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "lobe_coefs=np.zeros((19,5,2,8),dtype=datatype)\n",
    "lobe_exps=np.zeros((19,5,2,8),dtype=datatype)\n",
    "lobe_offsets=np.zeros((19,5,2,8),dtype=datatype)\n",
    "lobe_norms=np.zeros((19,5,2,8),dtype=datatype)\n",
    "\n",
    "lobe_coefs[6,3,0,:6]=np.array([0.64520464,0.88439881,0.33605098,0.64520464,0.88439881,0.33605098],dtype=datatype)\n",
    "lobe_exps[6,3,0,:6]=np.array([0.2670606,0.81133893,3.29524071,0.2670606,0.81133893,3.29524071],dtype=datatype)\n",
    "lobe_offsets[6,3,0,:6]=np.array([0.2,0.2,0.2,-0.2,-0.2,-0.2],dtype=datatype)\n",
    "lobe_norms[6,3,0,:6]=np.array([-1.0,-1.0,-1.0,1.0,1.0,1.0],dtype=datatype)*1.000657885155526\n",
    "lobe_coefs[7,3,0,:6]=np.array([0.64054726,0.9684976,0.39050546,0.64054726,0.9684976,0.39050546],dtype=datatype)\n",
    "lobe_exps[7,3,0,:6]=np.array([0.3292863,0.9914091,4.04400941,0.3292863,0.9914091,4.04400941],dtype=datatype)\n",
    "lobe_offsets[7,3,0,:6]=np.array([0.2,0.2,0.2,-0.2,-0.2,-0.2],dtype=datatype)\n",
    "lobe_norms[7,3,0,:6]=np.array([-1.0,-1.0,-1.0,1.0,1.0,1.0],dtype=datatype)*1.0004310541198355\n",
    "lobe_coefs[8,3,0,:6]=np.array([0.64437286,1.06711325,0.45753199,0.64437286,1.06711325,0.45753199],dtype=datatype)\n",
    "lobe_exps[8,3,0,:6]=np.array([0.42241359,1.26459378,5.20158956,0.42241359,1.26459378,5.20158956],dtype=datatype)\n",
    "lobe_offsets[8,3,0,:6]=np.array([0.2,0.2,0.2,-0.2,-0.2,-0.2],dtype=datatype)\n",
    "lobe_norms[8,3,0,:6]=np.array([-1.0,-1.0,-1.0,1.0,1.0,1.0],dtype=datatype)*1.000318589703924\n",
    "\n",
    "lobe_coefs[15,3,0,:6]=np.array([3.20780205,2.22347651,1.35755385,3.20780205,2.22347651,1.35755385],dtype=datatype)\n",
    "lobe_exps[15,3,0,:6]=np.array([7.67937533,2.51881708,32.39705451,7.67937533,2.51881708,32.39705451],dtype=datatype)\n",
    "lobe_offsets[15,3,0,:6]=np.array([0.1,0.1,0.1,-0.1,-0.1,-0.1],dtype=datatype)\n",
    "lobe_norms[15,3,0,:6]=np.array([-1.0,-1.0,-1.0,1.0,1.0,1.0],dtype=datatype)*1.000702490931977\n",
    "lobe_coefs[15,3,1,:6]=np.array([0.73776749,0.08185985,0.64707098,0.73776749,0.08185985,0.64707098],dtype=datatype)\n",
    "lobe_exps[15,3,1,:6]=np.array([0.2525002,0.11081551,0.59072838,0.2525002,0.11081551,0.59072838],dtype=datatype)\n",
    "lobe_offsets[15,3,1,:6]=np.array([0.2,0.2,0.2,-0.2,-0.2,-0.2],dtype=datatype)\n",
    "lobe_norms[15,3,1,:6]=np.array([-1.0,-1.0,-1.0,1.0,1.0,1.0],dtype=datatype)*1.0000599599379631\n",
    "lobe_coefs[16,3,0,:6]=np.array([3.42244003,2.2028318,1.53763642,3.42244003,2.2028318,1.53763642],dtype=datatype)\n",
    "lobe_exps[16,3,0,:6]=np.array([8.79554437,2.90676936,37.24211708,8.79554437,2.90676936,37.24211708],dtype=datatype)\n",
    "lobe_offsets[16,3,0,:6]=np.array([0.1,0.1,0.1,-0.1,-0.1,-0.1],dtype=datatype)\n",
    "lobe_norms[16,3,0,:6]=np.array([-1.0,-1.0,-1.0,1.0,1.0,1.0],dtype=datatype)*1.0006429068471574\n",
    "lobe_coefs[16,3,1,:6]=np.array([0.75966712,0.09877814,0.66719658,0.75966712,0.09877814,0.66719658],dtype=datatype)\n",
    "lobe_exps[16,3,1,:6]=np.array([0.29789993,0.13715709,0.69077193,0.29789993,0.13715709,0.69077193],dtype=datatype)\n",
    "lobe_offsets[16,3,1,:6]=np.array([0.2,0.2,0.2,-0.2,-0.2,-0.2],dtype=datatype)\n",
    "lobe_norms[16,3,1,:6]=np.array([-1.0,-1.0,-1.0,1.0,1.0,1.0],dtype=datatype)*1.0000721729039534\n",
    "\n",
    "\n",
    "lobe_coefs[6,2,0,:4]=np.array([0.96413977,0.82547949,0.96413977,0.82547949],dtype=datatype)\n",
    "lobe_exps[6,2,0,:4]=np.array([0.33941932,1.41201315,0.33941932,1.41201315],dtype=datatype)\n",
    "lobe_offsets[6,2,0,:4]=np.array([0.2,0.2,-0.2,-0.2],dtype=datatype)\n",
    "lobe_norms[6,2,0,:4]=np.array([-1.0,-1.0,1.0,1.0],dtype=datatype)*1.0028886026340327\n",
    "lobe_coefs[7,2,0,:4]=np.array([0.99478787,0.91921183,0.99478787,0.91921183],dtype=datatype)\n",
    "lobe_exps[7,2,0,:4]=np.array([0.42224616,1.75218641,0.42224616,1.75218641],dtype=datatype)\n",
    "lobe_offsets[7,2,0,:4]=np.array([0.2,0.2,-0.2,-0.2],dtype=datatype)\n",
    "lobe_norms[7,2,0,:4]=np.array([-1.0,-1.0,1.0,1.0],dtype=datatype)*1.002071766276696\n",
    "lobe_coefs[8,2,0,:4]=np.array([1.04707358,1.0237873,1.04707358,1.0237873],dtype=datatype)\n",
    "lobe_exps[8,2,0,:4]=np.array([0.5507524,2.29001396,0.5507524,2.29001396],dtype=datatype)\n",
    "lobe_offsets[8,2,0,:4]=np.array([0.2,0.2,-0.2,-0.2],dtype=datatype)\n",
    "lobe_norms[8,2,0,:4]=np.array([-1.0,-1.0,1.0,1.0],dtype=datatype)*1.001730293227881\n",
    "\n",
    "lobe_coefs[15,2,0,:4]=np.array([3.40067464,3.06307294,3.40067464,3.06307294],dtype=datatype)\n",
    "lobe_exps[15,2,0,:4]=np.array([3.23569931,13.74354402,3.23569931,13.74354402],dtype=datatype)\n",
    "lobe_offsets[15,2,0,:4]=np.array([0.1,0.1,-0.1,-0.1],dtype=datatype)\n",
    "lobe_norms[15,2,0,:4]=np.array([-1.0,-1.0,1.0,1.0],dtype=datatype)*1.0028505105813497\n",
    "lobe_coefs[15,2,1,:4]=np.array([0.6686712,0.79181905,0.6686712,0.79181905],dtype=datatype)\n",
    "lobe_exps[15,2,1,:4]=np.array([0.21070418,0.54247792,0.21070418,0.54247792],dtype=datatype)\n",
    "lobe_offsets[15,2,1,:4]=np.array([0.2,0.2,-0.2,-0.2],dtype=datatype)\n",
    "lobe_norms[15,2,1,:4]=np.array([-1.0,-1.0,1.0,1.0],dtype=datatype)*1.0002723419325867\n",
    "lobe_coefs[16,2,0,:4]=np.array([3.32374337,3.47888193,3.32374337,3.47888193],dtype=datatype)\n",
    "lobe_exps[16,2,0,:4]=np.array([16.01219981,3.76474575,16.01219981,3.76474575],dtype=datatype)\n",
    "lobe_offsets[16,2,0,:4]=np.array([0.1,0.1,-0.1,-0.1],dtype=datatype)\n",
    "lobe_norms[16,2,0,:4]=np.array([-1.0,-1.0,1.0,1.0],dtype=datatype)*1.0023555392051022\n",
    "lobe_coefs[16,2,1,:4]=np.array([0.68440713,0.83493367,0.68440713,0.83493367],dtype=datatype)\n",
    "lobe_exps[16,2,1,:4]=np.array([0.24322328,0.62787788,0.24322328,0.62787788],dtype=datatype)\n",
    "lobe_offsets[16,2,1,:4]=np.array([0.2,0.2,-0.2,-0.2],dtype=datatype)\n",
    "lobe_norms[16,2,1,:4]=np.array([-1.0,-1.0,1.0,1.0],dtype=datatype)*1.0002133800470114\n",
    "\n",
    "\n",
    "lobe_coefs[6,1,0,:2]=np.array([9.17565812,9.17565812],dtype=datatype)\n",
    "lobe_exps[6,1,0,:2]=np.array([0.52063838,0.52063838],dtype=datatype)\n",
    "lobe_offsets[6,1,0,:2]=np.array([0.03220062,-0.03220062],dtype=datatype)\n",
    "lobe_norms[6,1,0,:2]=np.array([-1.0,1.0],dtype=datatype)*1.02477824740855\n",
    "lobe_coefs[7,1,0,:2]=np.array([10.6436876,10.6436876],dtype=datatype)\n",
    "lobe_exps[7,1,0,:2]=np.array([0.66915081,0.66915081],dtype=datatype)\n",
    "lobe_offsets[7,1,0,:2]=np.array([0.02955688,-0.02955688],dtype=datatype)\n",
    "lobe_norms[7,1,0,:2]=np.array([-1.0,1.0],dtype=datatype)*1.0247957549429\n",
    "lobe_coefs[8,1,0,:2]=np.array([12.41217802,12.41217802],dtype=datatype)\n",
    "lobe_exps[8,1,0,:2]=np.array([0.89077673,0.89077673],dtype=datatype)\n",
    "lobe_offsets[8,1,0,:2]=np.array([0.02722474,-0.02722474],dtype=datatype)\n",
    "lobe_norms[8,1,0,:2]=np.array([-1.0,1.0],dtype=datatype)*1.02483494929325\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "orbital_parts_coeffs=np.zeros((18,2,7),dtype=datatype)\n",
    "orbital_parts_exps=np.zeros((18,2,7,2),dtype=datatype)\n",
    "orbital_parts_offsets=np.zeros((18,2,7),dtype=datatype)\n",
    "\n",
    "orbital_parts_coeffs[6,0]=np.array([0.21020597,-0.10733293,0.12119919,0.07106207,-0.05400071,0.05048129,0.18935931],dtype=datatype)*1.0072001798871546\n",
    "orbital_parts_exps[6,0,:,0]=np.array([0.5764236,0.87086635,4.74752682,0.22863708,0.32374581,1.46137983,1.516823],dtype=datatype)\n",
    "orbital_parts_exps[6,0,:,1]=np.array([0.96949833,18.27707337,14.12262395,0.34975632,2.30160144,56.80367948,3.43478416],dtype=datatype) #the shifted direction\n",
    "orbital_parts_offsets[6,0]=np.array([0.96183788,0.02043568,0.36447395,1.53245644,-0.14208569,0.16136831,0.63376153],dtype=datatype)\n",
    "\n",
    "orbital_parts_coeffs[7,0]=np.array([0.12594915,0.2063496,3.0087257,-0.0877023,-2.99593826,0.03994704,0.40324338],dtype=datatype)*1.0041560691795643\n",
    "orbital_parts_exps[7,0,:,0]=np.array([0.55053191,4.45342761,0.56341201,0.96059725,0.58047751,0.24416567,1.23328148],dtype=datatype)\n",
    "orbital_parts_exps[7,0,:,1]=np.array([1.77288519,13.06354044,4.0972497,41.14980098,4.26751697,0.62358979,3.60332721],dtype=datatype) #the shifted direction\n",
    "orbital_parts_offsets[7,0]=np.array([1.47613285,0.32624442,0.8411654,-0.02996572,0.84364999,2.04000418,0.72411866],dtype=datatype)\n",
    "\n",
    "orbital_parts_coeffs[8,0]=np.array([0.05957721,0.25223747,0.28753908,0.29850678,-0.08915678,0.21772122,-0.12416925],dtype=datatype)*1.0112732552315165\n",
    "orbital_parts_exps[8,0,:,0]=np.array([0.3262607,0.75808978,1.85098,14.39296814,0.53665137,4.5566118,1.58209237],dtype=datatype)\n",
    "orbital_parts_exps[8,0,:,1]=np.array([0.47470149,1.2008111,3.70769177,209.21137127,4.4360045,13.24945624,38.02792748],dtype=datatype) #the shifted direction\n",
    "orbital_parts_offsets[8,0]=np.array([1.26686064,0.82636302,0.57807172,0.17249301,-0.08838873,0.36008857,-0.02014936],dtype=datatype)\n",
    "\n",
    "\n",
    "orbital_parts_coeffs[15,0]=np.array([1.22961756,8.39115404,-2.57565278,0.81374749,0.24589321,-8.55022728,2.69403254],dtype=datatype)*1.0115313380573823\n",
    "orbital_parts_exps[15,0,:,0]=np.array([11.56045365,8.33496245,2.5728766,4.88488294,1.87827802,8.21259311,2.62899862],dtype=datatype)\n",
    "orbital_parts_exps[15,0,:,1]=np.array([23.1630487,80.60350661,12.16498862,8.63369543,3.12080396,78.57470156,12.14378531],dtype=datatype) #the shifted direction\n",
    "orbital_parts_offsets[15,0]=np.array([0.20994224,0.05841471,0.12521072,0.40181425,0.57244225,0.05325301,0.14185866],dtype=datatype)\n",
    "orbital_parts_coeffs[15,1]=np.array([0.09597981,0.05056336,-0.06168637,0.08630214,0.07481595,-0.03724176,0.12060358],dtype=datatype)*1.0057201407894794\n",
    "orbital_parts_exps[15,1,:,0]=np.array([0.63966982,0.32623491,0.2678816,0.19522489,0.47314754,0.19298332,0.43613297],dtype=datatype)\n",
    "orbital_parts_exps[15,1,:,1]=np.array([3.07613523,16.30538177,4.42319665,0.22930567,7.94012517,0.77526177,0.91420862],dtype=datatype) #the shifted direction\n",
    "orbital_parts_offsets[15,1]=np.array([1.03604633,0.2836936,0.20146867,1.28010504,0.59456785,-0.36530171,1.44961309],dtype=datatype)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "orbital_parts_coeffs[16,0]=np.array([-10.13669092,-0.66666356,-0.24129124,9.51745308,1.03294444,0.19423795,1.85596052],dtype=datatype)*1.0152183206062153\n",
    "orbital_parts_exps[16,0,:,0]=np.array([8.71597986,14.00945829,3.00237973,8.83381982,4.57601809,2.01192887,12.22370701],dtype=datatype)\n",
