CODE_3_MP2PES_2D.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "409700c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bbff1cb6",
   "metadata": {},
   "source": [
    "#### Import V_lambdas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "da2293b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_Vn = pd.read_csv('2D_Vlam.dat',sep=',')  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5dcac62a",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "      <th>0</th>\n",
       "      <th>2</th>\n",
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       "      <th>6</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1256.895511</td>\n",
       "      <td>1025.120059</td>\n",
       "      <td>109.648713</td>\n",
       "      <td>136.071870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>887.264354</td>\n",
       "      <td>793.555514</td>\n",
       "      <td>102.553127</td>\n",
       "      <td>58.351987</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>611.061814</td>\n",
       "      <td>581.225705</td>\n",
       "      <td>78.972119</td>\n",
       "      <td>25.401750</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>411.099894</td>\n",
       "      <td>411.871091</td>\n",
       "      <td>57.091952</td>\n",
       "      <td>10.889040</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>269.369246</td>\n",
       "      <td>284.128951</td>\n",
       "      <td>39.542237</td>\n",
       "      <td>4.470996</td>\n",
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       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>-0.005858</td>\n",
       "      <td>-0.003273</td>\n",
       "      <td>0.000129</td>\n",
       "      <td>0.000010</td>\n",
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       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>-0.005047</td>\n",
       "      <td>-0.001974</td>\n",
       "      <td>-0.000416</td>\n",
       "      <td>0.001024</td>\n",
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       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>-0.003658</td>\n",
       "      <td>-0.003119</td>\n",
       "      <td>0.000211</td>\n",
       "      <td>-0.000308</td>\n",
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       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>-0.002881</td>\n",
       "      <td>-0.002007</td>\n",
       "      <td>-0.000323</td>\n",
       "      <td>0.001012</td>\n",
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       "      <th>99</th>\n",
       "      <td>-0.001723</td>\n",
       "      <td>-0.002852</td>\n",
       "      <td>0.000546</td>\n",
       "      <td>-0.000797</td>\n",
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       "<p>100 rows × 4 columns</p>\n",
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      ],
      "text/plain": [
       "              0            2           4           6\n",
       "0   1256.895511  1025.120059  109.648713  136.071870\n",
       "1    887.264354   793.555514  102.553127   58.351987\n",
       "2    611.061814   581.225705   78.972119   25.401750\n",
       "3    411.099894   411.871091   57.091952   10.889040\n",
       "4    269.369246   284.128951   39.542237    4.470996\n",
       "..          ...          ...         ...         ...\n",
       "95    -0.005858    -0.003273    0.000129    0.000010\n",
       "96    -0.005047    -0.001974   -0.000416    0.001024\n",
       "97    -0.003658    -0.003119    0.000211   -0.000308\n",
       "98    -0.002881    -0.002007   -0.000323    0.001012\n",
       "99    -0.001723    -0.002852    0.000546   -0.000797\n",
       "\n",
       "[100 rows x 4 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_Vn"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe67c663",
   "metadata": {},
   "source": [
    "#### Declare important variables and import Legendre Coeff numpy file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "32cb9455",
   "metadata": {},
   "outputs": [],
   "source": [
    "lm=4                        # Radial terms\n",
    "nc=100                      # number of Radial coordinates (Must be same for all angles)\n",
