first_quantised_grid.ipynb

{"cells":[{"cell_type":"markdown","metadata":{},"source":["# LCAO in First Quantisation"]},{"cell_type":"markdown","metadata":{},"source":["## H2 Sigma Bonding"]},{"cell_type":"markdown","metadata":{},"source":["$$s_A = \\frac{1}{\\pi} \\sqrt{\\frac{1}{a_0}} e^{-{\\frac{|\\boldsymbol{r}- R_A|} {a_0}}} \\qquad s_B = \\frac{1}{\\pi} \\sqrt{\\frac{1}{a_0}} e^{-{\\frac{|\\boldsymbol{r}-R_B|} {a_0}}}$$\n"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["import numpy as np"]},{"cell_type":"markdown","metadata":{},"source":["- Ignore constants"]},{"cell_type":"code","execution_count":3,"metadata":{},"outputs":[],"source":["def s_orb_a (r):\n","    return np.exp(-abs(r-1.5))"]},{"cell_type":"code","execution_count":4,"metadata":{},"outputs":[],"source":["def s_orb_b (r):\n","    return np.exp(-abs(r+1.5))"]},{"cell_type":"code","execution_count":16,"metadata":{},"outputs":[],"source":["import math\n","def sigma_u(r):\n","    return (math.sqrt(2)**-1)*(s_orb_a(r) + s_orb_b(r))"]},{"cell_type":"code","execution_count":23,"metadata":{},"outputs":[],"source":["def density(r):\n","    return (abs(sigma_u(r))**2)"]},{"cell_type":"code","execution_count":24,"metadata":{},"outputs":[],"source":["r_list = np.linspace(-1,1,100)"]},{"cell_type":"code","execution_count":30,"metadata":{},"outputs":[{"ename":"ValueError","evalue":"If using all scalar values, you must pass an index","output_type":"error","traceback":["\u001b[0;31m---------------------------------------------------------------------------\u001b[0m","\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)","Cell \u001b[0;32mIn [30], line 5\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[39mimport\u001b[39;00m \u001b[39mpandas\u001b[39;00m \u001b[39mas\u001b[39;00m \u001b[39mpd\u001b[39;00m\n\u001b[1;32m      3\u001b[0m denisty_dict \u001b[39m=\u001b[39m {r : density(r) \u001b[39mfor\u001b[39;00m r \u001b[39min\u001b[39;00m r_list}\n\u001b[0;32m----> 5\u001b[0m pd\u001b[39m.\u001b[39;49mDataFrame\u001b[39m.\u001b[39;49mfrom_dict(denisty_dict)\u001b[39m.\u001b[39mset_index()\n","File \u001b[0;32m~/opt/miniconda3/envs/inquanto-dev/lib/python3.9/site-packages/pandas/core/frame.py:1763\u001b[0m, in \u001b[0;36mDataFrame.from_dict\u001b[0;34m(cls, data, orient, dtype, columns)\u001b[0m\n\u001b[1;32m   1757\u001b[0m     \u001b[39mraise\u001b[39;00m \u001b[39mValueError\u001b[39;00m(\n\u001b[1;32m   1758\u001b[0m         \u001b[39mf\u001b[39m\u001b[39m\"\u001b[39m\u001b[39mExpected \u001b[39m\u001b[39m'\u001b[39m\u001b[39mindex\u001b[39m\u001b[39m'\u001b[39m\u001b[39m, \u001b[39m\u001b[39m'\u001b[39m\u001b[39mcolumns\u001b[39m\u001b[39m'\u001b[39m\u001b[39m or \u001b[39m\u001b[39m'\u001b[39m\u001b[39mtight\u001b[39m\u001b[39m'\u001b[39m\u001b[39m for orient parameter. \u001b[39m\u001b[39m\"\u001b[39m\n\u001b[1;32m   1759\u001b[0m         \u001b[39mf\u001b[39m\u001b[39m\"\u001b[39m\u001b[39mGot \u001b[39m\u001b[39m'\u001b[39m\u001b[39m{\u001b[39;00morient\u001b[39m}\u001b[39;00m\u001b[39m'\u001b[39m\u001b[39m instead\u001b[39m\u001b[39m\"\u001b[39m\n\u001b[1;32m   1760\u001b[0m     )\n\u001b[1;32m   1762\u001b[0m \u001b[39mif\u001b[39;00m orient \u001b[39m!