https://github.com/ankit7540/raman-intensity-approxmn-test

Python module implementing the collocation method for 1D ro-vibrational Schroedinger equation. This repo also includes datasets on ro-vibrational wavefunctions and polarizabilities of 12 diatomic molecules.

https://github.com/ankit7540/raman-intensity-approxmn-test

Keywords

Repository

Python module implementing the collocation method for 1D ro-vibrational Schroedinger equation. This repo also includes datasets on ro-vibrational wavefunctions and polarizabilities of 12 diatomic molecules.

https://github.com/ankit7540/Raman-Intensity-Approxmn-Test/blob/main/

# Raman-Intensity-Approximn-Test

[![DOI](https://zenodo.org/badge/doi/10.5281/zenodo.6126144.svg)](https://doi.org/10.5281/zenodo.6126144)

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Article :

Testing the limitations of harmonic approximation in the determination of Raman intensities
e2069613, Molecular Physics (2022) [https://doi.org/10.1080/00268976.2022.2069613](https://doi.org/10.1080/00268976.2022.2069613)

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Set of python functions and datasets (rovibrational wavefunctions and polarizabilities) used to test the double harmonic approximation for computing Raman intensities of the fundamental vibration in selected diatomic molecules.

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**Table of Contents**

* [Raman-Intensity-Approximn-Test](#raman-intensity-approximn-test)
   * [About](#about)
   * [Bibliography](#bibliography)
   * [Authors](#authors)

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## About

The double harmonic approximation, where *(i) vibrational wavefunctions are  assumed to be harmonic and (ii) the change of polarizability is assumed to be a linear function of the nuclear displacement*, is widely used in theoretical chemistry to model the frequencies and intensities of vibrational transitions in molecules. With datasets and tool in this repository, we test the double harmonic approximation for computed Raman intensities.

**This repository includes :**
 - python module `diatomicSE`  corresponding to the program solving the 1D Schroedinger equation for the diatomic molecule. [(See here)](https://github.com/ankit7540/Raman-Intensity-Approxmn-Test/tree/main/python_functions)
 - python function which use reference datasets on experimental ro-vibrational energies to determine the accurate wavefunctions (based on the `diatomicSE` module).
 - python function which computes harmonic vibrational wavefunctions for given values of molecular parameters [(See here)](https://github.com/ankit7540/Raman-Intensity-Approxmn-Test/blob/main/python_functions/harmonic_wf.py).
 - examples to use the `diatomicSE` module (the mentioned cases)
 - distance-dependent static (wavelength independent) polarizabilities for selected diatomic molecules (H2, HF, HCl, CO, N2 and F2) computed using different *ab initio* techniques. See (`data` directory)[https://github.com/ankit7540/Raman-Intensity-Approxmn-Test/tree/main/data].
 - ro-vibrational wavefunctions (anharmonic and those computed under the harmonic approximation) for all the above molecules, and a few of their isotopologues. See (`data` directory)[https://github.com/ankit7540/Raman-Intensity-Approxmn-Test/tree/main/data].



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## Bibliography

- **NumPy** : Charles R. Harris, K. Jarrod Millman, Stfan J. van der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, Julian Taylor, Sebastian Berg, Nathaniel J. Smith, Robert Kern, Matti Picus, Stephan Hoyer, Marten H. van Kerkwijk, Matthew Brett, Allan Haldane, Jaime Fernndez del Ro, Mark Wiebe, Pearu Peterson, Pierre Grard-Marchant, Kevin Sheppard, Tyler Reddy, Warren Weckesser, Hameer Abbasi, Christoph Gohlke & Travis E. Oliphant. "Array programming with NumPy", *Nature*, 585, 357362 (2020) [10.1038/s41586-020-2649-2](https://doi.org/10.1038/s41586-020-2649-2)

- **Scipy** : Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stfan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelson, Eric Jones, Robert Kern, Eric Larson, CJ Carey, lhan Polat, Yu Feng, Eric W. Moore, Jake VanderPlas, Denis Laxalde, Josef Perktold, Robert Cimrman, Ian Henriksen, E.A. Quintero, Charles R Harris, Anne M. Archibald, Antnio H. Ribeiro, Fabian Pedregosa, Paul van Mulbregt, and SciPy 1.0 Contributors. (2020) "SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python". *Nature Methods*, 17(3), 261-272. [10.1038/s41592-019-0686-2](https://doi.org/10.1038/s41592-019-0686-2)

- **Non-linear optimization in SciPy** :  Travis E. Oliphant. "Python for Scientific Computing, *Computing in Science & Engineering*, 9, 10-20 (2007), DOI:10.1109/MCSE.2007.58


- **Matplotlib**  : J. D. Hunter, "Matplotlib: A 2D Graphics Environment", *Computing in Science & Engineering*, vol. 9, no. 3, pp. 90-95, 2007.


- **Orthogonal Distance Regression as used in SciPy** : (***i***) P. T. Boggs, R. Byrd, R. Schnabel, SIAM J. Sci. Comput. 1987, 8, 1052. (***ii***) P. T. Boggs, J. R. Donaldson, R. h. Byrd, R. B. Schnabel, ACM Trans. Math. Softw. 1989, 15, 348. (***iii***) J. W. Zwolak, P. T. Boggs, L. T. Watson, ACM Trans. Math. Softw. 2007, 33, 27. (***iv***)  P. T. Boggs and J. E. Rogers, Orthogonal Distance Regression, in Statistical analysis of measurement error models and applications: proceedings of the AMS-IMS-SIAM joint summer research conference held June 10-16, 1989, Contemporary Mathematics, vol. 112, pg. 186, 1990.

## Authors
Yen Bang Chao and Ankit Raj

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