    "ngm = 91                    # number of angular coordinates (91 for symmetric molecule, 181 for non-symm.)\n",
    "E_inf = -78.70465827  \n",
    "px = np.zeros((ngm,lm))     # Matrix to stores legendre coeffinients\n",
    "\n",
    "V_nf= np.zeros((nc,lm))     # Numpy 2D array to store generated potentials\n",
    "V_nf2= np.zeros((ngm,nc))   # Numpy 2D array to store ab_initio potentials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3da4bebd",
   "metadata": {},
   "outputs": [],
   "source": [
    "px = np.load(\"2D_L_coeff.npy\")\n",
    "V_n1 = px.dot(df_Vn.T)                 # save regenerated potentials"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5237ec37",
   "metadata": {},
   "source": [
    "#### convert regenerated potentials into dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ef8a80ff",
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
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       "      <th>81</th>\n",
       "      <th>82</th>\n",
       "      <th>83</th>\n",
       "      <th>84</th>\n",
       "      <th>85</th>\n",
       "      <th>86</th>\n",
       "      <th>87</th>\n",
       "      <th>88</th>\n",
       "      <th>89</th>\n",
       "      <th>90</th>\n",
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       "      <th>0</th>\n",
       "      <td>2527.736153</td>\n",
       "      <td>2526.665972</td>\n",
       "      <td>2523.460840</td>\n",
       "      <td>2518.136942</td>\n",
       "      <td>2510.721097</td>\n",
       "      <td>2501.250533</td>\n",
       "      <td>2489.772559</td>\n",
       "      <td>2476.344169</td>\n",
       "      <td>2461.031549</td>\n",
       "      <td>2443.909520</td>\n",
       "      <td>...</td>\n",
       "      <td>791.062978</td>\n",
       "      <td>781.235906</td>\n",
       "      <td>772.446043</td>\n",
       "      <td>764.736429</td>\n",
       "      <td>758.145390</td>\n",
       "      <td>752.706110</td>\n",
       "      <td>748.446261</td>\n",
       "      <td>745.387693</td>\n",
       "      <td>743.546188</td>\n",
       "      <td>742.931289</td>\n",
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       "      <th>1</th>\n",
       "      <td>1841.724982</td>\n",
       "      <td>1841.019792</td>\n",
       "      <td>1838.907111</td>\n",
       "      <td>1835.395590</td>\n",
       "      <td>1830.499572</td>\n",
       "      <td>1824.238983</td>\n",
       "      <td>1816.639186</td>\n",
       "      <td>1807.730784</td>\n",
       "      <td>1797.549392</td>\n",
       "      <td>1786.135373</td>\n",
       "      <td>...</td>\n",
       "      <td>539.391495</td>\n",
       "      <td>533.476475</td>\n",
       "      <td>528.211990</td>\n",
       "      <td>523.614447</td>\n",
       "      <td>519.698461</td>\n",
       "      <td>516.476688</td>\n",
       "      <td>513.959684</td>\n",
       "      <td>512.155787</td>\n",
       "      <td>511.071019</td>\n",
       "      <td>510.709024</td>\n",
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       "      <th>2</th>\n",
       "      <td>1296.661388</td>\n",
       "      <td>1296.194417</td>\n",
       "      <td>1294.795126</td>\n",
       "      <td>1292.468364</td>\n",
       "      <td>1289.222179</td>\n",
       "      <td>1285.067762</td>\n",
       "      <td>1280.019373</td>\n",
       "      <td>1274.094250</td>\n",
       "      <td>1267.312488</td>\n",
       "      <td>1259.696915</td>\n",
       "      <td>...</td>\n",
       "      <td>360.205881</td>\n",
       "      <td>356.449631</td>\n",
       "      <td>353.118668</td>\n",
       "      <td>350.219006</td>\n",
       "      <td>347.756002</td>\n",
       "      <td>345.734296</td>\n",
       "      <td>344.157758</td>\n",
       "      <td>343.029445</td>\n",
       "      <td>342.351568</td>\n",
       "      <td>342.125459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>890.951977</td>\n",
       "      <td>890.642077</td>\n",
       "      <td>889.713316</td>\n",
       "      <td>888.168515</td>\n",
       "      <td>886.012351</td>\n",
       "      <td>883.251339</td>\n",
       "      <td>879.893787</td>\n",
       "      <td>875.949752</td>\n",
       "      <td>871.430980</td>\n",
       "      <td>866.350840</td>\n",
