Deriving the exact nonadiabatic quantum propagator in the mapping variable representation
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Publication Date
2016-12Journal Title
Faraday Discussions
ISSN
1359-6640
Publisher
Royal Society of Chemistry
Volume
195
Pages
269-289
Language
English
Type
Article
This Version
AM
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Hele, T., & Ananth, N. (2016). Deriving the exact nonadiabatic quantum propagator in the mapping variable representation. Faraday Discussions, 195 269-289. https://doi.org/10.1039/c6fd00106h
Abstract
We derive an exact quantum propagator for nonadiabatic dynamics in multi-state systems using the mapping variable representation, where classical-like Cartesian variables are used to represent both continuous nuclear degrees of freedom and discrete electronic states. The resulting Liouvillian is a Moyal series that, when suitably approximated, can allow for the use of classical dynamics to efficiently model large systems. We demonstrate that different truncations of the exact Liouvillian lead to existing approximate semiclassical and mixed quantum-classical methods and we derive an associated error term for each method. Furthermore, by combining the imaginary-time path-integral representation of the Boltzmann operator with the exact Liouvillian, we obtain an analytic expression for thermal quantum real-time correlation functions. These results provide a rigorous theoretical foundation for the development of accurate and efficient classical-like dynamics to compute observables such as electron transfer reaction rates in complex quantized systems.
Identifiers
External DOI: https://doi.org/10.1039/c6fd00106h
This record's URL: https://www.repository.cam.ac.uk/handle/1810/265652
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