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A path integral methodology for obtaining thermodynamic properties of nonadiabatic systems using Gaussian mixture distributions

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1.5025058.pdf (899.18 KB)

Date

2018-05

Authors

Raymond, Neil
Iouchtchenko, Dmitri
Roy, Pierre-Nicholas
Nooijen, Marcel

Journal Title

Journal ISSN

Volume Title

Publisher

American Institute of Physics

Abstract

We introduce a new path integral Monte Carlo method for investigating nonadiabatic systems in thermal equilibrium and demonstrate an approach to reducing stochastic error. We derive a general path integral expression for the partition function in a product basis of continuous nuclear and discrete electronic degrees of freedom without the use of any mapping schemes. We separate our Hamiltonian into a harmonic portion and a coupling portion; the partition function can then be calculated as the product of a Monte Carlo estimator (of the coupling contribution to the partition function) and a normalization factor (that is evaluated analytically). A Gaussian mixture model is used to evaluate the Monte Carlo estimator in a computationally efficient manner. Using two model systems, we demonstrate our approach to reduce the stochastic error associated with the Monte Carlo estimator. We show that the selection of the harmonic oscillators comprising the sampling distribution directly affects the efficiency of the method. Our results demonstrate that our path integral Monte Carlo method’s deviation from exact Trotter calculations is dominated by the choice of the sampling distribution. By improving the sampling distribution, we can drastically reduce the stochastic error leading to lower computational cost.

Description

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Raymond, N., Iouchtchenko, D., Roy, P.-N., & Nooijen, M. (2018). A path integral methodology for obtaining thermodynamic properties of nonadiabatic systems using Gaussian mixture distributions. The Journal of Chemical Physics, 148(19), 194110 and may be found at https://doi.org/10.1063/1.5025058

Keywords

Thermodynamics, Mechanical systems, Monte Carlo methods, Statistical mechanics models, Stochastic processes, Thermodynamic properties, Metrology

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Citation

URI

http://dx.doi.org/10.1063/1.5025058
 http://hdl.handle.net/10012/13357

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Waterloo Research
Chemistry