       "      <td>...</td>\n",
       "      <td>234.822775</td>\n",
       "      <td>232.389091</td>\n",
       "      <td>230.236636</td>\n",
       "      <td>228.367252</td>\n",
       "      <td>226.782576</td>\n",
       "      <td>225.484028</td>\n",
       "      <td>224.472793</td>\n",
       "      <td>223.749805</td>\n",
       "      <td>223.315740</td>\n",
       "      <td>223.171006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>597.511431</td>\n",
       "      <td>597.307125</td>\n",
       "      <td>596.694766</td>\n",
       "      <td>595.676026</td>\n",
       "      <td>594.253687</td>\n",
       "      <td>592.431620</td>\n",
       "      <td>590.214768</td>\n",
       "      <td>587.609123</td>\n",
       "      <td>584.621695</td>\n",
       "      <td>581.260474</td>\n",
       "      <td>...</td>\n",
       "      <td>148.306724</td>\n",
       "      <td>146.719462</td>\n",
       "      <td>145.318212</td>\n",
       "      <td>144.103237</td>\n",
       "      <td>143.074771</td>\n",
       "      <td>142.233016</td>\n",
       "      <td>141.578139</td>\n",
       "      <td>141.110274</td>\n",
       "      <td>140.829516</td>\n",
       "      <td>140.735924</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>-0.008992</td>\n",
       "      <td>-0.008990</td>\n",
       "      <td>-0.008987</td>\n",
       "      <td>-0.008980</td>\n",
       "      <td>-0.008972</td>\n",
       "      <td>-0.008960</td>\n",
       "      <td>-0.008946</td>\n",
       "      <td>-0.008930</td>\n",
       "      <td>-0.008911</td>\n",
       "      <td>-0.008890</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.004307</td>\n",
       "      <td>-0.004280</td>\n",
       "      <td>-0.004256</td>\n",
       "      <td>-0.004235</td>\n",
       "      <td>-0.004217</td>\n",
       "      <td>-0.004203</td>\n",
       "      <td>-0.004192</td>\n",
       "      <td>-0.004183</td>\n",
       "      <td>-0.004179</td>\n",
       "      <td>-0.004177</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>-0.006414</td>\n",
       "      <td>-0.006416</td>\n",
       "      <td>-0.006421</td>\n",
       "      <td>-0.006429</td>\n",
       "      <td>-0.006441</td>\n",
       "      <td>-0.006456</td>\n",
       "      <td>-0.006474</td>\n",
       "      <td>-0.006494</td>\n",
       "      <td>-0.006516</td>\n",
       "      <td>-0.006540</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.004419</td>\n",
       "      <td>-0.004441</td>\n",
       "      <td>-0.004462</td>\n",
       "      <td>-0.004481</td>\n",
       "      <td>-0.004497</td>\n",
       "      <td>-0.004511</td>\n",
       "      <td>-0.004522</td>\n",
       "      <td>-0.004530</td>\n",
       "      <td>-0.004535</td>\n",
       "      <td>-0.004536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>-0.006873</td>\n",
       "      <td>-0.006871</td>\n",
       "      <td>-0.006865</td>\n",
       "      <td>-0.006854</td>\n",
       "      <td>-0.006840</td>\n",
       "      <td>-0.006821</td>\n",
       "      <td>-0.006799</td>\n",
       "      <td>-0.006773</td>\n",
       "      <td>-0.006743</td>\n",
       "      <td>-0.006709</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.002103</td>\n",
       "      <td>-0.002066</td>\n",
       "      <td>-0.002033</td>\n",
       "      <td>-0.002004</td>\n",
       "      <td>-0.001980</td>\n",
       "      <td>-0.001960</td>\n",
       "      <td>-0.001944</td>\n",
       "      <td>-0.001933</td>\n",
       "      <td>-0.001926</td>\n",
       "      <td>-0.001923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>-0.004199</td>\n",
       "      <td>-0.004201</td>\n",
       "      <td>-0.004206</td>\n",
       "      <td>-0.004215</td>\n",
       "      <td>-0.004228</td>\n",
       "      <td>-0.004243</td>\n",
       "      <td>-0.004262</td>\n",
       "      <td>-0.004283</td>\n",
       "      <td>-0.004307</td>\n",
       "      <td>-0.004333</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.002209</td>\n",
       "      <td>-0.002229</td>\n",
       "      <td>-0.002247</td>\n",
       "      <td>-0.002264</td>\n",
       "      <td>-0.002279</td>\n",
       "      <td>-0.002292</td>\n",
