Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space

Abstract

Despite the fact that quantum mechanical principles do not allow the establishment of an exact quantum analogue of the classical transition state theory (TST), the development of a quantum TST (QTST) with a proper dynamical justification, while recovering the TST in the classical limit, has been a long standing theoretical challenge in chemical physics. One of the most recent efforts of this kind was put forth by Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)], which can be specified for any cyclically invariant dividing surface defined in the space of the imaginary time path integral. The present work revisits the issue of the non-uniqueness of QTST and provides a detailed theoretical analysis of HA-QTST for a general class of such path integral dividing surfaces. While we confirm that HA-QTST reproduces the result based on the ring polymer molecular dynamics (RPMD) rate theory for dividing surfaces containing only a quadratic form of low frequency Fourier modes, we find that it produces different results for those containing higher frequency imaginary time paths which accommodate greater quantum fluctuations. This result confirms the assessment made in our previous work [Jang and Voth, J. Chem. Phys. 144, 084110 (2016)] that HA-QTST does notmore » provide a derivation of RPMD-TST in general and points to a new ambiguity of HA-QTST with respect to its justification for general cyclically invariant dividing surfaces defined in the space of imaginary time path integrals. Our analysis also offers new insights into similar path integral based QTST approaches.« less

Authors:
ORCiD logo [1]; ORCiD logo [2]
+ Show Author Affiliations
  1. City Univ. of New York (CUNY), NY (United States). Queens College
  2. Univ. of Chicago, IL (United States). James Franck Inst.
Publication Date:
Research Org.:
Queens College (CUNY), NY (United States); City Univ. of New York (CUNY), NY (United States); Univ. of Chicago, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division; National Science Foundation (NSF)
Contributing Org.:
University of Chicago
OSTI Identifier:
1465983
Alternate Identifier(s):
OSTI ID: 1361846; OSTI ID: 1755033
Report Number(s):
DOE-Queens-1393-19
Journal ID: ISSN 0021-9606; CHE- 1465248
Grant/Contract Number:  
SC0001393; CHE-1362926; CHE-1465248
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 146; Journal Issue: 17; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; polymers; carbon dioxide; classical mechanics; correlation functions; molecular dynamics; quantum fluctuations; transition state theory; surface dynamics; classical ensemble theory; quantum measurement theory; Quantum transition state theory; Uniqueness of rate expression; Path integral

Citation Formats

Jang, Seogjoo, and Voth, Gregory A. Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space. United States: N. p., 2017. Web. doi:10.1063/1.4982053.
Copy to clipboard
Jang, Seogjoo, & Voth, Gregory A. Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space. United States. https://doi.org/10.1063/1.4982053
Copy to clipboard
Jang, Seogjoo, and Voth, Gregory A. Sun . "Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space". United States. https://doi.org/10.1063/1.4982053. https://www.osti.gov/servlets/purl/1465983.
Copy to clipboard
@article{osti_1465983,
title = {Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space},
author = {Jang, Seogjoo and Voth, Gregory A.},
abstractNote = {Despite the fact that quantum mechanical principles do not allow the establishment of an exact quantum analogue of the classical transition state theory (TST), the development of a quantum TST (QTST) with a proper dynamical justification, while recovering the TST in the classical limit, has been a long standing theoretical challenge in chemical physics. One of the most recent efforts of this kind was put forth by Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)], which can be specified for any cyclically invariant dividing surface defined in the space of the imaginary time path integral. The present work revisits the issue of the non-uniqueness of QTST and provides a detailed theoretical analysis of HA-QTST for a general class of such path integral dividing surfaces. While we confirm that HA-QTST reproduces the result based on the ring polymer molecular dynamics (RPMD) rate theory for dividing surfaces containing only a quadratic form of low frequency Fourier modes, we find that it produces different results for those containing higher frequency imaginary time paths which accommodate greater quantum fluctuations. This result confirms the assessment made in our previous work [Jang and Voth, J. Chem. Phys. 144, 084110 (2016)] that HA-QTST does not provide a derivation of RPMD-TST in general and points to a new ambiguity of HA-QTST with respect to its justification for general cyclically invariant dividing surfaces defined in the space of imaginary time path integrals. Our analysis also offers new insights into similar path integral based QTST approaches.},
doi = {10.1063/1.4982053},
journal = {Journal of Chemical Physics},
number = 17,
volume = 146,
place = {United States},
year = {Sun May 07 00:00:00 EDT 2017},
month = {Sun May 07 00:00:00 EDT 2017}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1063/1.4982053
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 5 works
Citation information provided by
Web of Science
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Calculation of the Rate of Elementary Association Reactions
journal, September 1937

Statistical mechanics of isomerization dynamics in liquids and the transition state approximation
journal, January 1978

  • Chandler, David
  • The Journal of Chemical Physics, Vol. 68, Issue 6
  • DOI: 10.1063/1.436049

Quantum mechanical rate constants for bimolecular reactions
journal, November 1983