    "orbital_parts_exps[16,0,:,1]=np.array([70.28919659,22.01410401,15.36844365,74.26872175,6.95223015,3.11401983,14.06196848],dtype=datatype) #the shifted direction\n",
    "orbital_parts_offsets[16,0]=np.array([0.05482271,-0.05780663,-0.04124501,0.0603514,0.30744847,0.52949946,0.12796264],dtype=datatype)\n",
    "orbital_parts_coeffs[16,1]=np.array([0.15694047,0.10590538,0.05370748,0.0740629,0.05082452,1.11074957,-1.07687433],dtype=datatype)*1.0017166478392552\n",
    "orbital_parts_exps[16,1,:,0]=np.array([0.72395277,0.48092914,0.21892612,0.24555874,0.36743536,0.40806574,0.40162075],dtype=datatype)\n",
    "orbital_parts_exps[16,1,:,1]=np.array([2.90350593,1.37808715,0.53086674,1.53910575,20.90254615,6.50731129,6.44015996],dtype=datatype) #the shifted direction\n",
    "orbital_parts_offsets[16,1]=np.array([0.92661667,1.64834863,2.22262194,1.10123271,0.25207419,0.39454945,0.37554786],dtype=datatype)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalization for STO-nG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.8637517 , 1.81067394, 0.86770666, 0.47484718, 0.28016147,\n",
       "       0.17040995])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "pi=np.pi\n",
    "datatype='float64'\n",
    "exponent=np.array([0.1294439442E+02,0.3466625105E+01,0.1300021248E+01,0.5819134077E+00,0.2879592903E+00,0.1484042983E+00],dtype=datatype)\n",
    "(2*exponent/pi)**0.75"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lobe function fits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 480x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm of wavefunction: 0.9993953603178479\n",
      "[0.75966712 0.09877814 0.66719658 0.29789993 0.13715709 0.69077193\n",
      " 1.         1.        ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 480x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm of wavefunction: 0.9992283911956239\n",
      "Norm of difference: 0.00016724037487376338\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 480x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy as sc\n",
    "import matplotlib.pyplot as plt\n",
    "datatype='float32'\n",
    "\n",
    "\n",
    "exp_6g=sto_exps[16,6,2,:]\n",
    "coeff_6g=sto_coefs[16,6,4,:]\n",
    "sp=1\n",
    "\n",
    "\n",
    "x_min,x_max=-4.0,4.0\n",
    "y_min,y_max=-4.0,4.0\n",
    "z_min,z_max=-4.0,4.0\n",
    "pixel_length=0.1\n",
    "integration_correction=pixel_length**3\n",
    "points_x,points_y,points_z=int((x_max-x_min)/pixel_length)+1,int((y_max-y_min)/pixel_length)+1,int((z_max-z_min)/pixel_length)+1\n",
    "x,y,z=np.linspace(x_min,x_max,points_x,dtype=datatype),np.linspace(y_min,y_max,points_y,dtype=datatype),np.linspace(z_min,z_max,points_z,dtype=datatype)\n",
    "x,y,z=np.meshgrid(x,y,z,indexing='ij')\n",
    "xyz=np.stack((x.reshape(-1),y.reshape(-1),z.reshape(-1)))\n",
    "r=(x**2+y**2+z**2)**0.5\n",
    "# s-orbitals\n",
    "if (sp==0):\n",
    "    phi_H1s_sto6g=coeff_6g[0]*(2*exp_6g[0]/np.pi)**(3./4.)*np.exp(-exp_6g[0]*r**2) \\\n",
    "                +coeff_6g[1]*(2*exp_6g[1]/np.pi)**(3./4.)*np.exp(-exp_6g[1]*r**2) \\\n",
    "                +coeff_6g[2]*(2*exp_6g[2]/np.pi)**(3./4.)*np.exp(-exp_6g[2]*r**2) \\\n",
    "                +coeff_6g[3]*(2*exp_6g[3]/np.pi)**(3./4.)*np.exp(-exp_6g[3]*r**2) \\\n",
    "                +coeff_6g[4]*(2*exp_6g[4]/np.pi)**(3./4.)*np.exp(-exp_6g[4]*r**2) \\\n",
    "                +coeff_6g[5]*(2*exp_6g[5]/np.pi)**(3./4.)*np.exp(-exp_6g[5]*r**2)\n",
    "# p-orbitals\n",
    "else:\n",
    "    phi_H1s_sto6g=coeff_6g[0]*(2*exp_6g[0]/np.pi)**(3./4.)*z*(4*exp_6g[0])**0.5*np.exp(-exp_6g[0]*r**2) \\\n",
    "                +coeff_6g[1]*(2*exp_6g[1]/np.pi)**(3./4.)*z*(4*exp_6g[1])**0.5*np.exp(-exp_6g[1]*r**2) \\\n",
    "                +coeff_6g[2]*(2*exp_6g[2]/np.pi)**(3./4.)*z*(4*exp_6g[2])**0.5*np.exp(-exp_6g[2]*r**2) \\\n",
    "                +coeff_6g[3]*(2*exp_6g[3]/np.pi)**(3./4.)*z*(4*exp_6g[3])**0.5*np.exp(-exp_6g[3]*r**2) \\\n",
    "                +coeff_6g[4]*(2*exp_6g[4]/np.pi)**(3./4.)*z*(4*exp_6g[4])**0.5*np.exp(-exp_6g[4]*r**2) \\\n",
    "                +coeff_6g[5]*(2*exp_6g[5]/np.pi)**(3./4.)*z*(4*exp_6g[5])**0.5*np.exp(-exp_6g[5]*r**2)\n",
    "# normalize\n",
    "# phi_H1s_sto6g=(phi_H1s_sto6g**2/np.sum(phi_H1s_sto6g**2)/integration_correction)**0.5\n",
    "# plot the Gaussian-Type orbital\n",
    "plt.matshow(phi_H1s_sto6g[int(points_x/2)])\n",
    "plt.colorbar()\n",
    "plt.title('2p orbital')\n",
    "plt.show()\n",
    "# check the norm of the wavefunction (should be 1)\n",
    "print('Norm of wavefunction: '+str(np.sum(phi_H1s_sto6g**2)*integration_correction))\n",
    "\n",
    "# function to which the STO gets fitted\n",
    "def sto_fit(inputs,*coeff):\n",
    "    coeff=np.array(coeff)  \n",
    "    coeff=coeff.reshape(-1)\n",
    "    c=coeff\n",
    "    if (sp==0):\n",
    "        result=c[0]*np.exp(-0.2941249355E+01*((inputs[0])**2+(inputs[1])**2+(inputs[2])**2))+\\\n",
    "               c[1]*np.exp(-0.6834830964E+00*((inputs[0])**2+(inputs[1])**2+(inputs[2])**2))+\\\n",
    "               c[2]*np.exp(-0.2222899159E+00*((inputs[0])**2+(inputs[1])**2+(inputs[2])**2))\n",
    "    else:\n",
    "        h_o=0.2\n",
    "        result=c[0]*np.exp(-c[3]*((inputs[0])**2+(inputs[1])**2+(inputs[2]-h_o)**2))+\\\n",
    "               c[1]*np.exp(-c[4]*((inputs[0])**2+(inputs[1])**2+(inputs[2]-h_o)**2))+\\\n",
    "               c[2]*np.exp(-c[5]*((inputs[0])**2+(inputs[1])**2+(inputs[2]-h_o)**2))-\\\n",
    "               c[0]*np.exp(-c[3]*((inputs[0])**2+(inputs[1])**2+(inputs[2]+h_o)**2))-\\\n",
    "               c[1]*np.exp(-c[4]*((inputs[0])**2+(inputs[1])**2+(inputs[2]+h_o)**2))-\\\n",
    "               c[2]*np.exp(-c[5]*((inputs[0])**2+(inputs[1])**2+(inputs[2]+h_o)**2))\n",
    "    return result\n",
    "\n",
    "# fitting procedure\n",
    "popt,pcov=sc.optimize.curve_fit(sto_fit,xyz,phi_H1s_sto6g.reshape(-1),p0=np.array([1,1,1,1,1,1,1,1]),method='trf')\n",
    "coeff=np.array(popt)\n",
    "print(coeff)\n",
    "phi_H1s_sto=sto_fit(xyz,coeff).reshape((points_x,points_y,points_z))\n",
    "# plot the fitted Slater-Type orbital\n",
    "plt.matshow(phi_H1s_sto[int(points_x/2)])\n",
    "plt.colorbar()\n",
    "plt.title('Fitted lobe basis function')\n",
    "plt.show()\n",
    "# check the norm of the wavefunction (should be 1)\n",
    "print('Norm of wavefunction: '+str(np.sum(phi_H1s_sto**2)*integration_correction))\n",
    "difference=phi_H1s_sto-phi_H1s_sto6g\n",
    "plt.matshow(difference[int(points_x/2)])\n",
    "plt.colorbar()\n",
    "plt.title('Difference')\n",
    "print('Norm of difference: '+str(np.sum(difference**2)*integration_correction))\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0000721729039534\n"
     ]
    }
   ],
   "source": [
    "def overlap_and_kinetic_integral(gaussian_functions_coefficients_i,gaussian_functions_coefficients_j,gaussian_functions_exponents_i,gaussian_functions_exponents_j,\n",
    "                                 gaussian_functions_coordinates_i_x,gaussian_functions_coordinates_i_y,gaussian_functions_coordinates_i_z,\n",
    "                                 gaussian_functions_coordinates_j_x,gaussian_functions_coordinates_j_y,gaussian_functions_coordinates_j_z):\n",
    "    \n",
    "    prefactor=gaussian_functions_coefficients_i*gaussian_functions_coefficients_j\n",
    "    exp_sum=gaussian_functions_exponents_i+gaussian_functions_exponents_j\n",
    "    exp_product=gaussian_functions_exponents_i*gaussian_functions_exponents_j\n",
    "    product_sum_quotient=exp_product/exp_sum\n",
    "\n",
    "    distance_x=gaussian_functions_coordinates_i_x-gaussian_functions_coordinates_j_x\n",
    "    distance_y=gaussian_functions_coordinates_i_y-gaussian_functions_coordinates_j_y\n",
    "    distance_z=gaussian_functions_coordinates_i_z-gaussian_functions_coordinates_j_z\n",
    "    coordinate_distance=distance_x*distance_x+distance_y*distance_y+distance_z*distance_z\n",
    "\n",
    "    pi_divided_by_sum=np.pi/exp_sum\n",
    "    result_s=prefactor*pi_divided_by_sum*np.sqrt(pi_divided_by_sum)*np.exp(-product_sum_quotient*coordinate_distance)\n",
    "\n",
    "    return result_s\n",
    "\n",
    "element=16\n",
    "precision=3\n",
    "type=1\n",
    "lcoef=lobe_coefs[element,precision,type,:2*precision]*lobe_norms[element,precision,type,:2*precision]\n",
    "lexp=lobe_exps[element,precision,type,:2*precision]\n",
    "loffset=lobe_offsets[element,precision,type,:2*precision]\n",
    "num_gaussians=2*precision\n",
    "result=0.0\n",
    "for i in range(num_gaussians):\n",
    "    for j in range(num_gaussians):\n",
    "        result+=overlap_and_kinetic_integral(lcoef[i],lcoef[j],lexp[i],lexp[j],\n",
    "                                             loffset[i],0.0,0.0,\n",
    "                                             loffset[j],0.0,0.0)\n",
    "print(result**(-0.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Orbital parts functions fit (for estimates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1468.24x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm of wavefunction: 0.44711466980525855\n",
      "[[  0.21774563  -0.26766298   1.08405648   0.82351092  -0.28015315\n",
      "   -0.64093888   1.15258126]\n",
      " [  1.80600418   3.78879181   4.39406938  40.80623327   3.6320703\n",
      "   20.67666223  12.77180107]\n",
      " [  3.0906433  101.52220596   6.91430162  62.31172938  17.56711513\n",
      "  129.27163874  22.09693528]\n",
      " [  0.5886145    0.00692616   0.32307621   0.08442613  -0.05795017\n",
      "   -0.01745236   0.21268066]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1468.24x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm of wavefunction: 0.4470446404014554\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1468.24x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 480x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm of wavefunction: 0.5420588783197916\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 480x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm of wavefunction: 0.4727156894335978\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 480x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy as sc\n",
    "import matplotlib.pyplot as plt\n",
    "datatype='float32'\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "exp_6g=sto_exps[15,6,1,:]\n",
    "coeff_6g=sto_coefs[15,6,2,:]\n",
    "\n",
    "\n",
    "x_min,x_max=-2.55*0.7,2.55*0.7\n",
    "y_min,y_max=-2.55*0.7,2.55*0.7\n",
    "z_min,z_max=-1.05*0.7,4.05*0.7\n",
    "pixel_length=0.3*0.7\n",
    "pixel_length2=0.1*0.7\n",
    "integration_correction=pixel_length**2*pixel_length2\n",