       "      <td>-0.002302</td>\n",
       "      <td>-0.002309</td>\n",
       "      <td>-0.002313</td>\n",
       "      <td>-0.002315</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>-0.004827</td>\n",
       "      <td>-0.004824</td>\n",
       "      <td>-0.004814</td>\n",
       "      <td>-0.004800</td>\n",
       "      <td>-0.004779</td>\n",
       "      <td>-0.004752</td>\n",
       "      <td>-0.004720</td>\n",
       "      <td>-0.004683</td>\n",
       "      <td>-0.004640</td>\n",
       "      <td>-0.004593</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000115</td>\n",
       "      <td>-0.000060</td>\n",
       "      <td>-0.000010</td>\n",
       "      <td>0.000033</td>\n",
       "      <td>0.000071</td>\n",
       "      <td>0.000102</td>\n",
       "      <td>0.000126</td>\n",
       "      <td>0.000143</td>\n",
       "      <td>0.000154</td>\n",
       "      <td>0.000157</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 91 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             0            1            2            3            4   \\\n",
       "0   2527.736153  2526.665972  2523.460840  2518.136942  2510.721097   \n",
       "1   1841.724982  1841.019792  1838.907111  1835.395590  1830.499572   \n",
       "2   1296.661388  1296.194417  1294.795126  1292.468364  1289.222179   \n",
       "3    890.951977   890.642077   889.713316   888.168515   886.012351   \n",
       "4    597.511431   597.307125   596.694766   595.676026   594.253687   \n",
       "..          ...          ...          ...          ...          ...   \n",
       "95    -0.008992    -0.008990    -0.008987    -0.008980    -0.008972   \n",
       "96    -0.006414    -0.006416    -0.006421    -0.006429    -0.006441   \n",
       "97    -0.006873    -0.006871    -0.006865    -0.006854    -0.006840   \n",
       "98    -0.004199    -0.004201    -0.004206    -0.004215    -0.004228   \n",
       "99    -0.004827    -0.004824    -0.004814    -0.004800    -0.004779   \n",
       "\n",
       "             5            6            7            8            9   ...  \\\n",
       "0   2501.250533  2489.772559  2476.344169  2461.031549  2443.909520  ...   \n",
       "1   1824.238983  1816.639186  1807.730784  1797.549392  1786.135373  ...   \n",
       "2   1285.067762  1280.019373  1274.094250  1267.312488  1259.696915  ...   \n",
       "3    883.251339   879.893787   875.949752   871.430980   866.350840  ...   \n",
       "4    592.431620   590.214768   587.609123   584.621695   581.260474  ...   \n",
       "..          ...          ...          ...          ...          ...  ...   \n",
       "95    -0.008960    -0.008946    -0.008930    -0.008911    -0.008890  ...   \n",
       "96    -0.006456    -0.006474    -0.006494    -0.006516    -0.006540  ...   \n",
       "97    -0.006821    -0.006799    -0.006773    -0.006743    -0.006709  ...   \n",
       "98    -0.004243    -0.004262    -0.004283    -0.004307    -0.004333  ...   \n",
       "99    -0.004752    -0.004720    -0.004683    -0.004640    -0.004593  ...   \n",
       "\n",
       "            81          82          83          84          85          86  \\\n",
       "0   791.062978  781.235906  772.446043  764.736429  758.145390  752.706110   \n",
       "1   539.391495  533.476475  528.211990  523.614447  519.698461  516.476688   \n",
       "2   360.205881  356.449631  353.118668  350.219006  347.756002  345.734296   \n",
       "3   234.822775  232.389091  230.236636  228.367252  226.782576  225.484028   \n",
       "4   148.306724  146.719462  145.318212  144.103237  143.074771  142.233016   \n",
       "..         ...         ...         ...         ...         ...         ...   \n",
       "95   -0.004307   -0.004280   -0.004256   -0.004235   -0.004217   -0.004203   \n",
       "96   -0.004419   -0.004441   -0.004462   -0.004481   -0.004497   -0.004511   \n",
       "97   -0.002103   -0.002066   -0.002033   -0.002004   -0.001980   -0.001960   \n",
       "98   -0.002209   -0.002229   -0.002247   -0.002264   -0.002279   -0.002292   \n",
       "99   -0.000115   -0.000060   -0.000010    0.000033    0.000071    0.000102   \n",
       "\n",
       "            87          88          89          90  \n",