=\u001b[39m \u001b[39m\"\u001b[39m\u001b[39mtight\u001b[39m\u001b[39m\"\u001b[39m:\n\u001b[0;32m-> 1763\u001b[0m     \u001b[39mreturn\u001b[39;00m \u001b[39mcls\u001b[39;49m(data, index\u001b[39m=\u001b[39;49mindex, columns\u001b[39m=\u001b[39;49mcolumns, dtype\u001b[39m=\u001b[39;49mdtype)\n\u001b[1;32m   1764\u001b[0m \u001b[39melse\u001b[39;00m:\n\u001b[1;32m   1765\u001b[0m     realdata \u001b[39m=\u001b[39m data[\u001b[39m\"\u001b[39m\u001b[39mdata\u001b[39m\u001b[39m\"\u001b[39m]\n","File \u001b[0;32m~/opt/miniconda3/envs/inquanto-dev/lib/python3.9/site-packages/pandas/core/frame.py:663\u001b[0m, in \u001b[0;36mDataFrame.__init__\u001b[0;34m(self, data, index, columns, dtype, copy)\u001b[0m\n\u001b[1;32m    657\u001b[0m     mgr \u001b[39m=\u001b[39m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_init_mgr(\n\u001b[1;32m    658\u001b[0m         data, axes\u001b[39m=\u001b[39m{\u001b[39m\"\u001b[39m\u001b[39mindex\u001b[39m\u001b[39m\"\u001b[39m: index, \u001b[39m\"\u001b[39m\u001b[39mcolumns\u001b[39m\u001b[39m\"\u001b[39m: columns}, dtype\u001b[39m=\u001b[39mdtype, copy\u001b[39m=\u001b[39mcopy\n\u001b[1;32m    659\u001b[0m     )\n\u001b[1;32m    661\u001b[0m \u001b[39melif\u001b[39;00m \u001b[39misinstance\u001b[39m(data, \u001b[39mdict\u001b[39m):\n\u001b[1;32m    662\u001b[0m     \u001b[39m# GH#38939 de facto copy defaults to False only in non-dict cases\u001b[39;00m\n\u001b[0;32m--> 663\u001b[0m     mgr \u001b[39m=\u001b[39m dict_to_mgr(data, index, columns, dtype\u001b[39m=\u001b[39;49mdtype, copy\u001b[39m=\u001b[39;49mcopy, typ\u001b[39m=\u001b[39;49mmanager)\n\u001b[1;32m    664\u001b[0m \u001b[39melif\u001b[39;00m \u001b[39misinstance\u001b[39m(data, ma\u001b[39m.\u001b[39mMaskedArray):\n\u001b[1;32m    665\u001b[0m     \u001b[39mimport\u001b[39;00m \u001b[39mnumpy\u001b[39;00m\u001b[39m.\u001b[39;00m\u001b[39mma\u001b[39;00m\u001b[39m.\u001b[39;00m\u001b[39mmrecords\u001b[39;00m \u001b[39mas\u001b[39;00m \u001b[39mmrecords\u001b[39;00m\n","File \u001b[0;32m~/opt/miniconda3/envs/inquanto-dev/lib/python3.9/site-packages/pandas/core/internals/construction.py:494\u001b[0m, in \u001b[0;36mdict_to_mgr\u001b[0;34m(data, index, columns, dtype, typ, copy)\u001b[0m\n\u001b[1;32m    490\u001b[0m     \u001b[39melse\u001b[39;00m:\n\u001b[1;32m    491\u001b[0m         \u001b[39m# dtype check to exclude e.g. range objects, scalars\u001b[39;00m\n\u001b[1;32m    492\u001b[0m         arrays \u001b[39m=\u001b[39m [x\u001b[39m.\u001b[39mcopy() \u001b[39mif\u001b[39;00m \u001b[39mhasattr\u001b[39m(x, \u001b[39m\"\u001b[39m\u001b[39mdtype\u001b[39m\u001b[39m\"\u001b[39m) \u001b[39melse\u001b[39;00m x \u001b[39mfor\u001b[39;00m x \u001b[39min\u001b[39;00m arrays]\n\u001b[0;32m--> 494\u001b[0m \u001b[39mreturn\u001b[39;00m arrays_to_mgr(arrays, columns, index, dtype\u001b[39m=\u001b[39;49mdtype, typ\u001b[39m=\u001b[39;49mtyp, consolidate\u001b[39m=\u001b[39;49mcopy)\n","File \u001b[0;32m~/opt/miniconda3/envs/inquanto-dev/lib/python3.9/site-packages/pandas/core/internals/construction.py:119\u001b[0m, in \u001b[0;36marrays_to_mgr\u001b[0;34m(arrays, columns, index, dtype, verify_integrity, typ, consolidate)\u001b[0m\n\u001b[1;32m    116\u001b[0m \u001b[39mif\u001b[39;00m verify_integrity:\n\u001b[1;32m    117\u001b[0m     \u001b[39m# figure out the index, if necessary\u001b[39;00m\n\u001b[1;32m    118\u001b[0m     \u001b[39mif\u001b[39;00m index \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n\u001b[0;32m--> 119\u001b[0m         index \u001b[39m=\u001b[39m _extract_index(arrays)\n\u001b[1;32m    120\u001b[0m     \u001b[39melse\u001b[39;00m:\n\u001b[1;32m    121\u001b[0m         index \u001b[39m=\u001b[39m ensure_index(index)\n","File \u001b[0;32m~/opt/miniconda3/envs/inquanto-dev/lib/python3.9/site-packages/pandas/core/internals/construction.py:657\u001b[0m, in \u001b[0;36m_extract_index\u001b[0;34m(data)\u001b[0m\n\u001b[1;32m    654\u001b[0m         \u001b[39mraise\u001b[39;00m \u001b[39mValueError\u001b[39;00m(\u001b[39m\"\u001b[39m\u001b[39mPer-column arrays must each be 1-dimensional\u001b[39m\u001b[39m\"\u001b[39m)\n\u001b[1;32m    656\u001b[0m \u001b[39mif\u001b[39;00m \u001b[39mnot\u001b[39;00m indexes \u001b[39mand\u001b[39;00m \u001b[39mnot\u001b[39;00m raw_lengths:\n\u001b[0;32m--> 657\u001b[0m     \u001b[39mraise\u001b[39;00m \u001b[39mValueError\u001b[39;00m(\u001b[39m\"\u001b[39m\u001b[39mIf using all scalar values, you must pass an index\u001b[39m\u001b[39m\"\u001b[39m)\n\u001b[1;32m    659\u001b[0m \u001b[39melif\u001b[39;00m have_series:\n\u001b[1;32m    660\u001b[0m     index \u001b[39m=\u001b[39m union_indexes(indexes)\n","\u001b[0;31mValueError\u001b[0m: If using all scalar values, you must pass an index"]}],"source":["import pandas as pd\n","\n","denisty_dict = {r : density(r) for r in r_list}\n","\n","pd.DataFrame.from_dict(denisty_dict).set_index()"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":[]}],"metadata":{"kernelspec":{"display_name":"Python 3.9.13 ('inquanto-dev')","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":"3.9.13"},"orig_nbformat":4,"vscode":{"interpreter":{"hash":"c587e9c30b78c38c576cecc703b8dac6efb81c3ed6ecd4d56c6b4b90a025f909"}}},"nbformat":4,"nbformat_minor":2}