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Uniform Semiclassical Instanton Rate Theory
[Image: see text] The instanton expression for the thermal transmission probability through a one-dimensional barrier is derived by using the uniform semiclassical energy-dependent transmission coefficient of Kemble. The resulting theory does not diverge at the “crossover temperature” but changes sm...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
American Chemical Society
2023
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10641875/ https://www.ncbi.nlm.nih.gov/pubmed/37906954 http://dx.doi.org/10.1021/acs.jpclett.3c02779 |
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author | Upadhyayula, Sameernandan Pollak, Eli |
author_facet | Upadhyayula, Sameernandan Pollak, Eli |
author_sort | Upadhyayula, Sameernandan |
collection | PubMed |
description | [Image: see text] The instanton expression for the thermal transmission probability through a one-dimensional barrier is derived by using the uniform semiclassical energy-dependent transmission coefficient of Kemble. The resulting theory does not diverge at the “crossover temperature” but changes smoothly. The temperature-dependent energy of the instanton is the same as the barrier height when ℏβω(‡) = π and not 2π as in the “standard” instanton theory. The concept of a crossover temperature between tunneling and thermal activation, based on the divergence of the instanton rate, is obsolete. The theory is improved by assuring that at high energy when the energy-dependent transmission coefficient approaches unity the integrand decays exponentially as dictated by the Boltzmann factor and not as a Gaussian. This ensures that at sufficiently high temperatures the uniform theory reduces to the classical. Application to Eckart barriers demonstrates that the uniform theory provides a good estimate of the numerically exact result over the whole temperature range. |
format | Online Article Text |
id | pubmed-10641875 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | American Chemical Society |
record_format | MEDLINE/PubMed |
spelling | pubmed-106418752023-11-15 Uniform Semiclassical Instanton Rate Theory Upadhyayula, Sameernandan Pollak, Eli J Phys Chem Lett [Image: see text] The instanton expression for the thermal transmission probability through a one-dimensional barrier is derived by using the uniform semiclassical energy-dependent transmission coefficient of Kemble. The resulting theory does not diverge at the “crossover temperature” but changes smoothly. The temperature-dependent energy of the instanton is the same as the barrier height when ℏβω(‡) = π and not 2π as in the “standard” instanton theory. The concept of a crossover temperature between tunneling and thermal activation, based on the divergence of the instanton rate, is obsolete. The theory is improved by assuring that at high energy when the energy-dependent transmission coefficient approaches unity the integrand decays exponentially as dictated by the Boltzmann factor and not as a Gaussian. This ensures that at sufficiently high temperatures the uniform theory reduces to the classical. Application to Eckart barriers demonstrates that the uniform theory provides a good estimate of the numerically exact result over the whole temperature range. American Chemical Society 2023-10-31 /pmc/articles/PMC10641875/ /pubmed/37906954 http://dx.doi.org/10.1021/acs.jpclett.3c02779 Text en © 2023 The Authors. Published by American Chemical Society https://creativecommons.org/licenses/by/4.0/Permits the broadest form of re-use including for commercial purposes, provided that author attribution and integrity are maintained (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Upadhyayula, Sameernandan Pollak, Eli Uniform Semiclassical Instanton Rate Theory |
title | Uniform Semiclassical Instanton Rate Theory |
title_full | Uniform Semiclassical Instanton Rate Theory |
title_fullStr | Uniform Semiclassical Instanton Rate Theory |
title_full_unstemmed | Uniform Semiclassical Instanton Rate Theory |
title_short | Uniform Semiclassical Instanton Rate Theory |
title_sort | uniform semiclassical instanton rate theory |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10641875/ https://www.ncbi.nlm.nih.gov/pubmed/37906954 http://dx.doi.org/10.1021/acs.jpclett.3c02779 |
work_keys_str_mv | AT upadhyayulasameernandan uniformsemiclassicalinstantonratetheory AT pollakeli uniformsemiclassicalinstantonratetheory |