    "points_x,points_y,points_z=int((x_max-x_min)/pixel_length)+1,int((y_max-y_min)/pixel_length)+1,int((z_max-z_min)/pixel_length2)+1\n",
    "x,y,z=np.linspace(x_min,x_max,points_x,dtype=datatype),np.linspace(y_min,y_max,points_y,dtype=datatype),np.linspace(z_min,z_max,points_z,dtype=datatype)\n",
    "x,y,z=np.meshgrid(x,y,z,indexing='ij')\n",
    "xyz=np.stack((x.reshape(-1),y.reshape(-1),z.reshape(-1)))\n",
    "r=(x**2+y**2+z**2)**0.5\n",
    "# s-orbitals\n",
    "# phi_H1s_sto6g=coeff_6g[0]*(2*exp_6g[0]/np.pi)**(3./4.)*np.exp(-exp_6g[0]*r**2) \\\n",
    "#              +coeff_6g[1]*(2*exp_6g[1]/np.pi)**(3./4.)*np.exp(-exp_6g[1]*r**2) \\\n",
    "#              +coeff_6g[2]*(2*exp_6g[2]/np.pi)**(3./4.)*np.exp(-exp_6g[2]*r**2) \\\n",
    "#              +coeff_6g[3]*(2*exp_6g[3]/np.pi)**(3./4.)*np.exp(-exp_6g[3]*r**2) \\\n",
    "#              +coeff_6g[4]*(2*exp_6g[4]/np.pi)**(3./4.)*np.exp(-exp_6g[4]*r**2) \\\n",
    "#              +coeff_6g[5]*(2*exp_6g[5]/np.pi)**(3./4.)*np.exp(-exp_6g[5]*r**2)\n",
    "# p-orbitals\n",
    "phi_H1s_sto6g=coeff_6g[0]*(2*exp_6g[0]/np.pi)**(3./4.)*z*(4*exp_6g[0])**0.5*np.exp(-exp_6g[0]*r**2) \\\n",
    "             +coeff_6g[1]*(2*exp_6g[1]/np.pi)**(3./4.)*z*(4*exp_6g[1])**0.5*np.exp(-exp_6g[1]*r**2) \\\n",
    "             +coeff_6g[2]*(2*exp_6g[2]/np.pi)**(3./4.)*z*(4*exp_6g[2])**0.5*np.exp(-exp_6g[2]*r**2) \\\n",
    "             +coeff_6g[3]*(2*exp_6g[3]/np.pi)**(3./4.)*z*(4*exp_6g[3])**0.5*np.exp(-exp_6g[3]*r**2) \\\n",
    "             +coeff_6g[4]*(2*exp_6g[4]/np.pi)**(3./4.)*z*(4*exp_6g[4])**0.5*np.exp(-exp_6g[4]*r**2) \\\n",
    "             +coeff_6g[5]*(2*exp_6g[5]/np.pi)**(3./4.)*z*(4*exp_6g[5])**0.5*np.exp(-exp_6g[5]*r**2)\n",
    "phi_H1s_sto6g=np.where(phi_H1s_sto6g<0,0,phi_H1s_sto6g)\n",
    "# normalize\n",
    "# phi_H1s_sto6g=(phi_H1s_sto6g**2/np.sum(phi_H1s_sto6g**2)/integration_correction)**0.5\n",
    "# plot the Gaussian-Type orbital\n",
    "plt.matshow(phi_H1s_sto6g[int(points_x/2)])\n",
    "plt.colorbar()\n",
    "plt.title('STO-6G basis function for the Hydrogen Atom (1s orbital)')\n",
    "plt.show()\n",
    "# check the norm of the wavefunction (should be 1)\n",
    "print('Norm of wavefunction: '+str(np.sum(phi_H1s_sto6g**2)*integration_correction))\n",
    "\n",
    "# function to which the STO gets fitted\n",
    "def sto_fit(inputs,*coeff):\n",
    "    coeff=np.array(coeff)  \n",
    "    coeff=coeff.reshape(-1)\n",
    "    c=coeff\n",
    "    result=c[0]*np.exp(-c[1]*((inputs[0])**2+(inputs[1])**2)-c[2]*(inputs[2]-c[3])**2)+\\\n",
    "           c[4]*np.exp(-c[5]*((inputs[0])**2+(inputs[1])**2)-c[6]*(inputs[2]-c[7])**2)+\\\n",
    "           c[8]*np.exp(-c[9]*((inputs[0])**2+(inputs[1])**2)-c[10]*(inputs[2]-c[11])**2)+\\\n",
    "           c[12]*np.exp(-c[13]*((inputs[0])**2+(inputs[1])**2)-c[14]*(inputs[2]-c[15])**2)+\\\n",
    "           c[16]*np.exp(-c[17]*((inputs[0])**2+(inputs[1])**2)-c[18]*(inputs[2]-c[19])**2)+\\\n",
    "           c[20]*np.exp(-c[21]*((inputs[0])**2+(inputs[1])**2)-c[22]*(inputs[2]-c[23])**2)+\\\n",
    "           c[24]*np.exp(-c[25]*((inputs[0])**2+(inputs[1])**2)-c[26]*(inputs[2]-c[27])**2)\n",
    "    result=np.where(inputs[2]<0,result*1.0,result)\n",
    "    return result\n",
    "\n",
    "def sto_test(inputs,*coeff):\n",
    "    coeff=np.array(coeff)  \n",
    "    coeff=coeff.reshape(-1)\n",
    "    c=coeff\n",
    "    result=c[0]*np.exp(-c[1]*((inputs[0])**2+(inputs[1])**2)-c[2]*(inputs[2]-c[3])**2)+\\\n",
    "           c[4]*np.exp(-c[5]*((inputs[0])**2+(inputs[1])**2)-c[6]*(inputs[2]-c[7])**2)+\\\n",
    "           c[8]*np.exp(-c[9]*((inputs[0])**2+(inputs[1])**2)-c[10]*(inputs[2]-c[11])**2)+\\\n",
    "           c[12]*np.exp(-c[13]*((inputs[0])**2+(inputs[1])**2)-c[14]*(inputs[2]-c[15])**2)+\\\n",
    "           c[16]*np.exp(-c[17]*((inputs[0])**2+(inputs[1])**2)-c[18]*(inputs[2]-c[19])**2)+\\\n",
    "           c[20]*np.exp(-c[21]*((inputs[0])**2+(inputs[1])**2)-c[22]*(inputs[2]-c[23])**2)+\\\n",
    "           c[24]*np.exp(-c[25]*((inputs[0])**2+(inputs[1])**2)-c[26]*(inputs[2]-c[27])**2)\n",
    "    return result\n",
    "\n",
    "#p0=np.array([0.4,0.2,0.1,10.0,3.0,0.5,1.0,0.5,0.25])\n",
    "# fitting procedure\n",
    "popt,pcov=sc.optimize.curve_fit(sto_fit,xyz,phi_H1s_sto6g.reshape(-1),\n",
    "                                p0=np.ones(28)*0.1,method='trf')#bounds=(0.0,np.inf),\n",
    "coeff=np.array(popt)\n",
    "print(coeff.reshape(7,4).T)\n",
    "phi_H1s_sto=sto_test(xyz,coeff).reshape((points_x,points_y,points_z))\n",
    "# plot the fitted Slater-Type orbital\n",
    "# plt.scatter(coeff[4::5],coeff[3::5])\n",
    "plt.matshow(phi_H1s_sto[int(points_x/2)])\n",
    "plt.colorbar()\n",
    "plt.title('Fitted function')\n",
    "plt.show()\n",
    "# check the norm of the wavefunction (should be 1)\n",
    "print('Norm of wavefunction: '+str(np.sum(phi_H1s_sto**2)*integration_correction))\n",
    "plt.matshow(phi_H1s_sto[int(points_x/2)]-phi_H1s_sto6g[int(points_x/2)])\n",
    "plt.colorbar()\n",
    "plt.title('Difference')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "x_min,x_max=-2.55,2.55\n",
    "y_min,y_max=-2.55,2.55\n",
    "z_min,z_max=-2.55,2.55\n",
    "pixel_length=0.1\n",
    "integration_correction=pixel_length**3\n",
    "points_x,points_y,points_z=int((x_max-x_min)/pixel_length)+1,int((y_max-y_min)/pixel_length)+1,int((z_max-z_min)/pixel_length)+1\n",
    "x,y,z=np.linspace(x_min,x_max,points_x,dtype=datatype),np.linspace(y_min,y_max,points_y,dtype=datatype),np.linspace(z_min,z_max,points_z,dtype=datatype)\n",
    "x,y,z=np.meshgrid(x,y,z,indexing='ij')\n",
    "xyz=np.stack((x.reshape(-1),y.reshape(-1),z.reshape(-1)))\n",
    "r=(x**2+y**2+z**2)**0.5\n",
    "phi_H1s_sto6g=coeff_6g[0]*(2*exp_6g[0]/np.pi)**(3./4.)*z*(4*exp_6g[0])**0.5*np.exp(-exp_6g[0]*r**2) \\\n",
    "             +coeff_6g[1]*(2*exp_6g[1]/np.pi)**(3./4.)*z*(4*exp_6g[1])**0.5*np.exp(-exp_6g[1]*r**2) \\\n",
    "             +coeff_6g[2]*(2*exp_6g[2]/np.pi)**(3./4.)*z*(4*exp_6g[2])**0.5*np.exp(-exp_6g[2]*r**2) \\\n",
    "             +coeff_6g[3]*(2*exp_6g[3]/np.pi)**(3./4.)*z*(4*exp_6g[3])**0.5*np.exp(-exp_6g[3]*r**2) \\\n",
    "             +coeff_6g[4]*(2*exp_6g[4]/np.pi)**(3./4.)*z*(4*exp_6g[4])**0.5*np.exp(-exp_6g[4]*r**2) \\\n",
    "             +coeff_6g[5]*(2*exp_6g[5]/np.pi)**(3./4.)*z*(4*exp_6g[5])**0.5*np.exp(-exp_6g[5]*r**2)\\\n",
    "             +coeff_6g[5]*(2*exp_6g[5]/np.pi)**(3./4.)*z*(4*exp_6g[5])**0.5*np.exp(-exp_6g[5]*r**2)\n",
    "phi_H1s_sto6g=np.where(phi_H1s_sto6g<0,0,phi_H1s_sto6g)\n",
    "plt.matshow(phi_H1s_sto6g[int(points_x/2)])\n",
    "plt.colorbar()\n",
    "plt.title('Orbital part')\n",
    "plt.show()\n",
    "# check the norm of the wavefunction (should be 1)\n",
    "print('Norm of wavefunction: '+str(np.sum(phi_H1s_sto6g**2)*integration_correction))\n",
    "\n",
    "phi_H1s_sto=sto_fit(xyz,coeff).reshape((points_x,points_y,points_z))\n",
    "# plot the fitted Slater-Type orbital\n",
    "plt.matshow(phi_H1s_sto[int(points_x/2)])\n",
    "plt.colorbar()\n",
    "plt.title('Fitted function')\n",
    "plt.show()\n",
    "# check the norm of the wavefunction (should be 1)\n",
    "print('Norm of wavefunction: '+str(np.sum(phi_H1s_sto**2)*integration_correction))\n",
    "plt.matshow(phi_H1s_sto[int(points_x/2)]-phi_H1s_sto6g[int(points_x/2)])\n",
    "plt.colorbar()\n",
    "plt.title('Difference')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0112732552315165\n"
     ]
    }
   ],
   "source": [
    "\n",
    "def asymmetric_overlap_integral(gaussian_functions_coefficients_i,gaussian_functions_coefficients_j,\n",
    "                                gaussian_functions_exponents_i_x,gaussian_functions_exponents_j_x,\n",
    "                                gaussian_functions_exponents_i_y,gaussian_functions_exponents_j_y,\n",
    "                                gaussian_functions_exponents_i_z,gaussian_functions_exponents_j_z,\n",
    "                                gaussian_functions_coordinates_i_x,gaussian_functions_coordinates_i_y,gaussian_functions_coordinates_i_z,\n",
    "                                gaussian_functions_coordinates_j_x,gaussian_functions_coordinates_j_y,gaussian_functions_coordinates_j_z):\n",
    "    \n",
    "    prefactor=gaussian_functions_coefficients_i*gaussian_functions_coefficients_j\n",
    "    exp_sum_x=gaussian_functions_exponents_i_x+gaussian_functions_exponents_j_x\n",
    "    exp_product_x=gaussian_functions_exponents_i_x*gaussian_functions_exponents_j_x\n",
    "    product_sum_quotient_x=exp_product_x/exp_sum_x\n",
    "    exp_sum_y=gaussian_functions_exponents_i_y+gaussian_functions_exponents_j_y\n",
    "    exp_product_y=gaussian_functions_exponents_i_y*gaussian_functions_exponents_j_y\n",
    "    product_sum_quotient_y=exp_product_y/exp_sum_y\n",
    "    exp_sum_z=gaussian_functions_exponents_i_z+gaussian_functions_exponents_j_z\n",
    "    exp_product_z=gaussian_functions_exponents_i_z*gaussian_functions_exponents_j_z\n",
    "    product_sum_quotient_z=exp_product_z/exp_sum_z\n",
    "\n",
    "    distance_x=gaussian_functions_coordinates_i_x-gaussian_functions_coordinates_j_x\n",
    "    distance_y=gaussian_functions_coordinates_i_y-gaussian_functions_coordinates_j_y\n",
    "    distance_z=gaussian_functions_coordinates_i_z-gaussian_functions_coordinates_j_z\n",
    "    distance_x=distance_x*distance_x\n",
    "    distance_y=distance_y*distance_y\n",
    "    distance_z=distance_z*distance_z\n",
    "\n",
    "    pi_divided_by_sum_x=np.pi/exp_sum_x\n",
    "    pi_divided_by_sum_y=np.pi/exp_sum_y\n",
    "    pi_divided_by_sum_z=np.pi/exp_sum_z\n",
    "    exp_part=np.exp(-product_sum_quotient_x*distance_x-product_sum_quotient_y*distance_y-product_sum_quotient_z*distance_z)\n",
    "    result_s=prefactor*np.sqrt(pi_divided_by_sum_x)*np.sqrt(pi_divided_by_sum_y)*np.sqrt(pi_divided_by_sum_z)*exp_part\n",
    "\n",
    "    return result_s\n",
    "\n",
    "\n",
    "element=8\n",
    "type=0\n",
    "lcoef=orbital_parts_coeffs[element,type,:]\n",
    "lexp1=orbital_parts_exps[element,type,:,1]\n",
    "lexp2=orbital_parts_exps[element,type,:,0]\n",
    "loffset=orbital_parts_offsets[element,type,:]\n",
    "num_gaussians=7\n",
    "result=0.0\n",
    "for i in range(num_gaussians):\n",
    "    for j in range(num_gaussians):\n",
    "        result+=asymmetric_overlap_integral(lcoef[i],lcoef[j],\n",
    "                                            lexp1[i],lexp1[j],\n",
    "                                            lexp2[i],lexp2[j],\n",
    "                                            lexp2[i],lexp2[j],\n",
