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Volume 195, 2016

Deriving the exact nonadiabatic quantum propagator in the mapping variable representation

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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.

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Article information


Submitted
02 May 2016
Accepted
16 May 2016
First published
17 May 2016

Faraday Discuss., 2016,195, 269-289
Article type
Paper
Author version available

Deriving the exact nonadiabatic quantum propagator in the mapping variable representation

T. J. H. Hele and N. Ananth, Faraday Discuss., 2016, 195, 269 DOI: 10.1039/C6FD00106H

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