       "0   748.446261  745.387693  743.546188  742.931289  \n",
       "1   513.959684  512.155787  511.071019  510.709024  \n",
       "2   344.157758  343.029445  342.351568  342.125459  \n",
       "3   224.472793  223.749805  223.315740  223.171006  \n",
       "4   141.578139  141.110274  140.829516  140.735924  \n",
       "..         ...         ...         ...         ...  \n",
       "95   -0.004192   -0.004183   -0.004179   -0.004177  \n",
       "96   -0.004522   -0.004530   -0.004535   -0.004536  \n",
       "97   -0.001944   -0.001933   -0.001926   -0.001923  \n",
       "98   -0.002302   -0.002309   -0.002313   -0.002315  \n",
       "99    0.000126    0.000143    0.000154    0.000157  \n",
       "\n",
       "[100 rows x 91 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a12 = np.arange(ngm)            # creates header for angles\n",
    "df_Vnf = pd.DataFrame(V_n1.T, columns = a12) # saves final matrix into dataframe with appropriate header\n",
    "df_Vnf                     # prints regenerated potentials "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10386db3",
   "metadata": {},
   "source": [
    "#### import ab initio potentials --> convert into dataframe --> find error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "98a1deaa",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_inp2 = pd.read_csv('2D_PES.dat',header=None,sep='\\s+')       # importing ab initio data\n",
    "df_inp2[2] = (df_inp2[2] - E_inf)*219474.63                     # convert to cm-1\n",
    "df_inp2.sort_values(by = [ 0,1], inplace=True, ascending = True)    # sort by (R, theta) in ascending order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "bdcd70e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(91, 100)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.shape(V_nf2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "de71b097",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.64515653e+03,  1.87800051e+03,  1.30946685e+03, ...,\n",
       "        -6.58424100e-03, -4.38949296e-03, -4.38949296e-03],\n",
       "       [ 2.64081312e+03,  1.87650370e+03,  1.30866577e+03, ...,\n",
       "        -6.58424100e-03, -4.38949296e-03, -4.38949296e-03],\n",
       "       [ 2.63150959e+03,  1.87204178e+03,  1.30672780e+03, ...,\n",
       "        -6.58424100e-03, -4.38949296e-03, -4.38949296e-03],\n",
       "       ...,\n",
       "       [ 7.75006619e+02,  5.23657688e+02,  3.47722435e+02, ...,\n",
       "        -2.19474804e-03, -2.19474804e-03,  0.00000000e+00],\n",
       "       [ 7.73880714e+02,  5.22854411e+02,  3.47160580e+02, ...,\n",
       "        -2.19474804e-03, -2.19474804e-03,  0.00000000e+00],\n",
       "       [ 7.73511996e+02,  5.22623963e+02,  3.46956469e+02, ...,\n",
       "        -2.19474804e-03, -2.19474804e-03,  0.00000000e+00]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for i in range (nc):            # loop over all R   \n",
    "    ct = i*ngm                  # extract start point. Since input dataframe is sorted by R and theta, \n",
    "    f = df_inp2[2][ct:ct+ngm]   # potentials (V) are extracting for each R value at a time \n",
    "    V_nf2[:,i] = f           # ab initio data stored in 2D matrix one by one\n",
    "V_nf2                        # visualizing numoy file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "fe8b742a",
   "metadata": {},
   "outputs": [
    {
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       "      <td>791.917139</td>\n",
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       "      <td>782.894537</td>\n",
       "      <td>779.514628</td>\n",
       "      <td>776.885322</td>\n",
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       "      <td>1878.000514</td>\n",
       "      <td>1876.503697</td>\n",
       "      <td>1872.041778</td>\n",
       "      <td>1866.140105</td>\n",
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       "      <td>1819.857295</td>\n",
       "      <td>1803.754441</td>\n",
       "      <td>1786.699068</td>\n",
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       "      <td>539.703478</td>\n",
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       "      <td>529.282823</td>\n",