    "                                            -loffset[i],0.0,0.0,\n",
    "                                            -loffset[j],0.0,0.0)\n",
    "        result+=asymmetric_overlap_integral(-lcoef[i],-lcoef[j],\n",
    "                                            lexp1[i],lexp1[j],\n",
    "                                            lexp2[i],lexp2[j],\n",
    "                                            lexp2[i],lexp2[j],\n",
    "                                            loffset[i],0.0,0.0,\n",
    "                                            loffset[j],0.0,0.0)\n",
    "        result+=asymmetric_overlap_integral(-lcoef[i],lcoef[j],\n",
    "                                            lexp1[i],lexp1[j],\n",
    "                                            lexp2[i],lexp2[j],\n",
    "                                            lexp2[i],lexp2[j],\n",
    "                                            loffset[i],0.0,0.0,\n",
    "                                            -loffset[j],0.0,0.0)\n",
    "        result+=asymmetric_overlap_integral(lcoef[i],-lcoef[j],\n",
    "                                            lexp1[i],lexp1[j],\n",
    "                                            lexp2[i],lexp2[j],\n",
    "                                            lexp2[i],lexp2[j],\n",
    "                                            -loffset[i],0.0,0.0,\n",
    "                                            loffset[j],0.0,0.0)\n",
    "print(result**(-0.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "s-orbital fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 480x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm of wavefunction: 0.99999994\n",
      "[0.02801272 0.0360107  0.02213145 0.39228763 0.06846325 0.01590258\n",
      " 0.1        0.1       ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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OHTqIOXPmiIKCAmWbW8PFjx49KsaNGyfatm0rLBaLaNmypXjwwQfFkSNHpGUXwnm4uBBC3LhxQ0yePFkEBQWJJk2aiMcff1zk5+erhotfvnzZIf+tZay0bt068Ytf/EJYLBbRrFkzMXjwYLF7924l3Wq1ilGjRokmTZoIAMq1uTVcvNLmzZuV/QUHB4unnnpKfP/99zU6R2f3V31UUFAgAAhrTltx42I73Ys1p60A4HCv3qlMQhjk7SgRUT1UWFiIoKAgXMxp43bwQ3jn71FQUIDAwEAPlvD246M8IiIDsAkBmxvtBHfyGg2DH4iIyFDYYiIiMgAGP1RhxUREZAB2CNhYMQHgozwiIjIYtpiIiAyAj/KqsGIiIjIARuVV4aM8IiIyFENXTKmpqWjXrh0CAgIQExPjMObb7VY5hfXNS5cuXW7b8b/88ks89NBDCA8Ph8lkwvbt2x3ShRBYsGABWrVqhQYNGiAuLs7pAK63s0wTJ06sds2GDx/ulbKkpKSgb9++aNKkCVq2bImEhIRqg9UWFxdj2rRpaN68ORo3bowxY8YgLy/PK+WpaZmGDBlS7RrdOm+Rp6xevRq9evVCYGAgAgMDERsbi7///e9K+u2+PlrluZ3XxpnXX38dJpMJs2bNUtZ58xrZPbDUFYatmDZv3oykpCQsXLgQR48eRe/evREfH1+j+Xm8pXv37rh06ZKy3DrnjDcVFRWhd+/eSE1NdZr+xhtv4I9//CPS0tJw8OBBNGrUCPHx8V6dOEyrTAAwfPhwh2v217/+1Stl2bdvH6ZNm4YDBw5g9+7dKCsrw7Bhw1BUVKRsM3v2bHzyySfYsmUL9u3bh4sXLyrT1tdWmQBgypQpDtfojTfe8Ep52rRpg9dffx3Z2dk4cuQIHnjgATzyyCP45ptvANz+66NVHuD2XZtbHT58GO+++y569erlsN6b18j236g8d5Y6o5aHRFLVr18/MW3aNOXfNptNhIeHi5SUlFopz8KFC0Xv3r1r5di3AiC2bdum/Ntut4uwsDDx5ptvKuuuXr0qLBaL+Otf/1orZRKiYoy0Rx555LYc/1aV48rt27dPCFFxPfz8/BzG0Pv2228FAJGVlVUrZRJCiMGDB4uZM2feluM706xZM/GnP/3JENfn5vIIUXvX5tq1a6JTp05i9+7dDmXw1jWqHCvvxL9ainO5YbqXE/9qWWfGyjNki6m0tBTZ2dkOc/SYzWbExcUhKyur1sp1+vRphIeH46677sJTTz2FCxcu1FpZbnbu3DlYrVaH6xUUFISYmJhavV4AsHfvXrRs2RKdO3fG1KlTq00r4S0FBQUAgODgYABAdnY2ysrKHK5Rly5d0LZt29t2jW4tU6X3338fISEh6NGjB5KTk3Hjxg2vl8Vms2HTpk0oKipCbGxsrV+fW8tTqTauzbRp0zBq1Khqc4TV9jWqTwwZlXflyhXYbDaEhoY6rA8NDcWpU6dqpUwxMTHYsGEDOnfujEuXLmHx4sW47777cPLkSdXpEG4Xq9UKAE6vV2VabRg+fDhGjx6N9u3b4+zZs5g7dy5GjBiBrKwsr85oarfbMWvWLAwcOBA9evQAUHGN/P390bRpU4dtb9c1clYmAHjyyScRGRmJ8PBwnDhxAi+99BJycnKwdetWr5Tj66+/RmxsLIqLi9G4cWNs27YN3bp1w/Hjx2vl+qiVB7j91wYANm3ahKNHj+Lw4cPV0rx9D7n7nqguvWMyZMVkRCNGjFD+v1evXoiJiUFkZCQ++OADTJ48uRZLZlxPPPGE8v89e/ZEr1690KFDB+zduxdDhw712nGnTZuGkydP3tZ3gFrUyvTcc88p/9+zZ0+0atUKQ4cOxdmzZ9GhQwePl6Nz5844fvw4CgoK8OGHH2LChAnYt2+fx4/jbnm6det2269Nbm4uZs6cid27d9fK1OR2mGBDzWYQVstfVxjyUV5ISAh8fHyqRbvk5eUpM5LWtqZNm+Luu+/GmTNnarsoyjUx8vUCKqaFDwkJ8eo1mz59Onbs2IE9e/agTZs2yvqwsDCUlpZWm531dlwjtTI5ExMTAwBeu0b+/v7o2LEjoqOjkZKSgt69e2PFihW1dn3UyuOMt69NdnY28vPzcc8998DX1xe+vr7Yt28f/vjHP8LX1xehoaG1dg/VN4asmPz9/REdHY3MzExlnd1uR2ZmpsPz59p0/fp1nD17Fq1atartoqB9+/YICwtzuF6FhYU4ePCgYa4XAHz//ff48ccfvXLNhBCYPn06tm3bhi+++ALt27d3SI+Ojoafn5/DNcrJycGFCxe8do20yuTM8ePHAeC23Vd2ux0lJSW1cn1k5XHG29dm6NCh+Prrr3H8+HFl6dOnD5566inl/715jezC/aWuMOyjvKSkJEyYMAF9+vRBv379sHz5chQVFWHSpEm1Up4XXngBDz30ECIjI3Hx4kUsXLgQPj4+GDdu3G05/vXr1x1+KZ47dw7Hjx9HcHAw2rZti1mzZuHVV19Fp06d0L59e8yfPx/h4eFISEiolTIFBwdj8eLFGDNmDMLCwnD27Fm8+OKL6NixI+Lj4z1elmnTpiE9PR1/+9vf0KRJE+WZf1BQEBo0aICgoCBMnjwZSUlJCA4ORmBgIGbMmIHY2Fj079/f4+WpSZnOnj2L9PR0jBw5Es2bN8eJEycwe/ZsDBo0qFqYsickJydjxIgRaNu2La5du4b09HTs3bsXu3btqpXrIyvP7b42ANCkSROH938A0KhRIzRv3lxZ781rZHPzUZ47eQ2ntsMCZd555x3Rtm1b4e/vL/r16ycOHDhQa2VJTEwUrVq1Ev7+/qJ169YiMTFRnDlz5rYdv3Jq61uXCRMmCCEqQsbnz58vQkNDhcViEUOHDhU5OTm1VqYbN26IYcOGiRYtWgg/Pz8RGRkppkyZIqxWq1fK4qwcuGUa+59//ln85je/Ec2aNRMNGzYUjz76qLh06ZJXylOTMl24cEEMGjRIBAcHC4vFIjp27FhtGndPeuaZZ0RkZKTw9/cXLVq0EEOHDhWfffaZkn67r4+sPLf72qi5NWTdG9eoMlz84Ddh4psL4bqXg9+E6QoXX7lypYiMjBQWi0X069dPHDx4ULr9Bx98IDp37iwsFovo0aOH+PTTTx3Sr127JqZNmyZat24tAgICRNeuXcXq1atdKhOnViciqkWVU6vv/6YVGrsxtfr1a3YM6H7JpanVN2/ejPHjxyMtLQ0xMTFYvnw5tmzZgpycHLRs2bLa9vv378egQYOQkpKCBx98EOnp6Vi6dCmOHj2qtCqfe+45fPHFF/jTn/6Edu3a4bPPPsNvfvMbbN26FQ8//HCNysWKiYioFlVWTF+dDHe7Yrq3x0WXKqaYmBj07dsXK1euBFDxji8iIgIzZszAyy+/XG37xMREFBUVYceOHcq6/v37IyoqCmlpaQCAHj16IDExEfPnz1e2iY6OxogRI/Dqq6/WqFyGDH4gIiJ9CgsLHRa1YBI9AxlkZWVV63gcHx/vsP2AAQPw8ccf44cffoAQAnv27MG///1vDBs2rMbnwIqJiMgAKoMf3FkAICIiAkFBQcqSkpLi9HiygQzUOgxbrVbN7d955x1069YNbdq0gb+/P4YPH47U1FQMGjSoxtfCsFF5RET1iQ1m2NxoK9j++9/c3FyHR3kWi8XNkrnmnXfewYEDB/Dxxx8jMjISX375JaZNm4bw8PBqrS01rJiIiOqQymlEtOgZyCAsLEy6/c8//4y5c+di27ZtGDVqFICKkXKOHz+OP/zhDzWumPgoj4jIAIQwwe7GIoRr/Zj0DGQQGxvrsD0A7N69W9m+rKwMZWVlMJsdqxYfHx/Y7TUfzc/wFVNJSQkWLVqk+gLvdjNaeQDjlYnlkTNaeQDjlak+lsdT75hckZSUhPfeew8bN27Et99+i6lTpzoMZDB+/HgkJycr28+cORMZGRlYtmwZTp06hUWLFuHIkSOYPn06gIrW2uDBgzFnzhzs3bsX586dw4YNG/DnP/8Zjz76aI3LZfhw8cpQSldCIOtTeQDjlYnlubPKAxivTPWpPJX7/vuJ9mjkRrh40TU7RvQ653IZV65ciTfffBNWqxVRUVH44x//qIxLOGTIELRr1w4bNmxQtt+yZQvmzZuH8+fPo1OnTnjjjTcwcuRIJd1qtSI5ORmfffYZfvrpJ0RGRuK5557D7NmzYTLVrPLkOyYionps+vTpSovnVnv37q22buzYsRg7dqzq/sLCwrB+/Xq3ysSKiYjIAOwwwe7G2xV7HZpa3XAVk91ux8WLF9GkSROYTCYUFhYCgPLf2ma08gDGKxPLI2e08gDGK5PRyyOEwLVr1xAeHl7tRb9eHMS1itfeMaWmpirPLXv37o133nkH/fr108z3/fffIyIiwhtFIiLyqNzcXM05trRUvmP6+EQHNGqif2bnoms2PNzrrGHey7nDKy2mzZs3IykpyWFgwPj4eNWBAW9WOU35vRgJX/i5fnDZyzWT+i8bk1mST2MacOn7PNmvKVlGjV9h0peIsnORXAP5iWiky/arRVZenbResnrl95g7E+IISSitrKxa5yHbr6S8mtdHFvoryyvJp/knsdlUk4Ts2uu9thLlKMNX2Kl8X3mCTZhhE250sDV2HJtLvFIxvfXWW5gyZYoScpiWloZPP/0U69atczow4M0qv1B84Qdf022smKT5tComL1QEGl/08mPq3K9WBcGKSUMtVEyalaFkvyZJxaR1LiZZnxRJXkk+7WOq32NCci7Sa6D3b/bfbDWNMquJindMnFod8EI/JlcHBiwpKak26CAREdVfHq+YXB0YMCUlxWHAQb5fIqL6yP7fsfL0Lu5E9BlNrZ9JcnIyCgoKlCU3N7e2i0REdNtVvmNyZ6krPP6OydWBAS0Wy20f/ZaIiIzL4xXTzQMDJiQkAKgaGFCtd7FLNF42mmQRdDpf/Gu+4JRF0EnKozuyDpCfi48s4EJ/8IPugAsteiMX3aB7rzojzrT3K3mx707wgyyowqaeZpLlA6R/F72BJSaN6yeknyVZVJ6krJJIv4oNbl+km93Nx3HsYKshKSkJEyZMQJ8+fdCvXz8sX77cYWBAIiJyZBMm2FwcIfzW/HWFVyqmxMREXL58GQsWLFAGBszIyKgWEEFERHQrrw1JJBsYkIiIHLk/gy0f5RERkQfZhRl2NyLr7Bz5gYiIPIktpip1J/CdiIjqBLaYiIgMwA73Iuvc6KxgOMatmEwmp30lpP2UAO/0VdI6pqQfjslLfYpglpRJdp6yPkNa88ro7cfkzuCw3sinRe+zes0RufWNEm5yo++UsOsceNeu0b9H0m9I1gdKeoW0+ijKRheX3bp22edTekhJPyeTW2P2OuN+P6a68wCs7pwJERHVCcZtMRER1SPuz8dUd9oZrJiIiAyA8zFVqTtVLBER1QlsMRERGQAf5VVhxUREZADud7BlxeR9JrPzcFZZiCvgnZBwjTBqaUi4dBoO/SHqXjkXzRB1fdNTCIaLAwBMOsPFpSHhklDoimPKpr2QhV9rXFvZdBGSvjiyvboTfe2NUPKKHauVyuzxcHGqYtyKiYioHrELE+zudLDltBdERORJdjcf5dWlDrasmIiIDMD90cXrTsVUd86EiIjqBLaYiIgMwAYTbG50knUnr9GwYiIiMgA+yqti2IrJZDY5D4nWCGP1Rhi1NBxcc7/qafKRxzV+/ciOKduv5DyF1nlKRxB3Iwxd56jlwkvh4tLRvPWmARCycHFZWLfkC8dk05jsQDq6uCSsWxYOrpFXaJVJbZca6Xqjs3WHkgMwqUS6mYSpbs0zYTCGrZiIiOoTG9x7HKfxU+KOwoqJiMgA+CivSt05EyIicllqairatWuHgIAAxMTE4NChQ9Ltt2zZgi5duiAgIAA9e/bEzp07HdJNJpPT5c0336xxmVgxEREZQOUgru4srtq8eTOSkpKwcOFCHD16FL1790Z8fDzy8/Odbr9//36MGzcOkydPxrFjx5CQkICEhAScPHlS2ebSpUsOy7p162AymTBmzJgal8skhN6BwbyjsLAQQUFBuN93DHxNftU3qIUx5Bj8UIMyMfjBvanVpcEPkmnMNYMfZGPl6RtHT6tM0uAH2ZTtGseU71fnmIBafzOVvOWiDHvKP0JBQQECAwPl+9BQ+Z33ctYIWBo7+c6roZLrZXg99u/Izc11KJPFYoHFYnGaJyYmBn379sXKlSsBAHa7HREREZgxYwZefvnlatsnJiaiqKgIO3bsUNb1798fUVFRSEtLc3qMhIQEXLt2DZmZmTU+F7aYiIjqkIiICAQFBSlLSkqK0+1KS0uRnZ2NuLg4ZZ3ZbEZcXByysrKc5snKynLYHgDi4+NVt8/Ly8Onn36KyZMnu3QOHg9+WLRoERYvXuywrnPnzjh16pRrO/LxAUzVWwXSFlFlPjV6W0UarTTdrSI3RjSHr3peactHtl+tFpO0taWv1QMAQtrakhfJG6S/oSU/zKUjeQMaLR99rSlh1t9iMsnyan3OZPuVZHNrBHEv7FcrLF6ofUaFHSjXeVAVnpqPyVmLyZkrV67AZrMhNDTUYX1oaKjq97XVanW6vdVqdbr9xo0b0aRJE4wePbrG5wF4KSqve/fu+Pzzz6sO4svgPyIiGU+NLh4YGOj240VPWbduHZ566ikEBAS4lM8rNYavry/CwsK8sWsiIvKAkJAQ+Pj4IC8vz2F9Xl6e6vd3WFhYjbf/xz/+gZycHGzevNnlsnnlQcnp06cRHh6Ou+66C0899RQuXLigum1JSQkKCwsdFiKi+qZyBlt3Flf4+/sjOjraISjBbrcjMzMTsbGxTvPExsZWC2LYvXu30+3Xrl2L6Oho9O7d26VyAV6omGJiYrBhwwZkZGRg9erVOHfuHO677z5cu3bN6fYpKSkOL+oiIiI8XSQiIsOrfJTnzuKqpKQkvPfee9i4cSO+/fZbTJ06FUVFRZg0aRIAYPz48UhOTla2nzlzJjIyMrBs2TKcOnUKixYtwpEjRzB9+nSH/RYWFmLLli149tlndV0Ljz/KGzFihPL/vXr1QkxMDCIjI/HBBx84jcxITk5GUlKS8u/CwkJWTkRU79hhdmuyPz15ExMTcfnyZSxYsABWqxVRUVHIyMhQAhwuXLgA803BSQMGDEB6ejrmzZuHuXPnolOnTti+fTt69OjhsN9NmzZBCIFx48bpOpfb0o+pb9++iIuLUw1bvJnSj8nyuNN+TIzK+y9G5dUOg0XlSfsiaeSV9oEq1+jHpLffkN4+Tm7tV39/LbWvx3JRhj0lH3i0H9P0rx51ux/Tynu3eaRMtc3rH/vr16/j7NmzaNWqlbcPRUR0x7IJk9tLXeHxR3kvvPACHnroIURGRuLixYtYuHAhfHx8XG7SmUwqrSOtloQ3WkWSFpHmfmWh8npbNgCEpMUka01JWz2+GseUtrYkIzRojPwgbeHJsnpp5Af56A7qSVqjMJgkIz8ISYtJ1hIzletvMQmTemtB88rqnU5D0vmnVvo4aTwwUrv23rjzPBUuXhd4vGL6/vvvMW7cOPz4449o0aIF7r33Xhw4cAAtWrTw9KGIiKgO8njFtGnTJk/vkoiozhNuTnsh6tC0FxySgYjIAGwwuTlRYN15lFd3qlgiIqoT2GIiIjIAu3AvgEE2q8qdhhUTEZEBcGr1KsatmMxmwOTkQmtNFOiFkHDNiQL1hoRLyiMNBwfkHWwlYd+qw/gDgEa4uF2WLgkJF75aHWx1TgborUfqspBwWSdZu/z6mcplnWjV08ySkHCtaS9k0zrIOqtrTcJo0uqAq0r9syILJQfcmNrCC/tEHaoEjMi4FRMRUT1ihwl2N35tuZPXaFgxEREZgLujN9SlkR/YHiUiIkNhi4mIyAAY/FCFFRMRkQHY4eZYeXzHREREniTcDH4QrJhug4rhxZ2s1rj4zkLMb96nWpI78zF5IyRcI1xc+OkMF5fkk4aDa+1XMrq43Y1wcdlbULdCyXWGhMvnY5IHH5sl4eKy+Zhk19YsmwcLAMokadJRwOVkZ6r761FodAWRZRWyP4xkxgGT/G+mfo/VnUrAiIxbMRER1SOc9qIKKyYiIgNg8EOVunMmRERUJ7DFRERkAHyUV4UVExGRAXBIoip8lEdERIZi3BaT2ujistBirXRZ2Lcs9NisUX9L0vWGhMvCurXS7bJQcn/1smqFi9v9ZHllo4tLdwu7JORZ9j5XGmbuBlnYt0kSlWyWhHwDgF0yeLYslNxcJrunNUYBl9zXZpPeEcL1j9gtDcU3a4z1bZdcfNlnW3ZMrcdfajegFwIN+CivinErJiKieoQVUxU+yiMiIkNhi4mIyADYYqrCiomIyABYMVXhozwiIjIUtpiIiAxAwL2+SBoxjXcUVkxERAbAR3lVXK6YvvzyS7z55pvIzs7GpUuXsG3bNiQkJCjpQggsXLgQ7733Hq5evYqBAwdi9erV6NSpk0vHMZlMzvtgyKa1AACzen8G6ZQZsn4QWlNQeKGvklY/Jru/pB+TNE3SF8lPfmPbpH2g1PNpTXsh7QMl7cck2ak7017YJdNByPoxSfoiaaWby9WPKe2iI+vjBMCsc2oQd57xy6enkPQR09qxLK8kTUi+E6AxVYnatBgmL4yywIqpisv3X1FREXr37o3U1FSn6W+88Qb++Mc/Ii0tDQcPHkSjRo0QHx+P4uJitwtLRER1n8stphEjRmDEiBFO04QQWL58OebNm4dHHnkEAPDnP/8ZoaGh2L59O5544olqeUpKSlBSUqL8u7Cw0NUiERHd8dhiquLRqLxz587