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Title: Can the ring polymer molecular dynamics method be interpreted as real time quantum dynamics?

Abstract

The ring polymer molecular dynamics (RPMD) method has gained popularity in recent years as a simple approximation for calculating real time quantum correlation functions in condensed media. However, the extent to which RPMD captures real dynamical quantum effects and why it fails under certain situations have not been clearly understood. Addressing this issue has been difficult in the absence of a genuine justification for the RPMD algorithm starting from the quantum Liouville equation. To this end, a new and exact path integral formalism for the calculation of real time quantum correlation functions is presented in this work, which can serve as a rigorous foundation for the analysis of the RPMD method as well as providing an alternative derivation of the well established centroid molecular dynamics method. The new formalism utilizes the cyclic symmetry of the imaginary time path integral in the most general sense and enables the expression of Kubo-transformed quantum time correlation functions as that of physical observables pre-averaged over the imaginary time path. Upon filtering with a centroid constraint function, the formulation results in the centroid dynamics formalism. Upon filtering with the position representation of the imaginary time path integral, we obtain an exact quantum dynamics formalism involvingmore » the same variables as the RPMD method. The analysis of the RPMD approximation based on this approach clarifies that an explicit quantum dynamical justification does not exist for the use of the ring polymer harmonic potential term (imaginary time kinetic energy) as implemented in the RPMD method. It is analyzed why this can cause substantial errors in nonlinear correlation functions of harmonic oscillators. Such errors can be significant for general correlation functions of anharmonic systems. We also demonstrate that the short time accuracy of the exact path integral limit of RPMD is of lower order than those for finite discretization of path. The present quantum dynamics formulation also serves as the basis for developing new quantum dynamical methods that utilize the cyclic nature of the imaginary time path integral.« less

Authors:
 [1];
  1. Department of Chemistry and Biochemistry, Queens College and the Graduate Center, City University of New York, 65-30 Kissena Boulevard, Flushing, New York 11367 (United States)
Publication Date:
OSTI Identifier:
22253109
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 140; Journal Issue: 15; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; BOLTZMANN-VLASOV EQUATION; CORRELATION FUNCTIONS; HARMONIC OSCILLATORS; HARMONIC POTENTIAL; KINETIC ENERGY; MOLECULAR DYNAMICS METHOD; PATH INTEGRALS; POLYMERS

Citation Formats

Jang, Seogjoo, Sinitskiy, Anton V., and Voth, Gregory A., E-mail: gavoth@uchicago.edu. Can the ring polymer molecular dynamics method be interpreted as real time quantum dynamics?. United States: N. p., 2014. Web. doi:10.1063/1.4870717.
Jang, Seogjoo, Sinitskiy, Anton V., & Voth, Gregory A., E-mail: gavoth@uchicago.edu. Can the ring polymer molecular dynamics method be interpreted as real time quantum dynamics?. United States. https://doi.org/10.1063/1.4870717
Jang, Seogjoo, Sinitskiy, Anton V., and Voth, Gregory A., E-mail: gavoth@uchicago.edu. 2014. "Can the ring polymer molecular dynamics method be interpreted as real time quantum dynamics?". United States. https://doi.org/10.1063/1.4870717.
@article{osti_22253109,
title = {Can the ring polymer molecular dynamics method be interpreted as real time quantum dynamics?},
author = {Jang, Seogjoo and Sinitskiy, Anton V. and Voth, Gregory A., E-mail: gavoth@uchicago.edu},
abstractNote = {The ring polymer molecular dynamics (RPMD) method has gained popularity in recent years as a simple approximation for calculating real time quantum correlation functions in condensed media. However, the extent to which RPMD captures real dynamical quantum effects and why it fails under certain situations have not been clearly understood. Addressing this issue has been difficult in the absence of a genuine justification for the RPMD algorithm starting from the quantum Liouville equation. To this end, a new and exact path integral formalism for the calculation of real time quantum correlation functions is presented in this work, which can serve as a rigorous foundation for the analysis of the RPMD method as well as providing an alternative derivation of the well established centroid molecular dynamics method. The new formalism utilizes the cyclic symmetry of the imaginary time path integral in the most general sense and enables the expression of Kubo-transformed quantum time correlation functions as that of physical observables pre-averaged over the imaginary time path. Upon filtering with a centroid constraint function, the formulation results in the centroid dynamics formalism. Upon filtering with the position representation of the imaginary time path integral, we obtain an exact quantum dynamics formalism involving the same variables as the RPMD method. The analysis of the RPMD approximation based on this approach clarifies that an explicit quantum dynamical justification does not exist for the use of the ring polymer harmonic potential term (imaginary time kinetic energy) as implemented in the RPMD method. It is analyzed why this can cause substantial errors in nonlinear correlation functions of harmonic oscillators. Such errors can be significant for general correlation functions of anharmonic systems. We also demonstrate that the short time accuracy of the exact path integral limit of RPMD is of lower order than those for finite discretization of path. The present quantum dynamics formulation also serves as the basis for developing new quantum dynamical methods that utilize the cyclic nature of the imaginary time path integral.},
doi = {10.1063/1.4870717},
url = {https://www.osti.gov/biblio/22253109}, journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 15,
volume = 140,
place = {United States},
year = {2014},
month = {4}
}

Works referencing / citing this record:

Nuclear quantum effects enter the mainstream
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How to remove the spurious resonances from ring polymer molecular dynamics
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Communication: On the consistency of approximate quantum dynamics simulation methods for vibrational spectra in the condensed phase
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Communication: Relation of centroid molecular dynamics and ring-polymer molecular dynamics to exact quantum dynamics
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Non-equilibrium dynamics from RPMD and CMD
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Quantum mechanics/coarse-grained molecular mechanics (QM/CG-MM)
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Quantum theory of multiscale coarse-graining
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Ring-polymer molecular dynamics study on rate coefficient of the barrierless OH + CO system at low temperature
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State dependent ring polymer molecular dynamics for investigating excited nonadiabatic dynamics
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Non-equilibrium dynamics from RPMD and CMD
text, January 2016