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Volume 195, 2016
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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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Publication details

The article was received on 02 May 2016, accepted on 16 May 2016 and first published on 17 May 2016


Article type: Paper
DOI: 10.1039/C6FD00106H
Citation: Faraday Discuss., 2016,195, 269-289
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    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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