BarUiLi5OWRcUFISYmBhkZWU5zZOSkoKgoCBliYiI8GSRiIjuCJUVkzuLHqmpqWjXrh0CAgIQExODQ4cOSbffsmULunTpgoCAAPTs2RM7d+6sts23336Lhx9+GEFBQWjUqBH69u2LCxcu1LhMHq2YrFYrACA0NNRhfWhoqJJ2q+TkZBQUFChLbm6uJ4tEREQqNm/ejKSkJCxcuBBHjx5F7969ER8fj/z8fKfb79+/H+PGjcPkyZNx7NgxJCQkICEhASdPnlS2OXv2LO6991506dIFe/fuxYkTJzB//nwEBATUuFy13o/JYrEgMDDQYSEiqm+EMLm9uOqtt97ClClTMGnSJHTr1g1paWlo2LAh1q1b53T7FStWYPjw4ZgzZw66du2KJUuW4J577sHKlSuVbX73u99h5MiReOONN/CLX/wCHTp0wMMPP4yWLVvWuFwerZjCwsIAAHl5eQ7r8/LylDQiIqqucj4mdxag4j39zcvN7/BvVlpaiuzsbIdXL2azGXFxcaqvXrKyshy2B4D4+Hhle7vdjk8//RR333034uPj0bJlS8TExGD79u0uXQuP9mNq3749wsLCkJmZiaioKAAVF+ngwYOYOnWqazszm5xPReGjFS6uMyRcsl+hdUxZSLhkKglZmmzqCkB/SLgs5Ntm0QoXV0+XhZrb/KS7lU6LIZsSQ/azSuvHo0oU8H8PKjmkZGoLkyTkGwB8JKHd5jJZuLP6ifpIT8QNGrs1S6eSkIV1Sz4rsn0CMNllf3Cd015ofbaFys1g4ECDW9/TL1y4EIsWLaq23ZUrV2Cz2Zy+ejl16pTTfVutVumrmvz8fFy/fh2vv/46Xn31VSxduhQZGRkYPXo09uzZg8GDB9foHFyumK5fv44zZ84o/z537hyOHz+O4OBgtG3bFrNmzcKrr76KTp06oX379pg/fz7Cw8Md+joREZEjT0Xl5ebmOrwSsVgsbpetxmX475xZjzzyCGbPng0AiIqKwv79+5GWlua9iunIkSO4//77lX8nJSUBACZMmIANGzbgxRdfRFFREZ577jlcvXoV9957LzIyMlx68UVEVN/ofU90c34ANX5XHxISAh8fH5devYSFhUm3DwkJga+vL7p16+awTdeuXfHVV1/V+Fxcfsc0ZMgQCCGqLRs2bABQMbrCK6+8AqvViuLiYnz++ee4++67XT0MERF5kb+/P6Kjo5GZmamss9vtyMzMRGxsrNM8sbGxDtsDwO7du5Xt/f390bdvX+Tk5Dhs8+9//xuRkZE1LhvHyiMiMoDa6GCblJSECRMmoE+fPujXrx+WL1+OoqIiTJo0CQAwfvx4tG7dGikpKQCAmTNnYvDgwVi2bBlGjRqFTZs24ciRI1izZo2yzzlz5iAxMRGDBg3C/fffj4yMDHzyySfYu3dvjcvFiomIyAA89SjPFYmJibh8+TIWLFgAq9WKqKgoZGRkKAEOFy5cgPmm4JsBAwYgPT0d8+bNw9y5c9GpUyds374dPXr0ULZ59NFHkZaWhpSUFPz2t79F586d8dFHH+Hee++tcblMQisU5jYrLCxEUFAQhjZ9Gr4m/+ob+GrUpZLIO5Msr3SwVY1jStL1DtRq95cf025hVJ7xovLkx/Qpk+xXEpXnUypJK5F/fH1K1U/GLEsrsUn3ay5VP1lTmXpeWRrK5BfQJEsvV9+vKJfks8nPEyp5y0UpMq/+BQUFBW73vaz8zov+aDZ8G+kPVCgvKkH2mLc9UqbaZtwWk8nsfCRxjdHFTZLQWngjTSNdSCpKaaUlqUAANyqfAPVv7HKtikmSbnPyG6KSXVKhAYBdUnHJRi2Xji7uBvkI4rKQb/l+7bIKplTfCOvag1zru0iy0boBQMjCsyXXzySp2N35nMEs+cEg+3xqjC6u/n3j+ZtPuPkoz53WltEYt2IiIqpHBORdrmqSv65gxUREZAB2mNya58md2W+NptbHyiMiIroZW0xERAZQG1F5RsWKiYjIAOzCBBMnCgTAR3lERGQwxm0xmUzORwqXjR4OaISUSkJyZaMMa4xALBslHLIRxHWmARr9hiRh3bKQ8HJJKLnWfm2SoRBtGl0zpOHifpJRt2UDsGv9eJSEMJkkXVvM0hHC5Yf08dUXEu7WD2HZeUp2bLJp/GaVhH37SNKEZIRw6ejhmnllMf6y7wRJPkD9O8Pu+daJEG5G5dWhsDzjVkxERPUI3zFV4aM8IiIyFLaYiIgMgC2mKqyYiIgMgFF5Vfgoj4iIDIUtJiIiA2BUXhVWTEREBlBRMbnzjsmDhallxq2YTKaKpdpqrYl2ZPP3SJ5c6s0HQEjSZf2RZP2f7H7yY0qntpBMMyHti6Qx7UV5Q0l5JH2VbA3knxhZXru/pE+Mn2x+Bekh5f17ytSvrblUPZ9PicYhZf3opH9uSX8jrVkbZJdI1i9IY5oi2fQVdkmauVxyTK1pL3R/ttUvgtb3iVBL1/oeIrcYt2IiIqpHGJVXhRUTEZEBCLg3p1IdepLHiomIyAjYYqrCcHEiIjIUtpiIiIyAz/IUrJiIiIzAzUd57g1DbywuV0xffvkl3nzzTWRnZ+PSpUvYtm0bEhISlPSJEydi48aNDnni4+ORkZHh2oFM5oql2no3wsV1hpsKH41jytKlU22op9klUyRUpEvSZFNi+Kvnk01dAcjDussbqf9cszWU/5SzN1CPTTZJ0vz81NPMPvLpDOySaR3Ky9Tn07D9rJ4mJGmAGyHh0pBv6SFhLpfcY+WSkG+N+8+s856XfVa0PmfScHLpRdL5nVBxUNfWk0e4fHWLiorQu3dvpKamqm4zfPhwXLp0SVn++te/ulVIIqK6rnLkB3eWusLlFtOIESMwYsQI6TYWiwVhYWG6C0VEVN8wKq+KV9qje/fuRcuWLdG5c2dMnToVP/74o+q2JSUlKCwsdFiIiKj+8njFNHz4cPz5z39GZmYmli5din379mHEiBGw2Zy/D0hJSUFQUJCyREREeLpIRETGJ0zuL3WEx6PynnjiCeX/e/bsiV69eqFDhw7Yu3cvhg4dWm375ORkJCUlKf8uLCxk5URE9Q5HF6/i9dCSu+66CyEhIThz5ozTdIvFgsDAQIeFiIjqL6/3Y/r+++/x448/olWrVt4+VAXpCM46Q1y1RiCWHVMSdisLyRUafxlZXpufJJ905HH5MWWjhMtCwu1NyqX7tTRRH5Y7sFGxaloTi3o+P7N8eOwyu3po97US9QtRWKQeU1/iq3EBJR83eUi4+t9MFg4OALYyyUjfZbL7TyPEX3L/mWX3teSYmjMH6Pxsm2SfbSNhB1uFyxXT9evXHVo/586dw/HjxxEcHIzg4GAsXrwYY8aMQVhYGM6ePYsXX3wRHTt2RHx8vEcLTkRUlzAqr4rLFdORI0dw//33K/+ufD80YcIErF69GidOnMDGjRtx9epVhIeHY9iwYViyZAksFq1fk0RE9VwdavW4w+WKaciQIRCSt2y7du1yq0BERFS/caw8IiID4KO8KhzwiYjICIQHFh1SU1PRrl07BAQEICYmBocOHZJuv2XLFnTp0gUBAQHo2bMndu7c6ZA+ceJEmEwmh2X48OEulYkVExFRPbV582YkJSVh4cKFOHr0KHr37o34+Hjk5+c73X7//v0YN24cJk+ejGPHjiEhIQEJCQk4efKkw3bujpfKiomIyBBMHlhc89Zbb2HKlCmYNGkSunXrhrS0NDRs2BDr1q1zuv2KFSswfPhwzJkzB127dsWSJUtwzz33YOXKlQ7bVY6XWrk0a9bMpXIZ9x2T2eS834Js6HtA/xD3kjShcUzhI5kyQ2ffC7vGFAB6+0DZZX2cJGmAvJ+TbOoKWT8lAGgZdF01rV2g+jiLrQLUx1VsaC6VHvOGXX3+j0vF6p28z/s2V01z/huzSomkz5GtTP2PJjsVrb+Z9F6Q9bHTuP/MOu9r+WdF/jmT9nPywnQ3FelqHcy88D7HQ/2Ybh1v1GKxOI2KLi0tRXZ2NpKTk5V1ZrMZcXFxyMrKcnqIrKwsh5F6gIppjbZv3+6wrnK81GbNmuGBBx7Aq6++iubN1T87t2KLiYioDomIiHAYfzQlJcXpdleuXIHNZkNoaKjD+tDQUFitVqd5rFar5vaujpfqjHFbTERE9YmHWky5ubkOQ7vd7j6kro6X6gxbTERERuCh0cVvHXtUrWIKCQmBj48P8vLyHNbn5eWpzqcXFhbm0vaA9nipzrBiIiKqh/z9/REdHY3MzExlnd1uR2ZmJmJjY53miY2NddgeAHbv3q26PaBvvFRWTEREBlAbU6snJSXhvffew8aNG/Htt99i6tSpKCoqwqRJkwAA48ePdwiOmDlzJjIyMrBs2TKcOnUKixYtwpEjRzB9+nQAFWOpzpkzBwcOHMD58+eRmZmJRx55xOXxUvmOiYjICGphdPHExERcvnwZCxYsgNVqRVRUFDIyMpQAhwsXLsB8U+TigAEDkJ6ejnnz5mHu3Lno1KkTtm/fjh49egAAfHx8PDJe6p1XMWkNje+N/Wq1KyVZhc79Co1jytJlob52aSi5xlQH/urpJkm4uGzqCkAeEh7V5HvVtM4BF1XTmpjlx7xmV5++IscvXJpXTXG5/ON0pVg9ttterD4NhzTEXxLyDcjvBWFW/3tq3X/Se1cauq1vnxV5vfDZ99b3yR1k+vTpSovnVnv37q22buzYsRg7dqzT7Rs0aOCR8VLvvIqJiKgucnd69Do0Vh4rJiIiAzCJisWd/HUFKyYiIiPgDLYKRuUREZGhsMVERGQEfMekYMVERGQEfJSnqHsVk94RxN0JG9UZHis7pmyE5op0SaLOMHShHrFcke6nNtIy4OenHi7exCIfXVw2SrgsJLyn/xXVtCCz/GQK7OojmsvklamPPP6Dpak071W/hqppZZJrK3zUz8WtsG5pmsb9pzck3I3PmeyYukceJ0OqexUTEdGdiC0mBSsmIiIjYMWkYFQeEREZCltMRERGwKg8BSsmIiID4MgPVfgoj4iIDMWlFlNKSgq2bt2KU6dOoUGDBhgwYACWLl2Kzp07K9sUFxfj+eefx6ZNm1BSUoL4+HisWrWq2jzxWkwmkzwEtC5w5/SkYeie36dWutlHEkpuVg8lB4CG5lLVNNko4bKQ8CBzA+kxgZ91HVNWVq3zlF0jeYi1dLdS0nvBS/dfXaL2HeSV7yYGPyhcajHt27cP06ZNw4EDB7B7926UlZVh2LBhKCoqUraZPXs2PvnkE2zZsgX79u3DxYsXMXr0aI8XnIiI6iaXWkwZGRkO/96wYQNatmyJ7OxsDBo0CAUFBVi7di3S09PxwAMPAADWr1+Prl274sCBA+jfv7/nSk5ERHWSW++YCgoKAADBwcEAgOzsbJSVlSEuLk7ZpkuXLmjbti2ysrKc7qOkpASFhYUOCxFRfWNCVQCErqW2T8CDdFdMdrsds2bNwsCBA5Vpda1WK/z9/dG0aVOHbUNDQ2G1Wp3uJyUlBUFBQcoSERGht0hERHeuynBxd5Y6QnfFNG3aNJw8eRKbNm1yqwDJyckoKChQltzcXLf2R0R0RxIeWOoIXf2Ypk+fjh07duDLL79EmzZtlPVhYWEoLS3F1atXHVpNeXl5CAsLc7ovi8UCi8WipxhERFQHudRiEkJg+vTp2LZtG7744gu0b9/eIT06Ohp+fn7IzMxU1uXk5ODChQuIjY31TImJiOoitpgULrWYpk2bhvT0dPztb39DkyZNlPdGQUFBaNCgAYKCgjB58mQkJSUhODgYgYGBmDFjBmJjY12OyBNCQIjqV7ruPEWF1/os6O4BrpVPkm63qf/GKbPLp6C4YfdXTbtmD1BNk09dod5PqSKvep8j2TFlZdU6T9k1kl57b40GwD4zmpx9B8nWu4MjP1RxqWJavXo1AGDIkCEO69evX4+JEycCAN5++22YzWaMGTPGoYMtERFRTbhUMdXkV0JAQABSU1ORmpqqu1BERPUOR35QcBBXIiIjYMWk4CCuRERkKGwxEREZAIMfqrBiIiIyAk4UqKh7FZMsQEOSZpKkaf4QkR5TPUl2TJNdflSTXXITymZXkKXJZ22AqUz9yW95mXqo9LUSeQfqS8WBqmk5fuHyQqmQTV0ByEPCc4rVjykrq9Z5yq6R7NrK/i6yvycA/feC1v2n856XflY0yI+pM40Mqe5VTEREdyIGPyhYMRERGQDfMVVhVB4RERkKW0xEREbAR3kKVkxEREbg5qO8ulQx8VEeEZER1NLo4qmpqWjXrh0CAgIQExODQ4cOSbffsmULunTpgoCAAPTs2RM7d+5U3fbXv/41TCYTli9f7lKZ7rwWk7dCP2X71QrJ1RkSrjeUVyvdbFM/prlcPczcXCbvB2EuVU+z/aweCl1YpB6aDQDnfZtL09XklamHbjeUFRbyUcJlIeHnC9XLqnWeQnKNfEr1/V3M5dJDSu8Febi4fL/Se1dvKLnm58wLn/16Hkq+efNmJCUlIS0tDTExMVi+fDni4+ORk5ODli1bVtt+//79GDduHFJSUvDggw8iPT0dCQkJOHr0qDKTeaVt27bhwIEDCA93vcsHW0xEREbgoRZTYWGhw1JSUqJ6yLfeegtTpkzBpEmT0K1bN6SlpaFhw4ZYt26d0+1XrFiB4cOHY86cOejatSuWLFmCe+65BytXrnTY7ocffsCMGTPw/vvvw8/Pz+VLwYqJiMgAKsPF3VkAICIiAkFBQcqSkpLi9HilpaXIzs5GXFycss5sNiMuLg5ZWVlO82RlZTlsDwDx8fEO29vtdjz99NOYM2cOunfvruta3HmP8oiISFVubi4CA6seR1sszkckuXLlCmw2G0JDQx3Wh4aG4tSpU07zWK1Wp9tXThoLAEuXLoWvry9++9vf6j0FVkxERHVJYGCgQ8V0O2VnZ2PFihU4evQoTCb9Y/fxUR4RkRHc5qi8kJAQ+Pj4IC8vz2F9Xl4ewsLCnOYJCwuTbv+Pf/wD+fn5aNu2LXx9feHr64vvvvsOzz//PNq1a1fjsrFiIiKqh/z9/REdHY3MzExlnd1uR2ZmJmJjY53miY2NddgeAHbv3q1s//TTT+PEiRM4fvy4soSHh2POnDnYtWtXjctm3Ed5dpWfAHaNmFIvjEBs0jimyaaebrJLRo2WjOAsC/MFAHO5pLzSkHDJPiVpAOCjHtwjDYUu8ZWPup0vSSsuV79Ff7A0VU3zM8uHSi+z6xsNXRYSXnJNfp5mWbi45Nq68zczScLJZfeQ1v0nu3eladLPyu3/bGt+n6idi8bo63rUxlh5SUlJmDBhAvr06YN+/fph+fLlKCoqwqRJkwAA48ePR+vWrZUAipkzZ2Lw4MFYtmwZRo0ahU2bNuHIkSNYs2YNAKB58+Zo3tyxS4Wfnx/CwsLQuXPnGpfLuBUTEVF9c5u7VSUmJuLy5ctYsGABrFYroqKikJGRoQQ4XLhwAWZz1Y/rAQMGID09HfPmzcPcuXPRqVMnbN++vVofJnexYiIiqsemT5+O6dOnO03bu3dvtXVjx47F2LFja7z/8+fPu1wmVkxEREbAQVwVrJiIiAyA8zFVYVQeEREZCltMRERGwEd5ClZMREQGwEd5VVyqmFJSUrB161acOnUKDRo0wIABA7B06VKH+PQhQ4Zg3759Dvl+9atfIS0tzTMl1qKzf4WQ9UvQGBpf2m9D1ldEkmbXms5AktdHMk2CvVSSz1c+hIgwq6cL6UNh+W1WIul3daVYfWTiq34NVdPMPvL+KXabeoHLy9T7G8n6a8n6KQGAzw318/T5WZIm6+Mk+XsCgI+sD5S0L5x0txp59X0GNaeg0PnZ9kafI69gi0nh0jumffv2Ydq0aThw4AB2796NsrIyDBs2DEVFRQ7bTZkyBZcuXVKWN954w6OFJiKiusulFlNGRobDvzds2ICWLVsiOzsbgwYNUtY3bNhQdaylW5WUlDjMF1JYWOhKkYiI6ga2mBRuReUVFBQAAIKDgx3Wv//++wgJCUGPHj2QnJyMGzduqO4jJSXFYe6QiIgId4pERHRH8tR8THWB7uAHu92OWbNmYeDAgQ7DUTz55JOIjIxEeHg4Tpw4gZdeegk5OTnYunWr0/0kJycjKSlJ+XdhYSErJyKiekx3xTRt2jScPHkSX331lcP65557Tvn/nj17olWrVhg6dCjOnj2LDh06VNuPxWJRnciKiKje4KM8ha5HedOnT8eOHTuwZ88etGnTRrptTEwMAODMmTN6DkVEVD/c5vmYjMylFpMQAjNmzMC2bduwd+9etG/fXjPP8ePHAQCtWrVyrWTCXrFUW69Rl3ph+HuTxhQAQpYunQJAXyh5RbpsagtJSHip3pBvrXT1/Zo0ZhawlanfhvZi9RDsMj/JjrUmz5RcXlOZ+onKrp8srBvQHxLuUyxJK5UfU3YvmHVOiQFofCZk4dmSfFqfM+kUFd6YEgNw/h0kW08e4VLFNG3aNKSnp+Nvf/sbmjRposzzHhQUhAYNGuDs2bNIT0/HyJEj0bx5c5w4cQKzZ8/GoEGD0KtXL6+cABFRXcAOtlVcqphWr14NoKIT7c3Wr1+PiRMnwt/fH59//rky2VRERATGjBmDefPmeazARER1Et8xKVx+lCcTERFRbdQHIiIiV3CsPCIiA+CjvCqsmIiIjICP8hScj4mIiAzFuC0mIZyGcmq95zLpDAmXxkLL8gEwSdLN5eppwkcW8i2Pd/aRDGQtzOrnIjtNoRVirTMk3GSX79gsCXm2qw8uDiG7CO6Ei9vU02R/F7NkJG/AjZDwEkn4vyQNAHxko8mXSu7bMo17XnJfy+552WdF63Omt7uHLJ/W94lqXq18erDFpDBuxUREVI+YoP17Sit/XcGKiYjICNhiUvAdExERGQpbTEREBsBw8SqsmIiIjICP8hR8lEdERIZi3BaTEM5HKZaNXAzIw0bt6vWwySYJ6zbrD52V5TVLwsUhSwMgJGHLPrI2vRuhO9LdSi6RbCR0QB4SbvfVPxq6XvJzkaRphIubpaHb6vlkIeG+WuHiknT5yOPye16aLgsXl+WTfAYB+WdU+r0g/U7Q+j65jeHiQJ1q9bjDuBUTEVE9wndMVfgoj4iIDIUtJiIiI2Dwg4IVExGRAfBRXhU+yiMiIkNhi4mIyAj4KE/BFhMRkQFUPspzZ9EjNTUV7dq1Q0BAAGJiYnDo0CHp9lu2bEGXLl0QEBCAnj17YufOnQ7pixYtQpcuXdCoUSM0a9YMcXFxOHjwoEtlMm6LSdgBOOl/IOR9HYRkigX5kPuSvjZaw/FL0k02yRwKkn4vJpPGVBEa6ZKc6kkaN7bevko2SX8ZABCSu9Au68/lxhQe0g+x7Dxt6hlNkj5OAOAj+XvL+hRJp67QnPZC0o9OkmaSpAGAqUz9vpbe8+5Me6Ezr5BOiaE11YZKulY+PWqhxbR582YkJSUhLS0NMTExWL58OeLj45GTk4OWLVtW237//v0YN24cUlJS8OCDDyI9PR0JCQk4evQoevToAQC4++67sXLlStx11134+eef8fbbb2PYsGE4c+YMWrRoUaNymYTmhCS3V2FhIYKCgjC06dPwNflX38BXoy6VzNFjkuX1Vc8n/DSOKUkXfrL9qqfZ/eXHtFtkedW/sW2yNIv829zmr55u95NUTJIOtAArJsB4FZO5RFK5ADCXqp+stNKSpKFMfgFNsvRy9f2Kckk+WSUKACp5y0UpMq/+BQUFBQgMDJTvQ0Pld16vSb+Hj3+A7v3YSotxYv1cl8oUExODvn37YuXKlQAAu92OiIgIzJgxAy+//HK17RMTE1FUVIQdO3Yo6/r374+oqCikpaU5PUbl+X3++ecYOnRojcrFR3lEREYgPLCgoiK4eSkpcT5DZWlpKbKzsxEXF6esM5vNiIuLQ1ZWltM8WVlZDtsDQHx8vOr2paWlWLNmDYKCgtC7d+8aXIT/lqPGWxIRkdd46h1TREQEgoKClCUlJcXp8a5cuQKbzYbQ0FCH9aGhobBarU7zWK3WGm2/Y8cONG7cGAEBAXj77bexe/duhISE1PhaGPcdExERuSw3N9fhUZ7FYrntZbj//vtx/PhxXLlyBe+99x4ef/xxHDx40Ol7K2fYYiIiMgIPPcoLDAx0WNQqppCQEPj4+CAvL89hfV5eHsLCwpzmCQsLq9H2jRo1QseOHdG/f3+sXbsWvr6+WLt2bQ0vBCsmIiJDMAnh9uIKf39/REdHIzMzU1lnt9uRmZmJ2NhYp3liY2MdtgeA3bt3q25/837V3nU549KjvNWrV2P16tU4f/48AKB79+5YsGABRowYAQAoLi7G888/j02bNqGkpATx8fFYtWpVtWeSNWJXCczXGBofJkldK4vAkYRfmzSmvRAmSRSSLKxbkmaW7LMirzxZD5NGKJtJMm2IvVw2vYLGtBfSqS3U9yud9kLr+uicwkMeMi//YpCly6bTkEbWaYTiSyPvStXvMbMseg7y6SukU1tIouek01oA8s++NERdco20jnm7p724zZKSkjBhwgT06dMH/fr1w/Lly1FUVIRJkyYBAMaPH4/WrVsr76lmzpyJwYMHY9myZRg1ahQ2bdqEI0eOYM2aNQCAoqIivPbaa3j44YfRqlUrXLlyBampqfjhhx8wduzYGpfLpYqpTZs2eP3119GpUycIIbBx40Y88sgjOHbsGLp3747Zs2fj008