  • Miller, William H.; Schwartz, Steven D.; Tromp, John W.
  • The Journal of Chemical Physics, Vol. 79, Issue 10
  • DOI: 10.1063/1.445581

Ring-polymer molecular dynamics rate-theory in the deep-tunneling regime: Connection with semiclassical instanton theory
journal, December 2009

  • Richardson, Jeremy O.; Althorpe, Stuart C.
  • The Journal of Chemical Physics, Vol. 131, Issue 21
  • DOI: 10.1063/1.3267318

Derivation of a true ( t → 0 + ) quantum transition-state theory. I. Uniqueness and equivalence to ring-polymer molecular dynamics transition-state-theory
journal, February 2013

  • Hele, Timothy J. H.; Althorpe, Stuart C.
  • The Journal of Chemical Physics, Vol. 138, Issue 8
  • DOI: 10.1063/1.4792697

Quantum transition state theory
journal, August 1974

Derivation of a true ( t → 0 + ) quantum transition-state theory. II. Recovery of the exact quantum rate in the absence of recrossing
journal, August 2013

  • Althorpe, Stuart C.; Hele, Timothy J. H.
  • The Journal of Chemical Physics, Vol. 139, Issue 8
  • DOI: 10.1063/1.4819076

A new formulation of quantum transition state theory for adiabatic rate constants
journal, October 1994

  • Hansen, Nancy Fisher; Andersen, Hans C.
  • The Journal of Chemical Physics, Vol. 101, Issue 7
  • DOI: 10.1063/1.467318

A Modification of Path Integral Quantum Transition State Theory for Asymmetric and Metastable Potentials
journal, October 1999

  • Jang, Seogjoo; Schwieters, Charles D.; Voth, Gregory A.
  • The Journal of Physical Chemistry A, Vol. 103, Issue 47
  • DOI: 10.1021/jp992190+

Rigorous formulation of quantum transition state theory and its dynamical corrections
journal, December 1989

  • Voth, Gregory A.; Chandler, David; Miller, William H.
  • The Journal of Chemical Physics, Vol. 91, Issue 12
  • DOI: 10.1063/1.457242

Short-time behavior of quantum correlation functions in rate theory
journal, October 1981

Can quantum transition state theory be defined as an exact t = 0+ limit?
journal, February 2016

  • Jang, Seogjoo; Voth, Gregory A.
  • The Journal of Chemical Physics, Vol. 144, Issue 8
  • DOI: 10.1063/1.4942482

The Activated Complex in Chemical Reactions
journal, February 1935

  • Eyring, Henry
  • The Journal of Chemical Physics, Vol. 3, Issue 2
  • DOI: 10.1063/1.1749604

Generalized path integral based quantum transition state theory
journal, October 1997

Green’s functions in quantum transition state theory
journal, September 1991

  • Stuchebrukhov, A. A.
  • The Journal of Chemical Physics, Vol. 95, Issue 6
  • DOI: 10.1063/1.460781

Quantum-classical crossover of the transition rate in the damped double well
journal, August 1987

Path-integral virial estimator based on the scaling of fluctuation coordinates: Application to quantum clusters with fourth-order propagators
journal, September 2005

  • Yamamoto, Takeshi M.
  • The Journal of Chemical Physics, Vol. 123, Issue 10
  • DOI: 10.1063/1.2013257

Chemical reaction rates from ring polymer molecular dynamics
journal, February 2005

  • Craig, Ian R.; Manolopoulos, David E.
  • The Journal of Chemical Physics, Vol. 122, Issue 8
  • DOI: 10.1063/1.1850093

Beyond transition-state theory: a rigorous quantum theory of chemical reaction rates
journal, April 1993

A new quantum transition state theory
journal, February 1998

  • Pollak, Eli; Liao, Jie-Lou
  • The Journal of Chemical Physics, Vol. 108, Issue 7
  • DOI: 10.1063/1.475665

On transition‐state theory and the classical mechanics of collinear collisions
journal, February 1973

  • Pechukas, Philip; McLafferty, Francis J.
  • The Journal of Chemical Physics, Vol. 58, Issue 4
  • DOI: 10.1063/1.1679404

A unified framework for quantum activated rate processes. I. General theory
journal, October 1996

  • Cao, Jianshu; Voth, Gregory A.
  • The Journal of Chemical Physics, Vol. 105, Issue 16
  • DOI: 10.1063/1.471980

A refined ring polymer molecular dynamics theory of chemical reaction rates
journal, July 2005

  • Craig, Ian R.; Manolopoulos, David E.
  • The Journal of Chemical Physics, Vol. 123, Issue 3
  • DOI: 10.1063/1.1954769

An alternative derivation of ring-polymer molecular dynamics transition-state theory
journal, May 2016

  • Hele, Timothy J. H.; Althorpe, Stuart C.
  • The Journal of Chemical Physics, Vol. 144, Issue 17
  • DOI: 10.1063/1.4947589
    Sort by:
    [ × clear filter / sort ]

    Similar Records in DOE PAGES and OSTI.GOV collections: