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A semi-classical approach to the calculation of highly excited rotational energies for asymmetric-top molecules
We report a new semi-classical method to compute highly excited rotational energy levels of an asymmetric-top molecule. The method forgoes the idea of a full quantum mechanical treatment of the ro-vibrational motion of the molecule. Instead, it employs a semi-classical Green's function approach...
Autores principales: | , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Royal Society of Chemistry
2017
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5315013/ https://www.ncbi.nlm.nih.gov/pubmed/28000807 http://dx.doi.org/10.1039/c6cp05589c |
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author | Schmiedt, Hanno Schlemmer, Stephan Yurchenko, Sergey N. Yachmenev, Andrey Jensen, Per |
author_facet | Schmiedt, Hanno Schlemmer, Stephan Yurchenko, Sergey N. Yachmenev, Andrey Jensen, Per |
author_sort | Schmiedt, Hanno |
collection | PubMed |
description | We report a new semi-classical method to compute highly excited rotational energy levels of an asymmetric-top molecule. The method forgoes the idea of a full quantum mechanical treatment of the ro-vibrational motion of the molecule. Instead, it employs a semi-classical Green's function approach to describe the rotational motion, while retaining a quantum mechanical description of the vibrations. Similar approaches have existed for some time, but the method proposed here has two novel features. First, inspired by the path integral method, periodic orbits in the phase space and tunneling paths are naturally obtained by means of molecular symmetry analysis. Second, the rigorous variational method is employed for the first time to describe the molecular vibrations. In addition, we present a new robust approach to generating rotational energy surfaces for vibrationally excited states; this is done in a fully quantum-mechanical, variational manner. The semi-classical approach of the present work is applied to calculating the energies of very highly excited rotational states and it reduces dramatically the computing time as well as the storage and memory requirements when compared to the fullly quantum-mechanical variational approach. Test calculations for excited states of SO(2) yield semi-classical energies in very good agreement with the available experimental data and the results of fully quantum-mechanical calculations. |
format | Online Article Text |
id | pubmed-5315013 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2017 |
publisher | Royal Society of Chemistry |
record_format | MEDLINE/PubMed |
spelling | pubmed-53150132017-03-01 A semi-classical approach to the calculation of highly excited rotational energies for asymmetric-top molecules Schmiedt, Hanno Schlemmer, Stephan Yurchenko, Sergey N. Yachmenev, Andrey Jensen, Per Phys Chem Chem Phys Chemistry We report a new semi-classical method to compute highly excited rotational energy levels of an asymmetric-top molecule. The method forgoes the idea of a full quantum mechanical treatment of the ro-vibrational motion of the molecule. Instead, it employs a semi-classical Green's function approach to describe the rotational motion, while retaining a quantum mechanical description of the vibrations. Similar approaches have existed for some time, but the method proposed here has two novel features. First, inspired by the path integral method, periodic orbits in the phase space and tunneling paths are naturally obtained by means of molecular symmetry analysis. Second, the rigorous variational method is employed for the first time to describe the molecular vibrations. In addition, we present a new robust approach to generating rotational energy surfaces for vibrationally excited states; this is done in a fully quantum-mechanical, variational manner. The semi-classical approach of the present work is applied to calculating the energies of very highly excited rotational states and it reduces dramatically the computing time as well as the storage and memory requirements when compared to the fullly quantum-mechanical variational approach. Test calculations for excited states of SO(2) yield semi-classical energies in very good agreement with the available experimental data and the results of fully quantum-mechanical calculations. Royal Society of Chemistry 2017-01-21 2016-12-09 /pmc/articles/PMC5315013/ /pubmed/28000807 http://dx.doi.org/10.1039/c6cp05589c Text en This journal is © The Royal Society of Chemistry 2016 http://creativecommons.org/licenses/by/3.0/ This is an Open Access article distributed under the terms of the Creative Commons Attribution 3.0 Unported License (http://creativecommons.org/licenses/by/3.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
spellingShingle | Chemistry Schmiedt, Hanno Schlemmer, Stephan Yurchenko, Sergey N. Yachmenev, Andrey Jensen, Per A semi-classical approach to the calculation of highly excited rotational energies for asymmetric-top molecules |
title | A semi-classical approach to the calculation of highly excited rotational energies for asymmetric-top molecules |
title_full | A semi-classical approach to the calculation of highly excited rotational energies for asymmetric-top molecules |
title_fullStr | A semi-classical approach to the calculation of highly excited rotational energies for asymmetric-top molecules |
title_full_unstemmed | A semi-classical approach to the calculation of highly excited rotational energies for asymmetric-top molecules |
title_short | A semi-classical approach to the calculation of highly excited rotational energies for asymmetric-top molecules |
title_sort | semi-classical approach to the calculation of highly excited rotational energies for asymmetric-top molecules |
topic | Chemistry |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5315013/ https://www.ncbi.nlm.nih.gov/pubmed/28000807 http://dx.doi.org/10.1039/c6cp05589c |
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