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       "      <td>524.996483</td>\n",
       "      <td>523.657688</td>\n",
       "      <td>522.854411</td>\n",
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       "      <th>2</th>\n",
       "      <td>1309.466848</td>\n",
       "      <td>1308.665766</td>\n",
       "      <td>1306.727805</td>\n",
       "      <td>1303.448854</td>\n",
       "      <td>1298.984740</td>\n",
       "      <td>1293.245478</td>\n",
       "      <td>1286.426402</td>\n",
       "      <td>1278.681142</td>\n",
       "      <td>1269.983362</td>\n",
       "      <td>1260.122367</td>\n",
       "      <td>...</td>\n",
       "      <td>362.190203</td>\n",
       "      <td>358.988068</td>\n",
       "      <td>356.165624</td>\n",
       "      <td>353.722872</td>\n",
       "      <td>351.657615</td>\n",
       "      <td>349.969856</td>\n",
       "      <td>348.659592</td>\n",
       "      <td>347.722435</td>\n",
       "      <td>347.160580</td>\n",
       "      <td>346.956469</td>\n",
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       "      <th>3</th>\n",
       "      <td>896.951113</td>\n",
       "      <td>894.795872</td>\n",
       "      <td>893.648019</td>\n",
       "      <td>891.764927</td>\n",
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       "      <td>873.667049</td>\n",
       "      <td>867.677586</td>\n",
       "      <td>...</td>\n",
       "      <td>235.621379</td>\n",
       "      <td>233.413464</td>\n",
       "      <td>231.468919</td>\n",
       "      <td>229.785548</td>\n",
       "      <td>228.363353</td>\n",
       "      <td>227.202332</td>\n",
       "      <td>226.298096</td>\n",
       "      <td>225.655036</td>\n",
       "      <td>225.268760</td>\n",
       "      <td>225.126102</td>\n",
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       "      <th>4</th>\n",
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       "      <td>596.891983</td>\n",
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       "      <td>590.884962</td>\n",
       "      <td>588.025208</td>\n",
       "      <td>585.501249</td>\n",
       "      <td>581.833828</td>\n",
       "      <td>...</td>\n",
       "      <td>148.549209</td>\n",
       "      <td>147.052392</td>\n",
       "      <td>145.735544</td>\n",
       "      <td>144.596470</td>\n",
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       "      <td>143.029422</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>-0.008779</td>\n",
       "      <td>-0.008779</td>\n",
       "      <td>-0.008779</td>\n",
       "      <td>-0.008779</td>\n",
       "      <td>-0.008779</td>\n",
       "      <td>-0.008779</td>\n",
       "      <td>-0.008779</td>\n",
       "      <td>-0.008779</td>\n",
       "      <td>-0.008779</td>\n",
       "      <td>-0.008779</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>-0.006584</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "      <td>-0.002195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>-0.004389</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 91 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             0            1            2            3            4   \\\n",
       "0   2645.156525  2640.813122  2631.509593  2615.856662  2595.561843   \n",
       "1   1878.000514  1876.503697  1872.041778  1866.140105  1857.688137   \n",
       "2   1309.466848  1308.665766  1306.727805  1303.448854  1298.984740   \n",
       "3    896.951113   894.795872   893.648019   891.764927   889.302422   \n",
       "4    600.168739   598.961628   597.952045   596.891983   595.333713   \n",
       "..          ...          ...          ...          ...          ...   \n",
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       "99    -0.004389    -0.004389    -0.004389    -0.004389    -0.004389   \n",
       "\n",
       "             5            6            7            8            9   ...  \\\n",
       "0   2569.863559  2540.190589  2507.581048  2472.743840  2436.866322  ...   \n",
       "1   1846.828532  1834.206546  1819.857295  1803.754441  1786.699068  ...   \n",
       "2   1293.245478  1286.426402  1278.681142  1269.983362  1260.122367  ...   \n",
