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README.md

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# Multipole expansion
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# PES2MP (Potential Energy Surface Mapping to Multipole Expansion Series)
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## Multipole expansion
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2D and 4D multipole expansion code (using Legendre polynomials and Spherical Harmonics respectively)
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for fitting PES into radial coefficients is provided as jupyter-notebook files.
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for fitting PES into radial coefficients is provided as jupyter-notebook files. <br />
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Both codes use least square fit (achieved by taking pseudo-inverse of Legendre/Spherical-Harmonics coefficients stored in a 2D matrix).
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Both codes use least square fit (achieved by taking the pseudo-inverse of Legendre/Spherical-Harmonics coefficients stored in a 2D matrix).<br />
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Currently limited to rigid rotor - atom (2D) and rigid rotor - rigid rotor (4D) collision
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For any quaries contact [Dr. T. J. Dhilip Kumar](mailto:[email protected]) CC: AK(mailto:[email protected])
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For any queries contact [Dr. T. J. Dhilip Kumar](mailto:[email protected]) cc: (mailto:[email protected])<br />
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File 1: 2D_multipole_inv.ipynb
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2D PES (Atom - Rigid Rotor collision)
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![2D PES (Atom - Rigid Rotor)](https://github.com/apoorv-kushwaha/Multipole/blob/main/jacobi22.png)
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### File 1: 2D_multipole_inv.ipynb
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_Uses scipy.special for Legendre coefficient_
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# Citation
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---
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output:
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md_document:
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variant: markdown_github
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bibliography: bibliography.bib
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---
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2D PES (Atom - Rigid Rotor collision)<br />
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<img src="https://github.com/apoorv-kushwaha/Multipole/blob/main/jacobi22.png" width="250">
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[@benchPES]
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File 2: Use 4D_SF_expansion.ipynb
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4D PES (Two Rigid Rotors)
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![4D PES (two rigid rotors)](https://github.com/apoorv-kushwaha/Multipole/blob/main/jac_final.png)
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```diff
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# Citation: multipole expansion of 2D Potential Energy Surface
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@article{Kushwaha2023Jan,
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author = {Kushwaha, Apoorv and Kumar, Thogluva Janardhanan Dhilip},
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title = {{Benchmarking PES-Learn's machine learning models predicting accurate potential energy surface for quantum scattering}},
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journal = {Int. J. Quantum Chem.},
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volume = {123},
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number = {1},
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pages = {e27007},
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year = {2023},
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month = jan,
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issn = {0020-7608},
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publisher = {John Wiley {\&} Sons, Ltd},
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doi = {10.1002/qua.27007}
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}
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```
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### File 2: Use 4D_SF_expansion.ipynb
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_Uses pyshtools for calculating spherical harmonics_
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**(need separate installation: Instructions are provided in jupyter-notebook file)<br />**
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4D PES (Two Rigid Rotors)<br />
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<img src="https://github.com/apoorv-kushwaha/Multipole/blob/main/jac_final.png" width="500">
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```diff
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! bibliography: Upcoming.bib
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```

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