/xZYtWxAUFITp06dj9OjR+Oc//+nKYYiI6p9a6MeUmJiIy5cvY8GCBbBarYiKikJGRobSmLhw4QLM5qpfgAMGDEB6ejrmzZuHuXPnolOnTti+fbvSh8nHxwenTp3Cxo0bceXKFTRv3hx9+/bFP/7xD3Tv3r3G5XK7H1NwcDDefPNNPPbYY2jRogXS09Px2GOPAQBOnTqFrl27IisrC/3796/R/pR+TIH/47wfk6SfEgBpPyeTj+QntqyPk0Y/JiHpA+WNPk4AYPeX9WPS18dJ1hcJkPeBssv6IklaRFrpslYRW0xebDFJ0gDv9FUySVpTWnnV+hsBgJC1imR9nADVlli5KEVm4f96tB/TL556ze1+TMfe/51HylTbdL9jstls2LRpE4qKihAbG4vs7GyUlZU5xLh36dIFbdu2VY1xB4CSkpJqcfdERFR/uVwxff3112jcuDEsFgt+/etfY9u2bejWrRusViv8/f3RtGlTh+1lMfEAkJKS4hBzHxER4fJJEBHd8TwUlVcXuFwxde7cGcePH8fBgwcxdepUTJgwAf/61790FyA5ORkFBQXKkpubq3tfRER3qtoaxNWIXO5g6+/vj44dOwIAoqOjcfjwYaxYsQKJiYkoLS3F1atXHVpNsph4oKLzV210ACMiImNye+SHyvj06Oho+Pn5ITMzE2PGjAEA5OTk4MKFC5ox7s4IISCctE1NWqP62iWDOZolIeE6Q8kB+Xt2IQtDl+5VTtrUlb3Yl8S6mGzyBrQsgl0awOAr/yknG6hVHvzghZh5ACZJeLE0+EEywCsgH+RVGhhRJglgkIVmQz5KuCwkXBrAoJUuCwmXBThoBT9IPqPSGC7Jd4LmbAUq+/XK2Ne1EJVnVC5VTMnJyRgxYgTatm2La9euIT09HXv37sWuXbsQFBSEyZMnIykpCcHBwQgMDMSMGTMQGxtb44g8IqL6ilOrV3GpYsrPz8f48eNx6dKlimHae/XCrl278Mtf/hIA8Pbbb8NsNmPMmDEOHWyJiEgDW0wKlyomrbGOAgICkJqaitTUVLcKRURE9RdHFyciMoi69DjOHayYiIiMQAj3xuCrI+P3ARxdnIiIDIYtJiIiA2BUXhXjVkx2u/NOIxp9iqR/Hb19lexafackfZUkfTNk95FbfZwkTXohJIPDavXDkaSbJX2RtAZxNcv6I8n6MUmnFJEeUndfL0gHeNU/iKvs2sqmkdDsxyTrqySbukKjH5Puvkqyz5LW50z2d9E77YXG30y1TFr9KfVgVJ6Cj/KIiMhQjNtiIiKqR0wqD4lcyV9XsGIiIjICPspT8FEeEREZCltMREQGwKi8KqyYiIiMgB1sFcatmITzB65aw81Lp8UQkukVbJLQWekRoR3CrmO/WreY9Ig6w519NMLF7bJ0Sci3WSNcXDZ9hVsh4XrpnTZEI/TYJAkXl4UtS0PCtcLFJWHUsnBxrSkopCHhstBtyedMmg/yz6j0npd8J2hOX6GWXocqASMybsVERFSP8FFeFVZMRERGwKg8BSsmIiIDYIupCsPFiYjIUNhiIiIyAkblKVgxEREZAB/lVTFuxaQ2urgGb4zYrR26XS5J1XeJpSNcQx7mapKMIC4bxVrY5U92zeWSdMno4qJMI1zcR7JfWVadYfqapKHH6kkmWTgzNMLJZaOLS0bdloZ8A/IRu/WOEK61X9l1KFf/rEjDwQHAri9EXbpfjRD12zq6OCmMWzEREdUnjMpTsGIiIjIAPsqrwqg8IiIyFLaYiIiMwC60Z9TVyl9HsGIiIjICvmNS8FEeEREZikstptWrV2P16tU4f/48AKB79+5YsGABRowYAQAYMmQI9u3b55DnV7/6FdLS0lwumBCAcPITQBY6W7GBJGxZlq2G5XJ9v5JQcklYN8waI1XLyiMLdzar/xYxaYSLmyR5hSRc3KQR1i0k+zXcTyfJ7ad5b8pC/GUjt+sNzdbIKw1vdytcXGfotiwc3K396kyD+mfJG31ZTXAz+MFjJal9Ln3s27Rpg9dffx3Z2dk4cuQIHnjgATzyyCP45ptvlG2mTJmCS5cuKcsbb7zh8UITEdU5lSM/uLPokJqainbt2iEgIAAxMTE4dOiQdPstW7agS5cuCAgIQM+ePbFz504lraysDC+99BJ69uyJRo0aITw8HOPHj8fFixddKpNLFdNDDz2EkSNHolOnTrj77rvx2muvoXHjxjhw4ICyTcOGDREWFqYsgYGBLhWIiIhuj82bNyMpKQkLFy7E0aNH0bt3b8THxyM/P9/p9vv378e4ceMwefJkHDt2DAkJCUhISMDJkycBADdu3MDRo0cxf/58HD16FFu3bkVOTg4efvhhl8plEpozZTlns9mwZcsWTJgwAceOHUO3bt0wZMgQfPPNNxBCICwsDA899BDmz5+Phg0bqu6npKQEJSUlyr8LCwsRERGB+y2Pw9fkV73AWr39fWSPxySPsWSjD8j2CQBmyUgLevcre7wFAL7qeaUjKcj2K8unkVf2KE9rhAY+yuOjvIp91sKjPK3JCVX+ZuWiDHtKPkBBQYHbP74LCwsRFBSEex9YBF/fAN37KS8vxldfLHKpTDExMejbty9WrlwJALDb7YiIiMCMGTPw8ssvV9s+MTERRUVF2LFjh7Kuf//+iIqKUn1lc/jwYfTr1w/fffcd2rZtW6NyuRyV9/XXXyM2NhbFxcVo3Lgxtm3bhm7dugEAnnzySURGRiI8PBwnTpzASy+9hJycHGzdulV1fykpKVi8eLGrxSAiqls8FJVXWFjosNpiscBisVTbvLS0FNnZ2UhOTlbWmc1mxMXFISsry+khsrKykJSU5LAuPj4e27dvVy1WQUEBTCYTmjZtWrPzgI6KqXPnzjh+/DgKCgrw4YcfYsKECdi3bx+6deuG5557TtmuZ8+eaNWqFYYOHYqzZ8+iQ4cOTveXnJzscKKVLSYiovrEJITmGJla+QFU+/5cuHAhFi1aVG37K1euwGazITQ01GF9aGgoTp065fQYVqvV6fZWq9Xp9sXFxXjppZcwbtw4l1qWLldM/v7+6NixIwAgOjoahw8fxooVK/Duu+9W2zYmJgYAcObMGdWKSa02JyIi1+Xm5jpUArX1/VpWVobHH38cQgisXr3apbxud7C12+0O74hudvz4cQBAq1at3D0MEVHdZof0HWaN8gMIDAysUeskJCQEPj4+yMvLc1ifl5eHsLAwp3nCwsJqtH1lpfTdd9/hiy++cPk9nEsVU3JyMkaMGIG2bdvi2rVrSE9Px969e7Fr1y6cPXsW6enpGDlyJJo3b44TJ05g9uzZGDRoEHr16uVSoQBUvJQ0VX/zLTQCEUxaw9irqJ0+ThLuvEiX9UeSBTBo9GOSBTHI+jjBLL+C0oAWWb80L017IX2cojcNkA8ZI/t7S4Mm3Jj2wp3pICRl0h3goBWI4IUAB83YL7W8Qt/3jIynHuXVlL+/P6Kjo5GZmYmEhAQAFQ2NzMxMTJ8+3Wme2NhYZGZmYtasWcq63bt3IzY2Vvl3ZaV0+vRp7NmzB82bN3f5XFyqmPLz8zF+/HhcunQJQUFB6NWrF3bt2oVf/vKXyM3Nxeeff47ly5ejqKgIERERGDNmDObNm+dyoYiIyPuSkpIwYcIE9OnTB/369VO+vydNmgQAGD9+PFq3bo2UlBQAwMyZMzF48GAsW7YMo0aNwqZNm3DkyBGsWbMGQEWl9Nhjj+Ho0aPYsWMHbDab8v4pODgY/v7+NSqXSxXT2rVrVdMiIiKqjfpAREQ1VAtj5SUmJuLy5ctYsGABrFYroqKikJGRoQQ4XLhwAeabnoYMGDAA6enpmDdvHubOnYtOnTph+/bt6NGjBwDghx9+wMcffwwAiIqKcjjWnj17MGTIkBqVS3c/Jm+pjOm/33eM035MWn2KpI+FvNHHSXO/Ovs4udNfS2c/Jmn/J60yufEoT7pfPsrjo7wa7ff2PsorF2XYU/6RR/sxDRo43+1+TF/+c4lHylTbjNZ9kYiI6jlOe0FEZACcwbYKKyYiIiNwYyBWJX8dYdiKSdgFhJOfACaNnwVC9trGC6HkgP5wciEkz8W13qVJ33Xom05Dc6w32Xskk3pe4c47Jmk2Lw30r/cDrpHPJHvHJMsrnbZB673WbQ6jrsis75huvS/TeS4a10+opBvs1XydY9iKiYioPjHZpb/vapS/rmDFRERkBHyUp2BUHhERGQpbTERERlALHWyNihUTEZEB3O6x8oyMFRMRkRHwHZPCuBWTUBkDXmiECEtGyPZGKDngxgjiTkZPr9qpVli8JCRcNoSNdOggrSGJZPOKy0Ye9064uO58WrwULi4NTdY71JFGiL/QG2quNc259FwkXQf0DisEeCckXNZlQ5aulY/cYtyKiYioPhFwbz6mutNgYsVERGQEfMdUheHiRERkKGwxEREZgYCbwQ8eK0mtY8VERGQEjMpT8FEeEREZinFbTMJ5N2ihEdZtkg3K7a1QctlsnpJs0pHSNcPiJXklM9GqjZYMADDLQ4Kko3m7E7otHbXcSyHherkRuq13v+6Mji0Na5aFbmuFQ0uOKy2v7LOkFfruhZBwre8T1b+LN1onduifqqAyfx1h3IqJiKgeYVReFT7KIyIiQ2GLiYjICBj8oGDFRERkBKyYFHyUR0REhsIWExGREbDFpGDFRERkBAwXV7hVMb3++utITk7GzJkzsXz5cgBAcXExnn/+eWzatAklJSWIj4/HqlWrEBoa6onyak8HIeuXIOk3ZJL0GxI+ss5RgEln/xUh66Mj61gFrT5QsukpZNNeyD8V0vLK9qtFo/+UHtI+V9DoE6OXVp8iGdnfzFv9mPT2RQLkfY509vXSPKZs2gu9U1sYqJXBcPEqur9NDh8+jHfffRe9evVyWD979mx88skn2LJlC/bt24eLFy9i9OjRbheUiIjqB10V0/Xr1/HUU0/hvffeQ7NmzZT1BQUFWLt2Ld566y088MADiI6Oxvr167F//34cOHDA6b5KSkpQWFjosBAR1TuV75jcWeoIXRXTtGnTMGrUKMTFxTmsz87ORllZmcP6Ll26oG3btsjKynK6r5SUFAQFBSlLRESEniIREd3Z7ML9pY5wuWLatGkTjh49ipSUlGppVqsV/v7+aNq0qcP60NBQWK1Wp/tLTk5GQUGBsuTm5rpaJCIiqkNcCn7Izc3FzJkzsXv3bgQEBHikABaLBRaLxSP7IiK6YzFcXOFSxZSdnY38/Hzcc889yjqbzYYvv/wSK1euxK5du1BaWoqrV686tJry8vIQFhZWo2NURuaUo0znxFeyaCz1BqIsKk9rpGVp/Jc0us6NqDxpXn3XAHaNWFVvReW5FSOrssf6EpWndR4696t5fXSXVxaVJz8khCQqT+cx9X6Zl6NM+7guc/c9UT2tmIYOHYqvv/7aYd2kSZPQpUsXvPTSS4iIiICfnx8yMzMxZswYAEBOTg4uXLiA2NjYGh3j2rVrAICvsNOVolWR/W1kabK6p1xfUYiobrt27RqCgoJquxh1jksVU5MmTdCjRw+HdY0aNULz5s2V9ZMnT0ZSUhKCg4MRGBiIGTNmIDY2Fv3796/RMcLDw5Gbm4smTZrAZDKhsLAQERERyM3NRWBgoCvF9QqjlQcwXplYnjurPIDxymT08gghcO3aNYSHh3vuIHyUp/D4yA9vv/02zGYzxowZ49DBtqbMZjPatGlTbX1gYKAhbtBKRisPYLwysTxyRisPYLwyGbk8Hm8p2Z1PjupaftelpqbizTffhNVqRe/evfHOO++gX79+qttv2bIF8+fPx/nz59GpUycsXboUI0eOVNK3bt2KtLQ0ZGdn46effsKxY8cQFRXlUpncHsR17969yqgPABAQEIDU1FT89NNPKCoqwtatW2v8fomIiG6fzZs3IykpCQsXLsTRo0fRu3dvxMfHIz8/3+n2+/fvx7hx4zB58mQcO3YMCQkJSEhIwMmTJ5VtioqKcO+992Lp0qW6y8XRxYmIjEDY3V+AagMWlJSUqB7yrbfewpQpUzBp0iR069YNaWlpaNiwIdatW+d0+xUrVmD48OGYM2cOunbtiiVLluCee+7BypUrlW2efvppLFiwoFo/V1cYvmKyWCxYuHChYULKjVYewHhlYnnkjFYewHhlqpfl8dDIDxEREQ6DFjjrcwoApaWlyM7OdqhAzGYz4uLiVAdEyMrKqlbhxMfHq26vl0l4JW6WiIhqorCwEEFBQYhr/Wv4mvVXfOX2Enz+Q1q1gBG1vqIXL15E69atsX//foeo6RdffBH79u3DwYMHq+Xx9/fHxo0bMW7cOGXdqlWrsHjxYuTl5Tlse/78ebRv317XOyZOe0FEVIcYLWBED1ZMRERGcJvDxUNCQuDj41OtpSMbECEsLMyl7fUy/DsmIqJ6QcDNd0yuHc7f3x/R0dHIzMxU1tntdmRmZqoOiBAbG+uwPQDs3r27xgMo1BRbTERE9VRSUhImTJiAPn36oF+/fli+fDmKioowadIkAMD48ePRunVrJYBi5syZGDx4MJYtW4ZRo0Zh06ZNOHLkCNasWaPs86effsKFCxdw8eJFABWj/wAVra2atqxYMRERGUEtjPyQmJiIy5cvY8GCBbBarYiKikJGRoYy4/iFCxdgNlc9WBswYADS09Mxb948zJ07F506dcL27dsdRgT6+OOPlYoNAJ544gkAwMKFC7Fo0aIalYtReUREtUiJymv5LHzN/rr3U24vxef5f0JBQcEdH/zAd0xERGQofJRHRGQEHMRVwYqJiMgIWDEp+CiPiIgMhS0mIiIjqKVpL4yIFRMRkQEIYYeQTQNfg/x1BR/lERGRobDFRERkBEK49ziuDgU/sGIiIjIC4eY7JlZMRETkUXY7YHLjPRHfMREREXkHW0xEREbAR3kKVkxERAYg7HYINx7lMVyciIjIS9hiIiIyAj7KU7BiIiIyArsATKyYAD7KIyIig2GLiYjICIQA4E4/prrTYmLFRERkAMIuINx4lCfqUMXER3lERGQobDERERmBsMO9R3l1px8TKyYiIgPgo7wqfJRHRESGwhYTEZEBlIsStx7HlaPMg6WpXayYiIhqkb+/P8LCwvCVdafb+woLC4O/v78HSlW7TKIuPZgkIroDFRcXo7S01O39+Pv7IyAgwAMlql2smIiIyFAY/EBERIbCiomIiAyFFRMRERkKKyYiIjIUVkxERGQorJiIiMhQWDEREZGh/H+6pL283Dbc/wAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 480x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Norm of wavefunction: 0.9999280353655258\n",
      "Norm of difference: 7.180422883487404e-05\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 480x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy as sc\n",
    "import matplotlib.pyplot as plt\n",
    "datatype='float32'\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "x_min,x_max=-8.0,8.0\n",
    "y_min,y_max=-8.0,8.0\n",
    "z_min,z_max=-8.0,8.0\n",
    "pixel_length=0.4\n",
    "integration_correction=pixel_length**3\n",
    "points_x,points_y,points_z=int((x_max-x_min)/pixel_length)+1,int((y_max-y_min)/pixel_length)+1,int((z_max-z_min)/pixel_length)+1\n",
    "x,y,z=np.linspace(x_min,x_max,points_x,dtype=datatype),np.linspace(y_min,y_max,points_y,dtype=datatype),np.linspace(z_min,z_max,points_z,dtype=datatype)\n",
    "x,y,z=np.meshgrid(x,y,z,indexing='ij')\n",
    "xyz=np.stack((x.reshape(-1),y.reshape(-1),z.reshape(-1)))\n",
    "r=(x**2+y**2+z**2)**0.5\n",
    "# s-orbitals\n",
    "phi_H1s_sto6g=np.exp(-0.31*r) \n",
    "# normalize\n",
    "phi_H1s_sto6g=(phi_H1s_sto6g**2/np.sum(phi_H1s_sto6g**2)/integration_correction)**0.5\n",
    "# plot the Gaussian-Type orbital\n",
    "plt.matshow(phi_H1s_sto6g[int(points_x/2)])\n",
    "plt.colorbar()\n",
    "plt.title('2p orbital')\n",
    "plt.show()\n",
    "# check the norm of the wavefunction (should be 1)\n",
    "print('Norm of wavefunction: '+str(np.sum(phi_H1s_sto6g**2)*integration_correction))\n",
    "\n",
    "# function to which the STO gets fitted\n",
    "def sto_fit(inputs,*coeff):\n",
    "    coeff=np.array(coeff)  \n",
    "    coeff=coeff.reshape(-1)\n",
    "    c=coeff\n",
    "    result=c[0]*np.exp(-c[3]*((inputs[0])**2+(inputs[1])**2+(inputs[2])**2))+\\\n",
    "            c[1]*np.exp(-c[4]*((inputs[0])**2+(inputs[1])**2+(inputs[2])**2))+\\\n",
    "            c[2]*np.exp(-c[5]*((inputs[0])**2+(inputs[1])**2+(inputs[2])**2))\n",
    "    return result\n",
    "\n",
    "# fitting procedure\n",
    "popt,pcov=sc.optimize.curve_fit(sto_fit,xyz,phi_H1s_sto6g.reshape(-1),p0=np.array([1,1,1,1,1,1,1,1])*0.1,method='trf')\n",
    "coeff=np.array(popt)\n",
    "print(coeff)\n",
    "phi_H1s_sto=sto_fit(xyz,coeff).reshape((points_x,points_y,points_z))\n",
    "# plot the fitted Slater-Type orbital\n",
    "plt.matshow(phi_H1s_sto[int(points_x/2)])\n",
    "plt.colorbar()\n",
    "plt.title('Fitted lobe basis function')\n",
    "plt.show()\n",
    "# check the norm of the wavefunction (should be 1)\n",
    "print('Norm of wavefunction: '+str(np.sum(phi_H1s_sto**2)*integration_correction))\n",
    "difference=phi_H1s_sto-phi_H1s_sto6g\n",
    "plt.matshow(difference[int(points_x/2)])\n",
    "plt.colorbar()\n",
    "plt.title('Difference')\n",
