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Exact quantum statistics for electronically nonadiabatic systems using continuous path variables

Ananth, Nandini and Miller, Thomas F., III (2010) Exact quantum statistics for electronically nonadiabatic systems using continuous path variables. Journal of Chemical Physics, 133 (23). Art. No. 234103. ISSN 0021-9606.

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We derive an exact, continuous-variable path integral (PI) representation of the canonical partition function for electronically nonadiabatic systems. Utilizing the Stock–Thoss (ST) mapping for an N-level system, matrix elements of the Boltzmann operator are expressed in Cartesian coordinates for both the nuclear and electronic degrees of freedom. The PI discretization presented here properly constrains the electronic Cartesian coordinates to the physical subspace of the mapping. We numerically demonstrate that the resulting PI–ST representation is exact for the calculation of equilibrium properties of systems with coupled electronic and nuclear degrees of freedom. We further show that the PI–ST formulation provides a natural means to initialize semiclassical trajectories for the calculation of real-time thermal correlation functions, which is numerically demonstrated in applications to a series of nonadiabatic model systems.

Item Type:Article
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URLURL TypeDescription DOIArticle PublisherArticle
Miller, Thomas F., III0000-0002-1882-5380
Additional Information:© 2010 American Institute of Physics. Received 13 September 2010; accepted 18 October 2010; published online 15 December 2010. The authors sincerely thank Bill Miller for valuable comments and insights. This work is supported in part by the U. S. Army Research Laboratory and the U. S. Army Research Office under Grant W911NF-10-1-0202 and in part by the U. S. Office of Naval Research under Grant N00014-10-1-0884. T.F.M. additionally acknowledges support from a Camille and Henry Dreyfus Foundation New Faculty Award and an Alfred P. Sloan Foundation Research Fellowship.
Funding AgencyGrant Number
Army Research Laboratory (ARL)UNSPECIFIED
Army Research Office (ARO)W911NF-10-1-0202
Office of Naval Research (ONR)N00014-10-1-0884
Camille and Henry Dreyfus FoundationUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:electronic structure, quantum statistical mechanics, thermodynamics
Issue or Number:23
Classification Code:PACS: 05.30.-d; 05.70.Ce
Record Number:CaltechAUTHORS:20110201-140605973
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Official Citation:Miller, N. A. T. F. and Iii (2010). "Exact quantum statistics for electronically nonadiabatic systems using continuous path variables." The Journal of Chemical Physics 133(23): 234103-234109.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:21954
Deposited By: Tony Diaz
Deposited On:14 Feb 2011 18:20
Last Modified:03 Oct 2019 02:32

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