       "3    885.990550   882.015864   877.406897   873.667049   867.677586  ...   \n",
       "4    593.336494   590.884962   588.025208   585.501249   581.833828  ...   \n",
       "..          ...          ...          ...          ...          ...  ...   \n",
       "95    -0.008779    -0.008779    -0.008779    -0.008779    -0.008779  ...   \n",
       "96    -0.006584    -0.006584    -0.006584    -0.006584    -0.006584  ...   \n",
       "97    -0.006584    -0.006584    -0.006584    -0.006584    -0.006584  ...   \n",
       "98    -0.004389    -0.004389    -0.004389    -0.004389    -0.004389  ...   \n",
       "99    -0.004389    -0.004389    -0.004389    -0.004389    -0.004389  ...   \n",
       "\n",
       "            81          82          83          84          85          86  \\\n",
       "0   803.830222  797.454484  791.917139  787.029439  782.894537  779.514628   \n",
       "1   544.264161  539.703478  535.680508  532.197446  529.282823  526.870797   \n",
       "2   362.190203  358.988068  356.165624  353.722872  351.657615  349.969856   \n",
       "3   235.621379  233.413464  231.468919  229.785548  228.363353  227.202332   \n",
       "4   148.549209  147.052392  145.735544  144.596470  143.632977  143.029422   \n",
       "..         ...         ...         ...         ...         ...         ...   \n",
       "95   -0.004389   -0.004389   -0.004389   -0.004389   -0.004389   -0.004389   \n",
       "96   -0.004389   -0.004389   -0.004389   -0.004389   -0.004389   -0.004389   \n",
       "97   -0.002195   -0.002195   -0.002195   -0.002195   -0.002195   -0.002195   \n",
       "98   -0.002195   -0.002195   -0.002195   -0.002195   -0.002195   -0.002195   \n",
       "99    0.000000    0.000000    0.000000    0.000000    0.000000    0.000000   \n",
       "\n",
       "            87          88          89          90  \n",
       "0   776.885322  775.006619  773.880714  773.511996  \n",
       "1   524.996483  523.657688  522.854411  522.623963  \n",
       "2   348.659592  347.722435  347.160580  346.956469  \n",
       "3   226.298096  225.655036  225.268760  225.126102  \n",
       "4   142.412698  141.973749  141.710379  141.613810  \n",
       "..         ...         ...         ...         ...  \n",
       "95   -0.004389   -0.004389   -0.004389   -0.004389  \n",
       "96   -0.004389   -0.004389   -0.004389   -0.004389  \n",
       "97   -0.002195   -0.002195   -0.002195   -0.002195  \n",
       "98   -0.002195   -0.002195   -0.002195   -0.002195  \n",
       "99    0.000000    0.000000    0.000000    0.000000  \n",
       "\n",
       "[100 rows x 91 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_Vnf2 = pd.DataFrame(V_nf2.T, columns = a12) # saves final matrix into dataframe with angular header\n",
    "df_Vnf2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14427df4",
   "metadata": {},
   "source": [
    "#### Warning! : Recreating 91 ab-initio angles from 4 radial coefficients. Ideally,\n",
    "    {no of angular terms = no of V lambdas}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "30765c11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07725962381725983"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Error at minima (approx location)\n",
    "st, end = 10, 40\n",
    "rmse_min = np.sqrt(np.mean(np.square(df_Vnf[st:end]-df_Vnf2[st:end])))\n",
    "rmse_min.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1122c2a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.689645770749555"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Error at high energy (approx location)\n",
    "end = 10\n",
    "rmse_min = np.sqrt(np.mean(np.square(df_Vnf[:end]-df_Vnf2[:end])))\n",
    "rmse_min.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "5d77668f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0005873395789656107"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Error at asymptotic (approx location)\n",
    "st = 40\n",
    "rmse_min = np.sqrt(np.mean(np.square(df_Vnf[st:]-df_Vnf2[st:])))\n",
    "rmse_min.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e0133a5f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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