    "print('Norm of difference: '+str(np.sum(difference**2)*integration_correction))\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Two Gaussians for a p-orbital"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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oajMLTkN0PpYXIvJ6mYW1AIAJg0Lgo1ULTuMepg4Jw5DIALSYrPgoh5dNk3theSEir9d5M8Irk8IEJ3EfkiTh/o5bBrzHy6bJzbC8EJFXk2W5q7xMSuQpo3PdNn4gAn00OFVrxLdHedk0uQ+WFyLyaqdqjahuaodOrcLYuGDRcdyKn06DOyfaL5tew8umyY2wvBCRV8s6YV/vMjYumOtdunFfWgIkCdh+tBrHq5pExyECwPJCRF4uu+OU0eQknjLqTlyoH9KHRQEA3uXsC7kJlhci8mpc73JpnXeb/jinFA1GXjZN4rG8EJHXKjljRGl9K9QqCePjQ0THcVtpSWFIiQ5Eq9mKD/YUiY5DxPJCRN6r85TRqIFB8NdrBKdxX5Ikdc2+vLfrNCxWm9hA5PVYXojIa2Wd6FjvwlNGl3TL2IEI8dOitL4VX+dXio5DXo7lhYi8VvYpLtZ1lI9WjbsnxwMAVu88JTYMeT2WFyLySlWNbThZ0wJJAlIHsbw44t4rE6BWScg+WYe8sgbRcciLsbwQkVfqvMpo+AADgny1gtMoQ3SQD64bGQ0AWMPZFxKI5YWIvFI2L5Huk0VT7Xeb/iy3DNVN7YLTkLdieSEir5R10r6z7uRE3oyxN8bHB2NsXDBMVhv+/f1p0XHIS7G8EJHXOdNiwtHKZgDAxATu79IbkiThgWn22Zd/f38abWar4ETkjVheiMjr7Cs+AwBIivBHWIBecBrluW5kNGKCfFDbYsJnuWWi45AXYnkhIq+z93Q9AHBX3T7SqFVYOCUBALB650nIsiw2EHkdlhci8jo5p+0zL6mDWF766s5J8fDTqXGkogk7j9eKjkNehuWFiLyKxWrD/pJ6AJx5uRxBvlrMT40FALyz44TgNORtWF6IyKscqWiC0WRFoF6D5MgA0XEUbdHUREgSsLWgGsermkXHIS/C8kJEXmVfkf2U0dj4YKhUkuA0ypYQ7o/0YVEA7GtfiPoLywsReRWud3GuBzsum/44pwQ1zdy0jvoHywsReZW9RfUAuN7FWSYlhmJMbBDaLTb8M5Ob1lH/YHkhIq9R3dSOojojJMl+2ogunyRJeGjGYADAPzNPwWiyCE5E3qBfysvKlSuRkJAAHx8fTJ48GdnZ2Rd97ltvvYXp06cjJCQEISEhSE9P7/H5RESO2tux3mVoZCAMPrwZo7PMHRmN+FA/1BvN+HBPieg45AVcXl4++OADLF26FM888wz27t2LMWPGYM6cOaiqqur2+du2bcNdd92FrVu3IjMzE3FxcZg9ezZKS0tdHZWIPNzejvUu47nexanUKgmLp9vXvry94wQsVpvgROTpXF5eXnnlFSxevBiLFi3C8OHDsWrVKvj5+WH16tXdPn/t2rV45JFHMHbsWKSkpODtt9+GzWbDli1bXB2ViDxc58zLeJ4ycrrbU+MQ6q9DcV0rNuVViI5DHk7jyoObTCbk5ORg2bJlXY+pVCqkp6cjMzPToWMYjUaYzWaEhnZ/2/r29na0t59d4d7Y2AgAMJvNMJvNl5H+Qp3Hc/ZxPRHHynEcK8ddzliZLDbsL2kAAIwZGOjx493fnyuNBCyYFItXt57AG98WYnZKOCRJOZei88+h41w1Vr05nkvLS01NDaxWK6Kios57PCoqCkeOHHHoGL/+9a8RExOD9PT0bn9/+fLlePbZZy94fPPmzfDz8+t9aAdkZGS45LieiGPlOI6V4/oyVqebAJNFA3+NjMNZ3yJfOT9XL0t/fq6izYBWUuNgaSP+vn4TkoOUd88j/jl0nLPHymg0Ovxcl5aXy/X8889j/fr12LZtG3x8fLp9zrJly7B06dKuXzc2NnatkzEYDE7NYzabkZGRgVmzZkGr5WK/nnCsHMexctzljNWaXaeBQwWYNDgCN9ww3kUJ3Yeoz1We6jDWZZcg1xSJX1yf2m/ve7n459BxrhqrzjMnjnBpeQkPD4darUZlZeV5j1dWViI6OrrH17788st4/vnn8fXXX2P06NEXfZ5er4def+Et7bVarcs+gK48tqfhWDmOY+W4vozV/lL7N8YJCWFeNc79/bl6+OpkfLCnFDuO1yK/sgWjY4P77b2dgX8OHefsserNsVy6YFen0yE1NfW8xbadi2/T0tIu+roXX3wRzz33HDZt2oQJEya4MiIReYncjs3pxnGxrkvFhfrhljExAIDXthYKTkOeyuVXGy1duhRvvfUW3nvvPeTn5+Phhx9GS0sLFi1aBAC47777zlvQ+8ILL+D3v/89Vq9ejYSEBFRUVKCiogLNzbzpFxH1TVVTG0rrWyFJUNxMgBI9fLV907pNeRU4VtkkOA15IpeXlzvuuAMvv/wynn76aYwdOxa5ubnYtGlT1yLeoqIilJeXdz3/9ddfh8lkwu23344BAwZ0fb388suujkpEHupAsf0qo+TIAATo3Xqpn0dIjgrEnBH27/Gvb+PsCzlfv/wpXrJkCZYsWdLt723btu28X586dcr1gYjIq+wvqQcAjOGsS7959Joh+CqvEhv3l+GXs4YiLtQ1V3+Sd+K9jYjI4+UW1wMAxsQFC83hTUbHBmN6cjisNhlvbOfsCzkXywsReTRZlnGgY3O6sSwv/erRa4YAAP6zpwSVjW2C05AnYXkhIo92utaIhlYzdBoVrogOFB3Hq0xODMWEQSEwWWxc+0JOxfJCRB6tc73LiBgDtGp+y+tPkiTh8fShAIB12UWoaODsCzkH/yQTkUfrWu/CxbpCTB0ShokJnbMvx0XHIQ/B8kJEHm1/R3nhehcxJEnCLztmX97PLkZ5Q6vgROQJWF6IyGOZrTYcKrPfFoBXGomTNjgMkxJDYbLauOsuOQXLCxF5rIKKJpgsNhh8NEgI4z4jopw7+7J+dxFK6zn7QpeH5YWIPNa5+7tIkiQ2jJdLGxyGK5NCYbbKWLmVa1/o8rC8EJHH4noX99I5+/Kf3cU4XdsiOA0pGcsLEXks3hbAvUxOCsOMoRGw2GT8ZfNR0XFIwVheiMgjNbdbcKzKfjf60XFBgtNQp1/PvQIA8Nn+MhwqbRCchpSK5YWIPNLBkgbIMjAw2BeRgT6i41CHETFBuGVsDADghU1HBKchpWJ5ISKP1HXKiLMubueJWVdAq5bw3bEa7DxeIzoOKRDLCxF5pIMdN2MczfUubic+zA8LJg8CADz/5RHYbLLgRKQ0LC9E5JEOlNYDAEYP5MyLO1py7RD469Q4WNqALw6Vi45DCsPyQkQep95oQnGdfSO0ESwvbik8QI+HZgwGYF/70ma2Ck5ESsLyQkQe52DHVSwJYX4I8tUKTkMX8+D0REQZ9Ciua8XqnSdFxyEFYXkhIo/TWV5GctbFrfnrNXjquhQAwD++OY7KxjbBiUgpWF6IyOOcXazL8uLu5o0diPHxwTCarLx0mhzG8kJEHudACWdelEKSJDxz0wgAwCd7S7Gv6IzgRKQELC9E5FHqWkxddy1meVGGMXHBuD01FgDw7H8P89JpuiSWFyLyKJ3rXZLC/WHw4WJdpfi/OVfAX6dGbnE9PtlXKjoOuTmWFyLyKIe4WFeRIg0+eGxmMgDgz1/ko67FJDgRuTOWFyLyKAc6bgvAxbrK88C0RKREB6KuxYQ/f5EvOg65MZYXIvIoh0obAXDmRYm0ahX+fNsoSBLwUU4JdhXyvkfUPZYXIvIYNc3tKK1vhSQBI2IMouNQH4yPD8E9Hfc9+u2GQ9x5l7rF8kJEHqNzsW5iuD8CuVhXsZ6cewUiA/U4WdOC17YeFx2H3BDLCxF5jEOdm9PxlJGiGXy0+MPN9r1fXv+2EAUVTYITkbtheSEij3GAVxp5jOtGRiN9WBTMVhm//CAXJotNdCRyIywvROQxOi+THh0bLDYIXTZJkvDn20YixE+Lw+WN+PuWY6IjkRtheSEij1Dd1I7yhjYu1vUgkYE++POtowAAr207jr28dQB1YHkhIo9w6Jyddf31GsFpyFmuGzUAt44bCJsMPPGf/TCaLKIjkRtgeSEij8BTRp7rDzePQLTBBydrWrD8C955mlheiMhDHCqzlxeeMvI8Qb5avDR/NADgX9+fxqZDFYITkWgsL0TkEbizrmebnhyBh2YkAQCe/Gg/Tte2CE5EIrG8EJHinWkxobS+FQAwnDMvHuvJOVdgwqAQNLVZ8Mjavdx914uxvBCR4uWV2WddBoX5wcCddT2WVq3Cq3ePQ6i/DnlljXju88OiI5EgLC9EpHid611GxvCUkacbEOSLFXeMhSQBa7OK8Om+UtGRSACWFyJSvM4rjUYM5CkjbzBjaAQeu2YIAODXHx9AbnG92EDU71heiEjxOk8bcebFe/wifShmpkSi3WLDg+/t6VrzRN6B5YWIFK2pzYyTNfYrT3iZtPdQqyT87a5xSIkORE1zOx54dzea27mBnbdgeSEiRTvcMesSE+SDsAC94DTUnwL0Grxz/0SEB+hxpKIJv3h/H6w2WXQs6gcsL0SkaIc6yssI7u/ilQYG++Kt+1Kh16iw5UgVnt54CLLMAuPpWF6ISNHySnmlkbcbFx+CV3589gqk5zcdYYHxcCwvRKRoXZdJ80ojr3bD6AFY3nEH6je+PYGVW48LTkSuxPJCRIrVarLieFUzAN4WgIA7J8XjdzcMAwC8vPkoVu84KTgRuQrLCxEpVn5FI2wyEB6gR2QgF+sS8OD0JPwyfSgA4I+fH2aB8VAsL0SkWF3rXQYaIEmS4DTkLn4+cwh+epX9Jo5//PwwVnx9lGtgPAzLCxEpFjeno+5IkoSn5qbgiVn2GZgVXx/DHz8/DBsvo/YYLC9EpFhcrEsXI0kSHpuZjGdvHgEAWLPzFJ786ABMFpvgZOQMLC9EpEgmiw0FFU0AgBGceaGLWDglAa/8eAzUKgkf7y3BPW9noba5XXQsukwsL0SkSEcrm2C2yjD4aBAb4is6Drmx28bH4p2FExCo1yD7VB1u/sfOrp2ZSZlYXohIkTp/+IyICeJiXbqkq6+IxIZHpyIx3B+l9a340eu78PmBMtGxqI9YXohIkTrXu/BmjOSoIZEB+PSRqZieHI5WsxVL1u3Drz86AKOJN3RUGpYXIlKkriuNuDkd9UKQnxZr7p+IR64eDEkCPthTjBv/vgOHSnkaSUlYXohIcaw2GfnlnaeNOPNCvaNRq/B/c1Ow7sErEW3wwYmaFvz4rSx8WSyhnVcjKQLLCxEpzulaI4wmK3y0KiRFBIiOQwqVNjgMmx6fjutGRsNslbGpRI2bV+7CrsIa0dHoElheiEhx8jpmXVKiDVCruFiX+i7YT4fXFozH3348GgatjBM1Rtz9VhaW/icXFQ1touPRRbC8EJHiHC637+/CzenIGSRJwvWjorFsrBULJsVBkoBP9pbiqpe24vkvj6DBaBYdkX6A5YWIFOdw+dnLpImcxU8D/OGmYfjk4SmYmBCCdosNq74txPQXv8Fr246jsY0lxl2wvBCRosgykF/eubMuZ17I+cbFh+A/P03D2/dNwNCoADS2WfDipgJMWf4N/vxFPsobWkVH9Hoa0QGIiHrjjAk4YzRDrZIwNCpQdBzyUJIkIX14FK5JicTG3FK8vq0Qx6qa8eb2E1i94ySuHzUAd06Mw5VJYVBx3VW/Y3khIkUpbbH/oEiODICPVi04DXk6tUrCbeNjMW/sQGw7WoU3vj2BrJN1+Gx/GT7bX4b4UD/cMTEON4+JQVyon+i4XoPlhYgUpaSjvHC9C/UnlUrCtSlRuDYlCgdLGrB+dxE+yy1DUZ0RL31VgJe+KsDo2CBcN3IArhsZjYRwf9GRPRrLCxEpSkmL/Z9c70KijIoNwqjYUfjtDcPwxcEKfJxTgqyTtThQ0oADJQ14YdMRJIT5YcbQCExPjkDa4DAE6Pnj1pk4mkSkKGdnXlheSCw/nQa3p8bi9tRY1DS3Y3NeJb48VI7MwlqcqjXiVOZp/DPzNFSSfU+iCQkhSB0UgrFxwYgP9eMNRS9Dv5SXlStX4qWXXkJFRQXGjBmDV199FZMmTbro8z/88EP8/ve/x6lTp5CcnIwXXngB119/fX9EJSI3VtdiQr3J/g1/OMsLuZHwAD3unhyPuyfHo6nNjO9P1GH70WpsP1aN07VGHC5vxOHyRvwz8zQAIFCvwbAYA4YPMGBoVCAGR/hjcGQAwvx1LDUOcHl5+eCDD7B06VKsWrUKkydPxooVKzBnzhwUFBQgMjLygufv2rULd911F5YvX44bb7wR69atw7x587B3716MHDnS1XGJyI11bk43KNQPgT5awWmIuhfoo8Ws4VGYNTwKAFDR0Iac02ew53Qdck6fwZHyJjS1W5B9sg7ZJ+vOe22QrxZxob6IC/FDXKgfYoJ8EB3kgyiD/Z/hAXpo1dzlxOXl5ZVXXsHixYuxaNEiAMCqVavwv//9D6tXr8ZTTz11wfP/9re/Ye7cuXjyyScBAM899xwyMjLwj3/8A6tWrXJ1XCJyY52b0w0fwEukSTmig3xww+gBuGH0AACA2WrD8apm5JU1Ir+8EYXVzThe1YzS+lY0tJrRUGru8S7XQb5ahPnrEBagQ5CvDsF+WgT52r8C9BoE+GgQqNfAX6+Bn04NX50afjoNfLVq+GhV0GvU0GtUir7E26XlxWQyIScnB8uWLet6TKVSIT09HZmZmd2+JjMzE0uXLj3vsTlz5uDTTz/t9vnt7e1ob2/v+nVjo/1/uNlshtnsvN0Qy+pb8VVeBY5WSKj7/hT0Wg1UkgSNSoK640ujUkGrkaBVq6BRSdCpVdBpVNCqJeg0Zz8wnR8eT74nS+fYO/P/gafiWDkur7QBAHBFlD/H6xL4ueqd/h6vIeG+GBLui1tGR3U91mqyoqjOiJIzrSipb0XJmVaUNbShqqkdlY3tqG5qh8Um2wtOqxknalouK4NWffbnlE6tgkbd8XNMLUHT8XNMrZKgVUtQSfZ/V0kSJMjwa1NhlpPHqjdj79LyUlNTA6vViqioqPMej4qKwpEjR7p9TUVFRbfPr6io6Pb5y5cvx7PPPnvB45s3b4afn/Ouuc+vl7AqXw1AjY9OHnXKMTWSDJ0a0KkAvRrwUQM+arnjn/atqv00Mvw0gL8WCNAAgVoZAVr77ymh+2RkZIiOoBgcq0vbU6gGIKGt7Bi++MI5fw49HT9XveMu4xXR8TUuCEDHrgA2GTBagGaz/avJIsFoQceXhFYL0Gbt/JLQbgVMNsDU+U8bYJPP/uAwW2WYrVa0mKy9zjcs2PljZTQaHX6u4q82WrZs2XkzNY2NjYiLi8Ps2bNhMDhvQV9CeSNOSSdQVlGB8IhIyABsNsBik2G12WCxyfYvqwyz1dbxobDBZLXZ/2mR0W6xwmyVu45pkSVYLMD5/7scayRatYTIQD0iA/WINvhgYIgvYkN8ERfii0GhfhgY7AONwPOiZrMZGRkZmDVrFrRark3oCcfKMS3tFjye+Q0A4O7rZ2BACPfR6Ak/V73jLeNlsdrQbrGhzWKDyWL/GWXq+Hf7zzD7P01WG2ydP9NsMmw2GVbZ/k+TxYLio3lOH6vOMyeOcGl5CQ8Ph1qtRmVl5XmPV1ZWIjo6utvXREdH9+r5er0eer3+gse1Wq1TB3VMfBhevcuAL774AtdfP77Px7ba7CWmzWyD0WRBq8kKo8mKFpMFLe1WNLeb0dxmQWObxT41aDSjvtWEMy1m1LS026+2MJphtsoorW9DaX0bgIYL3kenViEh3A+DIwIwNCoQI2IMGB5jwMBg335dye7s/w+ejGPVs+OlTZABBGllDAjx51g5iJ+r3vH08dJqAd/LPIbZbMYXVYecPla9OZZLy4tOp0Nqaiq2bNmCefPmAQBsNhu2bNmCJUuWdPuatLQ0bNmyBY8//njXYxkZGUhLS3Nl1H6jVknw02ngpwNC/XV9OobJYkN1czsqGtpQ2diGso5zoyVnjCiua8Xpuha0mW04WtmMo5XN+PLQ2VNuwX5ajIkNxsSEEKQOCsXYuGD46rjFOrm/vDL738oG+suXeCYReTqXnzZaunQpFi5ciAkTJmDSpElYsWIFWlpauq4+uu+++zBw4EAsX74cAPCLX/wCV111Ff7yl7/ghhtuwPr167Fnzx68+eabro6qGDqNCgODfTEwuPv+bLPJKK1v7VrBnl/ehMPljThW2YR6oxnfHq3Gt0erAdhPP42PD8GMoRGYkRyBETEGRa9AJ891qGOxbizPFhF5PZeXlzvuuAPV1dV4+umnUVFRgbFjx2LTpk1di3KLioqgUp1dmzFlyhSsW7cOv/vd7/Cb3/wGycnJ+PTTT7nHSy+oVBLiQu17BFx9xdm9dNotVhRUNHXsN3AGOafOoKKxDVkn65B1sg4vfVWA8AAdZo+Ixg2jBmByYqjQdTNE5+qceYnlzAuR1+uXBbtLliy56Gmibdu2XfDY/PnzMX/+fBen8j56jRqjY4MxOjYYi6YmQpZlFNUZsf1YDbYfrUZmYS1qmk1Yl1WEdVlFCPHTdtz2PR4jBxq46yMJY7LYcKzKvkEdywsRKf5qI+o7SZIwKMwf94b5494rB8FkseH7E7X48lA5vsqrRF2LCWuzirA2qwjDBhhw58Q43Dp+IAzc2ZT62dHKJpitMoJ8NQjVW0THISLBWF6oi06jsq99GRqB526xIfNELT7cU4JNhyqQX96IZz7Lw0tfFeDuyfFYNDUBA4Iud806kWPyyuzrXYZFB0KS2gSnISLRWF6oWxq1CtOT7bdzrzea8Om+Uvw7qwjHq5rx5vYTWL3jJG4eG4OfX5uMhHCuoCTX6lzvMiLGANiqBachItG4GpMuKdhPh/unJmLz4zOw+v4JmJwYCotNxid7S5H+yrf4/aeHUNXEvw2T63SWl2EDeCdpImJ5oV5QqSRcmxKFD36ahk8fnYqrr4iAxSbjX9+fxlUvbsMrmwvQ2odtpol6YrXJyOcNGYnoHCwv1Cdj44Lx7qJJeH/xlRgTF4xWsxV//+Y4Zq/4FlsLqkTHIw9yqrYFRpMVPloVkniKkojA8kKXKW1wGD59ZApeWzAeMUE+KK5rxaI1u/Hz9fvRYBKdjjxB5+Z0wwYYPPpO7ETkOJYXumySJOH6UQOQsfQqPDgtESoJ+DKvEs/nqrEpr/LSByDqweFzF+sSEYHlhZzIX6/B724cjs+WTMPIGAOMVgmPrd+PZZ8cgNHEvTmob85eaRQkOAkRuQuWF3K6kQOD8MHiSUiPsUGSgPezi3Hjqzu69uogcpQsy12fG868EFEnlhdyCZ1GhZsG2fDP+ycg2uCDE9UtuP31TPzvQLnoaKQgZQ1tOGM0Q62SMDSKVxoRkR3LC7nUlUmh+PIX0zFjaARazVY8um4vXsk4CpuN96ehS8vrWKybHBkAH61acBoichcsL+RyIf46rF44AQ9OSwQA/H3LMTy8NofrYOiSuN6FiLrD8kL9QqNW4Xc3DseLt4+GTq3CV3mVWPB2FhqMZtHRyI3l8UojIuoGywv1qx9PiMO6xZNh8NFgX1E97ngzk7cWoIvqXKw7KpYzL0R0FssL9bsJCaH4z8/SEBGox5GKJvx4VSaK64yiY5GbqWluR3lDGySJ9zQiovOxvJAQKdEGfPjTNMSG+OJUrRHzV2XidG2L6FjkRjpPGSWG+yNArxGchojcCcsLCZMQ7o+PfjYFQyIDUNHYhrvfykJ5Q6voWOQmOm8LMJKLdYnoB1heSKjoIB+sWzwZCWF+KK1vxYK3s1DT3C46FrmBzvUuIwfylBERnY/lhYSLDPTBvx+cjJgg+2Z2976TzauQCIdK7aeNOPNCRD/E8kJuITbED2sXX4nwAD3yyxux6N1stJmtomORIA1GM4o6FnFzjxci+iGWF3IbieH++PeDkxDkq8Xeonr86sP9kGXuxOuN8srtp4ziQn0R5KcVnIaI3A3LC7mVlGgDXr9nPDQqCZ8fKMeKr4+JjkQC5PGUERH1gOWF3M6UweH4060jAQB/23IMG3NLBSei/naId5Imoh6wvJBbumNiPH46IwkA8ORHB5Bz+ozgRNSfOi+THjGQMy9EdCGWF3Jb/zc3BbOGR8FkseHhf+fwEmov0dJuwYka+4aFPG1ERN1heSG3pVZJWHHHWCRHBqCqqR2/WL8PVhsX8Hq6/PJGyDIQZdAjIlAvOg4RuSGWF3Jr/noNXlswHr5aNXYer8Xft3ABr6fjzrpEdCksL+T2kqMC8efb7At4//7NMWw/Wi04EbnSoY57GnG9CxFdDMsLKcKt42Jx16R4yDLw+Ae5qGhoEx2JXOTszAuvNCKi7rG8kGI8c9NwDB9gQF2LCU98mAsb1794nDazFceqmgEAIznzQkQXwfJCiuGjVeMfd4+Dj1aFncdr8a/vT4uORE5WUNEEq01GqL8OA4J8RMchIjfF8kKKkhQRgN9cPwwAsPzLfBRWNwtORM50sPTs5nSSJAlOQ0TuiuWFFOeeyYMwPTkcbWYblv5nPyxWm+hI5CQHS+zlZXQsTxkR0cWxvJDiqFQSXrx9NAJ9NNhfXI/XthWKjkRO0jnzMorrXYioBywvpEgDgnzx3C0dl09vOYa8jnvhkHK1ma04WtkEABgVGyw2DBG5NZYXUqxbxsZg7ohoWGwyfvPJQe6+q3BHKppg6VisG8PFukTUA5YXUixJkvDsLSMQqNdgf0kD/pV5SnQkugwHS+oB2E8ZcbEuEfWE5YUULcrgg/+7LgUA8NJXBShvaBWciPqK612IyFEsL6R4CybFY1x8MFpMVvzhszzRcaiPDnRcaTSKVxoR0SWwvJDiqVQSlt82ChqVhK/yKrE5r0J0JOqlc3fW5WXSRHQpLC/kEVKiDVg8IwkA8MxneTCaLIITUW8cLm+E1SYjPECHaAMX6xJRz1heyGP8YmYyYkN8Ud7QhlXc+0VRDp2z3oWLdYnoUlheyGP4aNX43Q32Wwe8sf0EiuuMghORo7rWu3CxLhE5gOWFPMqcEdFISwpDu8WG5V/mi45DDuqaeeHmdETkAJYX8iiSJOHpm4ZDJQFfHKxAZmGt6Eh0Ca2mc3bW5cwLETmA5YU8zrABBiyYPAgA8Ox/87jzrps7XN4ImwxEBOoRZdCLjkNECsDyQh5p6ayhCPLV4khFE97PLhIdh3rAnXWJqLdYXsgjhfjr8Mv0ZADAXzOOormdl067q4OljQB4yoiIHMfyQh5rwZWDkBjuj9oWE97+7oToOHQRB0vrAbC8EJHjWF7IY2nVKvxq9hUAgLe2n0BNc7vgRPRDRpMFxzt21uVtAYjIUSwv5NGuHxWNMbFBaDFZ8Y9vjouOQz+QV2ZfrBtl0COKO+sSkYNYXsijSZKEX8+133V6bdZpnK5tEZyIzrW/uB4AMDYuWGgOIlIWlhfyeFOGhGPG0AiYrTL+svmo6Dh0jtyO8jKG5YWIeoHlhbzC/82xr335bH9Z126uJN7+jsukx3BnXSLqBZYX8gojBwbhlrExAIBXMjj74g5qm9tRXNcKgIt1iah3WF7IazyePhRqlYRvjlR1na4gcTpvxjg4wh8GH63gNESkJCwv5DUSw/0xb+xAAMCKrzn7IhrXuxBRX7G8kFf5+cwhUKskbCuoxt6iM6LjeLXO9S680oiIeovlhbzKoDB/3DbOPvvyV659EUaW5a7LpLlYl4h6i+WFvM5j1yZDo5Lw3bEa5JyuEx3HKxXXteKM0QydWoWUAYGi4xCRwrC8kNeJD/PD7amxAIC/ZhwTnMY75XacMhoWY4BeoxYbhogUh+WFvNKj1wyBRiVhx/Ea7DnF2Zf+1rWzLi+RJqI+YHkhrxQXenb2ZeVW3vOov+3nlUZEdBlYXshr/eyqwVBJwNaCau6624/MVhsOldnHm+WFiPqC5YW8VkK4P24cbd919/VthYLTeI+jlU1oM9sQ6KNBYpi/6DhEpEAsL+TVHrlmMADgi0PlKKxuFpzGO+wv7ph1iQ2GSiUJTkNESsTyQl4tJdqA9GFRkGVgFWdf+sXZ9S5crEtEfeOy8lJXV4cFCxbAYDAgODgYDzzwAJqbL/4327q6Ojz22GO44oor4Ovri/j4ePz85z9HQwPXIpBrPdox+7JhXylK61sFp/F8nTvrjubmdETURy4rLwsWLEBeXh4yMjLw+eefY/v27XjooYcu+vyysjKUlZXh5ZdfxqFDh/Duu+9i06ZNeOCBB1wVkQgAMC4+BFOHhMFik/Hmt5x9caWmNjMKKpsAAOPig8WGISLF0rjioPn5+di0aRN2796NCRMmAABeffVVXH/99Xj55ZcRExNzwWtGjhyJjz/+uOvXgwcPxp/+9Cfcc889sFgs0GhcEpUIAPDo1UOw83gt1u8uxmMzkxEeoBcdySPlFtdDloG4UF9EBvqIjkNECuWSRpCZmYng4OCu4gIA6enpUKlUyMrKwq233urQcRoaGmAwGHosLu3t7Whvb+/6dWNjIwDAbDbDbDb38b+ge53Hc/ZxPZHSxmpCvAGjBxpwoLQR7+44gV/MHNJv7620sbocu0/WArBvTteX/15vGqvLxbHqHY6X41w1Vr05nkvKS0VFBSIjI89/I40GoaGhqKiocOgYNTU1eO6553o81QQAy5cvx7PPPnvB45s3b4afn5/joXshIyPDJcf1REoaq/H+Eg5AjTU7CjHIeBS6ft61Xklj1VebD6sAqKBvKsUXX5T0+TjeMFbOwrHqHY6X45w9Vkaj0eHn9qq8PPXUU3jhhRd6fE5+fn5vDtmtxsZG3HDDDRg+fDj+8Ic/9PjcZcuWYenSpee9Ni4uDrNnz4bBYLjsLOcym83IyMjArFmzoNVqnXpsT6PEsZpjk7FlxQ4Un2lFc+RI3DM5vl/eV4lj1Rc2m4zf7dsKwIJ75k7FiJje//n0lrFyBo5V73C8HOeqseo8c+KIXpWXJ554Avfff3+Pz0lKSkJ0dDSqqqrOe9xisaCurg7R0dE9vr6pqQlz585FYGAgNmzYcMmB0ev10OsvXJ+g1Wpd9gF05bE9jZLGSgtg8YwkPL0xD2t2FeHetERo1P23m4CSxqovjlY2oanNAl+tGiNjQy5rbD19rJyJY9U7HC/HOXusenOsXpWXiIgIREREXPJ5aWlpqK+vR05ODlJTUwEA33zzDWw2GyZPnnzR1zU2NmLOnDnQ6/X47LPP4OPDBX3Uv+anxuGvGUdRVGfEpryKrh146fLtPX0GgH1/l/4shUTkeVzyHWTYsGGYO3cuFi9ejOzsbOzcuRNLlizBnXfe2XWlUWlpKVJSUpCdnQ3AXlxmz56NlpYWvPPOO2hsbERFRQUqKipgtVpdEZPoAr46Ne5NSwAAvLn9BGRZFhvIg+R0lJfUQSGCkxCR0rnsrz9r165FSkoKZs6cieuvvx7Tpk3Dm2++2fX7ZrMZBQUFXQt09u7di6ysLBw8eBBDhgzBgAEDur6Ki4tdFZPoAgvTBkGvUeFASQO+P1EnOo7H2FvE8kJEzuGyzVNCQ0Oxbt26i/5+QkLCeX+rvfrqq/m3XHILYQF63J4ai7VZRXhzeyHSBoeJjqR49UYTCqtbAADj4lheiOjy8MQzUTcenJ4ESQK2FlTjeBVv2Hi59hXVAwCSIvwR4q8TG4aIFI/lhagbieH+mJkSBQBYs/Ok4DTK17neZXw8Z12I6PKxvBBdxAPTEgEAH+8twZkWk+A0ysb1LkTkTCwvRBdxZVIohg8woM1sw7rsItFxFMtitSG3uB4AZ16IyDlYXoguQpKkrtmX93adgsliE5xImQoqm2A0WRGo1yA5MkB0HCLyACwvRD24aUwMIgP1qGpqx/8OlomOo0idm9ONjQ+GSiUJTkNEnoDlhagHOo0K96UNAgC8s+MkL+fvgz1crEtETsbyQnQJd0+2b1p3qLQRWSe5aV1vyLKMrI6N/iYnhgpOQ0SeguWF6BJC/XX4UWosAGD1Dl423RvFda2oaGyDVi1hHGdeiMhJWF6IHLBoSgIAICO/EsV1RrFhFCTrZC0AYHRsMHx1asFpiMhTsLwQOSA5KhDTk8Mhy/Yrj8gx2R2n2SbxlBERORHLC5GDFk1NAAB8sKcYLe0WsWEUonONENe7EJEzsbwQOejqoZFIDPdHU5sFn+wtER3H7ZU3tKKozgiVxJ11ici5WF6IHKRSSVjYcdn0ml2nYLPxsumedJ4yGjkwCIE+WsFpiMiTsLwQ9cLtE+IQqNfgRHULth+rFh3HrXWeMpqUwFNGRORcLC9EvRCg12D+hDgAwJqdp8SGcXNZJ+xXGnGxLhE5G8sLUS/dPyUBkgR8e7QahdXNouO4pZrmdhRWtwBgeSEi52N5Ieql+DA/zEyJAgD8k5dNd6tzvUtKdCCC/XSC0xCRp2F5IeqDn3RcNv1RTgka28xiw7ihbF4iTUQuxPJC1Adpg8MwNCoALSYrPtzDy6Z/6Puu9S5hgpMQkSdieSHqA0mScP+URAD2HXetvGy6S73RhILKJgDAxETu70JEzsfyQtRH88bFIMhXi6I6I7YVVImO4zZ2nzoDWQaSIvwRGegjOg4ReSCWF6I+8tNpcOdE+2XT73Lhbpedx2sAAFcm8ZQREbkGywvRZbjnykFQScB3x2pwrONUibf7rmPzvhnJ4YKTEJGnYnkhugxxoX6YNdx+2fR7mafEhnEDZfWtKKxugUoC0gazvBCRa7C8EF2mzoW7H+eUosHo3ZdN7zhmP2U0OjYYQb68nxERuQbLC9FlujIpFCnRgWg1W/HBniLRcYT6rmO9y3SeMiIiF2J5IbpMkiRhUcemde/tOg2L1SY2kCA2m9y1WHd6coTgNETkyVheiJzglrEDEeKnRWl9K77OrxQdR4jD5Y2oazHBX6fGuPhg0XGIyIOxvBA5gY9WjbsnxwMAVnvp3aa/O3b2Emmtmt9aiMh1+B2GyEnuvTIBGpWE7JN1yCtrEB2n3+04br9EehrXuxCRi7G8EDlJdJAPrhs1AACwxstmX9rMVuw+dQYAF+sSkeuxvBA5UefC3c9yy1DT3C42TD/KPlkHk8WGAUE+GBwRIDoOEXk4lhciJxofH4IxccEwWW14P8t7Lpvu3FV32pBwSJIkOA0ReTqWFyIn+0nH7Ms/vz+NdotVbJh+0rlYl+tdiKg/sLwQOdl1IwcgyqBHdVM7Pt9fLjqOy1U1teFIhf2+TlOHsLwQkeuxvBA5mU6jwsIpCQCAt3echCzLYgO52Jb8KgDA6NgghAfoBachIm/A8kLkAndPioevVo388kZkFtaKjuNSGYftm/LNGhYlOAkReQuWFyIXCPbTYf6EWADAOztOCk7jOkaTBTs6bgkwawTLCxH1D5YXIhdZNDURkgRsOVKFwupm0XFcYvvRGpgsNsSF+uKKqEDRcYjIS7C8ELlIYrg/ZqbYZyNWe+jsy9lTRtG8RJqI+g3LC5ELPTg9EQDw8d4S1LWYBKdxLqtNxjdH7OUlfXik4DRE5E1YXohcaHJiKEYONKDNbMPa70+LjuNUOafP4IzRjCBfLSYlhIqOQ0RehOWFyIUkScLi6UkAgHd3nUKb2XM2rcs4XAEAuDYlEhreRZqI+hG/4xC52A2jBmBgsC9qW0z4MKdEdBynkGX57HqX4bzKiIj6F8sLkYtp1Cos7lj78tb2E7BYbYITXb7C6macqjVCp1ZhxtAI0XGIyMuwvBD1gx9PjEOInxZFdUZ8eahCdJzLtrlj1iVtcBgC9BrBaYjI27C8EPUDP52m65YBq74tVPwtA3jKiIhEYnkh6icL0xLgq1Ujr6yxa1daJSqqNWJfUT0kieWFiMRgeSHqJyH+OtwxMQ6AffZFqTbmlgIApg4OR5TBR3AaIvJGLC9E/ejB6YnQqCTsPF6LAyX1ouP0mizL2NBRXuaNGyg4DRF5K5YXon4UG+KHm8fGAAD+vuW44DS9d7C0ASeqW+CjVWHuyGjRcYjIS7G8EPWzJdcMgUoCvs6vxKHSBtFxemXDPvusy+zh0bzKiIiEYXkh6mdJEQG4Zaz9lMuKr48JTuM4i9WG/+4vAwDcylNGRCQQywuRAEuuPTv7klfWKDqOQ3Ycr0FNswlh/jpMSw4XHYeIvBjLC5EAgyMCcPMY+9qXf2xVxpVHn3acMrppTAy0vJcREQnE70BEgiy5Ntk++3KkGiUtotP0rKXdgq/y7BvT8SojIhKN5YVIkCGRAbipY/ZlU7F7/1HcfLgCrWYrEsP9MSY2SHQcIvJy7v0dk8jDPXZtMiQJOHhGhf0l7nvl0fvZxQCAeWMHQpIkwWmIyNuxvBAJNCQyAPM69n15flOBW97z6FBpA7JP1kGjknDnpDjRcYiIWF6IRPvlzCHQSjL2nK7vuuGhO1m94yQA4MbRA3g7ACJyCywvRIINCPLBVTH2GZfnNx2B2WoTnOisqsY2/PeAfW+Xn0xLFJyGiMiO5YXIDcyKsSHUX4sT1S1Yv7tYdJwu//7+NMxWGRMGhWB0bLDoOEREAFheiNyCjwZ47JrBAIAVGUfR1GYWnAhoM1vx76wiAJx1ISL3wvJC5CbumBCLpHB/1LaY8Ma3J0THwWe5ZahrMWFgsC9mD48SHYeIqAvLC5Gb0KpV+L+5KQCAN7efQGF1s7Assixj9U77Qt2FUwZBwx11iciN8DsSkRuZMyIKM4ZGwGS14TefHITNJubS6e+O1eBIRRP8dGrcMTFeSAYiootxWXmpq6vDggULYDAYEBwcjAceeADNzY79TVKWZVx33XWQJAmffvqpqyISuR1JkvCneSPhq1Uj62QdPszp/8W7VpuM5788AgC4Y2Icgny1/Z6BiKgnLisvCxYsQF5eHjIyMvD5559j+/bteOihhxx67YoVK7iLJ3mtuFA/PDF7KADgT//LR1VTW7++/8d7S3C4vBGBPho8dm1yv743EZEjXFJe8vPzsWnTJrz99tuYPHkypk2bhldffRXr169HWVlZj6/Nzc3FX/7yF6xevdoV0YgU4f4pCRg1MAiNbRb88b+H++19W9oteOmrAgDAz69NRqi/rt/em4jIURpXHDQzMxPBwcGYMGFC12Pp6elQqVTIysrCrbfe2u3rjEYj7r77bqxcuRLR0dEOvVd7ezva29u7ft3Y2AgAMJvNMJude7lp5/GcfVxPxLFy3MXG6rmbh+FHb2Th8wPluHFUKWamRLo8y2tbj6O6qR3xob64a+JAt/v/x8+V4zhWvcPxcpyrxqo3x3NJeamoqEBk5PnfaDUaDUJDQ1FRUXHR1/3yl7/ElClTcMsttzj8XsuXL8ezzz57weObN2+Gn5+f46F7ISMjwyXH9UQcK8d1N1ZXRavwTZkKT3ywD78abUWo3nXvf6YdeDNXDUBCengztmze5Lo3u0z8XDmOY9U7HC/HOXusjEajw8/tVXl56qmn8MILL/T4nPz8/N4csstnn32Gb775Bvv27evV65YtW4alS5d2/bqxsRFxcXGYPXs2DAZDn7JcjNlsRkZGBmbNmgWtlosYe8KxclxPYzXTbMWdb+/GobJGbKgMxboHJ0Gvcc1StV99dBBmWzkmDArGU/dMdMt1Z/xcOY5j1TscL8e5aqw6z5w4olfl5YknnsD999/f43OSkpIQHR2Nqqqq8x63WCyoq6u76Omgb775BoWFhQgODj7v8R/96EeYPn06tm3b1u3r9Ho99PoL/zqq1Wpd9gF05bE9DcfKcd2NlVarxap7U3HjqztwoLQRf950FH++dZTT3/ubI5XYuL8cAPD0TSOg07n3Whd+rhzHseodjpfjnD1WvTlWr8pLREQEIiIiLvm8tLQ01NfXIycnB6mpqQDs5cRms2Hy5Mndvuapp57Cgw8+eN5jo0aNwl//+lfcdNNNvYlJ5FFiQ/zwtzvH4f412ViXVYTx8SG4PTXWacc/VdOCx9fnAgAWpg3iPYyIyO25ZP552LBhmDt3LhYvXozs7Gzs3LkTS5YswZ133omYmBgAQGlpKVJSUpCdnQ0AiI6OxsiRI8/7AoD4+HgkJvK+KuTdrhoagcdn2i+f/u2Gg8g5XeeU4xpNFvzs3zlobLNgfHwwfnvDcKccl4jIlVy2z8vatWuRkpKCmTNn4vrrr8e0adPw5ptvdv2+2WxGQUFBrxboEHmzx64dgmtTItFuseHed7Kx63jNZR1PlmUs++QgjlQ0ITxAj9fvSYXORetpiIicySVXGwFAaGgo1q1bd9HfT0hIgCz3vPX5pX6fyJuoVBJW3j0eD/1rD747VoP7392N1xeMx8xhfbtp4lvfncDG3DJoVBJeWzAeUQYfJycmInIN/jWLSEF8dWq8vXACZg+Pgsliw0//lYP/7u9548cfardY8dsNB/HnL+y3APjtDcMwKTHUFXGJiFyC5YVIYfQaNVYuGI9bxsbAYpPx2Pv78OjavSiuu/Qp2OI6I+avysTarCJIEvB4ejLun5Lg+tBERE7kstNGROQ6WrUKr/x4LCID9Xhnx0n872A5MvIrsXh6Ih6cloSQc7b1l2UZx6qasSW/Cm9sL0S90YxgPy1W3DEWV1/h+l17iYicjeWFSKHUKgm/vWE4bhsfi+c+P4xdhbVYubUQK7cWIjxAh6SIAMQE+WDP6TMoOdPa9brRsUF4bcF4xIa4ZgdqIiJXY3khUrhhAwxY++BkbD5cib9sLsDRymbUNJtQ03z2cmqdRoW0pDCkD4/CjyfEQq9RC0xMRHR5WF6IPIAkSZgzIhpzRkSjud2Ck9UtKKxuRskZI1KiDZgyJAx+Ov5xJyLPwO9mRB4mQK/BqNggjIoNEh2FiMgleLURERERKQrLCxERESkKywsREREpCssLERERKQrLCxERESkKywsREREpCssLERERKQrLCxERESkKywsREREpCssLERERKQrLCxERESkKywsREREpCssLERERKYrH3VValmUAQGNjo9OPbTabYTQa0djYCK1W6/TjexKOleM4Vo7jWDmOY9U7HC/HuWqsOn9ud/4c74nHlZempiYAQFxcnOAkRERE1FtNTU0ICgrq8TmS7EjFURCbzYaysjIEBgZCkiSnHruxsRFxcXEoLi6GwWBw6rE9DcfKcRwrx3GsHMex6h2Ol+NcNVayLKOpqQkxMTFQqXpe1eJxMy8qlQqxsbEufQ+DwcAPt4M4Vo7jWDmOY+U4jlXvcLwc54qxutSMSycu2CUiIiJFYXkhIiIiRWF56QW9Xo9nnnkGer1edBS3x7FyHMfKcRwrx3Gseofj5Th3GCuPW7BLREREno0zL0RERKQoLC9ERESkKCwvREREpCgsL0RERKQoLC99dPPNNyM+Ph4+Pj4YMGAA7r33XpSVlYmO5XZOnTqFBx54AImJifD19cXgwYPxzDPPwGQyiY7mlv70pz9hypQp8PPzQ3BwsOg4bmflypVISEiAj48PJk+ejOzsbNGR3M727dtx0003ISYmBpIk4dNPPxUdyW0tX74cEydORGBgICIjIzFv3jwUFBSIjuWWXn/9dYwePbprY7q0tDR8+eWXwvKwvPTRNddcg//85z8oKCjAxx9/jMLCQtx+++2iY7mdI0eOwGaz4Y033kBeXh7++te/YtWqVfjNb34jOppbMplMmD9/Ph5++GHRUdzOBx98gKVLl+KZZ57B3r17MWbMGMyZMwdVVVWio7mVlpYWjBkzBitXrhQdxe19++23ePTRR/H9998jIyMDZrMZs2fPRktLi+hobic2NhbPP/88cnJysGfPHlx77bW45ZZbkJeXJyaQTE6xceNGWZIk2WQyiY7i9l588UU5MTFRdAy3tmbNGjkoKEh0DLcyadIk+dFHH+36tdVqlWNiYuTly5cLTOXeAMgbNmwQHUMxqqqqZADyt99+KzqKIoSEhMhvv/22kPfmzIsT1NXVYe3atZgyZQpvpe6AhoYGhIaGio5BCmIymZCTk4P09PSux1QqFdLT05GZmSkwGXmShoYGAOD3p0uwWq1Yv349WlpakJaWJiQDy8tl+PWvfw1/f3+EhYWhqKgIGzduFB3J7R0/fhyvvvoqfvrTn4qOQgpSU1MDq9WKqKio8x6PiopCRUWFoFTkSWw2Gx5//HFMnToVI0eOFB3HLR08eBABAQHQ6/X42c9+hg0bNmD48OFCsrC8nOOpp56CJEk9fh05cqTr+U8++ST27duHzZs3Q61W47777oPsJRsW93asAKC0tBRz587F/PnzsXjxYkHJ+19fxoqI+tejjz6KQ4cOYf369aKjuK0rrrgCubm5yMrKwsMPP4yFCxfi8OHDQrLw9gDnqK6uRm1tbY/PSUpKgk6nu+DxkpISxMXFYdeuXcKm0fpTb8eqrKwMV199Na688kq8++67UKm8pzf35XP17rvv4vHHH0d9fb2L0ymDyWSCn58fPvroI8ybN6/r8YULF6K+vp6znhchSRI2bNhw3pjRhZYsWYKNGzdi+/btSExMFB1HMdLT0zF48GC88cYb/f7emn5/RzcWERGBiIiIPr3WZrMBANrb250ZyW31ZqxKS0txzTXXIDU1FWvWrPGq4gJc3ueK7HQ6HVJTU7Fly5auH8Q2mw1btmzBkiVLxIYjxZJlGY899hg2bNiAbdu2sbj0ks1mE/Yzj+WlD7KysrB7925MmzYNISEhKCwsxO9//3sMHjzYK2ZdeqO0tBRXX301Bg0ahJdffhnV1dVdvxcdHS0wmXsqKipCXV0dioqKYLVakZubCwAYMmQIAgICxIYTbOnSpVi4cCEmTJiASZMmYcWKFWhpacGiRYtER3Mrzc3NOH78eNevT548idzcXISGhiI+Pl5gMvfz6KOPYt26ddi4cSMCAwO71k8FBQXB19dXcDr3smzZMlx33XWIj49HU1MT1q1bh23btuGrr74SE0jINU4Kd+DAAfmaa66RQ0NDZb1eLyckJMg/+9nP5JKSEtHR3M6aNWtkAN1+0YUWLlzY7Vht3bpVdDS38Oqrr8rx8fGyTqeTJ02aJH///feiI7mdrVu3dvsZWrhwoehobudi35vWrFkjOprb+clPfiIPGjRI1ul0ckREhDxz5kx58+bNwvJwzQsREREpinctPiAiIiLFY3khIiIiRWF5ISIiIkVheSEiIiJFYXkhIiIiRWF5ISIiIkVheSEiIiJFYXkhIiIiRWF5ISIiIkVheSEiIiJFYXkhIiIiRWF5ISIiIkX5/+JOAL5tLRP+AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z2=z[60,60,:]\n",
    "plt.plot(z2,z2*np.exp(-z2**2))\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z2=z[60,60,:]\n",
    "plt.plot(z2,np.exp(-(z2-0.3)**2),c='green')\n",
    "plt.plot(z2,-np.exp(-(z2+0.3)**2),c='red')\n",
    "# plt.plot(z2,(np.exp(-(z2-0.3)**2)-np.exp(-(z2+0.3)**2)))\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(z[60,60,:],phi_H1s_sto6g[60,60,:])\n",
    "plt.grid()"
   ]
  }
 ],
 "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": "3.10.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}