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

Jang, Seogjoo; Voth, Gregory A.

doi:10.1063/1.4982053

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

Journal Article · Sun May 07 00:00:00 EDT 2017 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4982053· OSTI ID:1465983

^[1];

^[2]

City Univ. of New York (CUNY), NY (United States). Queens College
Univ. of Chicago, IL (United States). James Franck Inst.

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.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Queens College (CUNY), NY (United States); City Univ. of New York (CUNY), NY (United States); Univ. of Chicago, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division; National Science Foundation (NSF)

Contributing Organization:: University of Chicago

Grant/Contract Number:: SC0001393; CHE-1362926; CHE-1465248

OSTI ID:: 1465983

Alternate ID(s):: OSTI ID: 1361846; OSTI ID: 1755033

Report Number(s):: DOE-Queens-1393-19; CHE- 1465248

Journal Information:: Journal of Chemical Physics, Vol. 146, Issue 17; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 5 works

Citation information provided by
Web of Science

References (25)

Calculation of the Rate of Elementary Association Reactions Wigner, E. The Journal of Chemical Physics, Vol. 5, Issue 9 https://doi.org/10.1063/1.1750107	journal	September 1937
Statistical mechanics of isomerization dynamics in liquids and the transition state approximation Chandler, David The Journal of Chemical Physics, Vol. 68, Issue 6 https://doi.org/10.1063/1.436049	journal	January 1978
Quantum mechanical rate constants for bimolecular reactions Miller, William H.; Schwartz, Steven D.; Tromp, John W. The Journal of Chemical Physics, Vol. 79, Issue 10 https://doi.org/10.1063/1.445581	journal	November 1983
Ring-polymer molecular dynamics rate-theory in the deep-tunneling regime: Connection with semiclassical instanton theory Richardson, Jeremy O.; Althorpe, Stuart C. The Journal of Chemical Physics, Vol. 131, Issue 21 https://doi.org/10.1063/1.3267318	journal	December 2009
Derivation of a true ( t → 0 ₊ ) quantum transition-state theory. I. Uniqueness and equivalence to ring-polymer molecular dynamics transition-state-theory Hele, Timothy J. H.; Althorpe, Stuart C. The Journal of Chemical Physics, Vol. 138, Issue 8 https://doi.org/10.1063/1.4792697	journal	February 2013
Quantum transition state theory McLafferty, Francis J.; Pechukas, Philip Chemical Physics Letters, Vol. 27, Issue 4 https://doi.org/10.1016/0009-2614(74)80293-9	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 Althorpe, Stuart C.; Hele, Timothy J. H. The Journal of Chemical Physics, Vol. 139, Issue 8 https://doi.org/10.1063/1.4819076	journal	August 2013
A new formulation of quantum transition state theory for adiabatic rate constants Hansen, Nancy Fisher; Andersen, Hans C. The Journal of Chemical Physics, Vol. 101, Issue 7 https://doi.org/10.1063/1.467318	journal	October 1994
A Modification of Path Integral Quantum Transition State Theory for Asymmetric and Metastable Potentials Jang, Seogjoo; Schwieters, Charles D.; Voth, Gregory A. The Journal of Physical Chemistry A, Vol. 103, Issue 47 https://doi.org/10.1021/jp992190+	journal	October 1999
Rigorous formulation of quantum transition state theory and its dynamical corrections Voth, Gregory A.; Chandler, David; Miller, William H. The Journal of Chemical Physics, Vol. 91, Issue 12 https://doi.org/10.1063/1.457242	journal	December 1989
Short-time behavior of quantum correlation functions in rate theory Costley, Jennifer; Pechuka, Philip Chemical Physics Letters, Vol. 83, Issue 1 https://doi.org/10.1016/0009-2614(81)80306-5	journal	October 1981
Can quantum transition state theory be defined as an exact t = 0+ limit? Jang, Seogjoo; Voth, Gregory A. The Journal of Chemical Physics, Vol. 144, Issue 8 https://doi.org/10.1063/1.4942482	journal	February 2016
The Activated Complex in Chemical Reactions Eyring, Henry The Journal of Chemical Physics, Vol. 3, Issue 2 https://doi.org/10.1063/1.1749604	journal	February 1935
Generalized path integral based quantum transition state theory Mills, G.; Schenter, G. K.; Makarov, D. E. Chemical Physics Letters, Vol. 278, Issue 1-3 https://doi.org/10.1016/S0009-2614(97)00886-5	journal	October 1997
Green’s functions in quantum transition state theory Stuchebrukhov, A. A. The Journal of Chemical Physics, Vol. 95, Issue 6 https://doi.org/10.1063/1.460781	journal	September 1991
Quantum-classical crossover of the transition rate in the damped double well Gillan, M. J. Journal of Physics C: Solid State Physics, Vol. 20, Issue 24 https://doi.org/10.1088/0022-3719/20/24/005	journal	August 1987
Path-integral virial estimator based on the scaling of fluctuation coordinates: Application to quantum clusters with fourth-order propagators Yamamoto, Takeshi M. The Journal of Chemical Physics, Vol. 123, Issue 10 https://doi.org/10.1063/1.2013257	journal	September 2005
Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems Kubo, Ryogo Journal of the Physical Society of Japan, Vol. 12, Issue 6 https://doi.org/10.1143/jpsj.12.570	journal	June 1957
Chemical reaction rates from ring polymer molecular dynamics Craig, Ian R.; Manolopoulos, David E. The Journal of Chemical Physics, Vol. 122, Issue 8 https://doi.org/10.1063/1.1850093	journal	February 2005
Beyond transition-state theory: a rigorous quantum theory of chemical reaction rates Miller, William H. Accounts of Chemical Research, Vol. 26, Issue 4 https://doi.org/10.1021/ar00028a007	journal	April 1993
A new quantum transition state theory Pollak, Eli; Liao, Jie-Lou The Journal of Chemical Physics, Vol. 108, Issue 7 https://doi.org/10.1063/1.475665	journal	February 1998
On transition‐state theory and the classical mechanics of collinear collisions Pechukas, Philip; McLafferty, Francis J. The Journal of Chemical Physics, Vol. 58, Issue 4 https://doi.org/10.1063/1.1679404	journal	February 1973
A unified framework for quantum activated rate processes. I. General theory Cao, Jianshu; Voth, Gregory A. The Journal of Chemical Physics, Vol. 105, Issue 16 https://doi.org/10.1063/1.471980	journal	October 1996
A refined ring polymer molecular dynamics theory of chemical reaction rates Craig, Ian R.; Manolopoulos, David E. The Journal of Chemical Physics, Vol. 123, Issue 3 https://doi.org/10.1063/1.1954769	journal	July 2005
An alternative derivation of ring-polymer molecular dynamics transition-state theory Hele, Timothy J. H.; Althorpe, Stuart C. The Journal of Chemical Physics, Vol. 144, Issue 17 https://doi.org/10.1063/1.4947589	journal	May 2016

Similar Records

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

Journal Article · Thu Feb 25 00:00:00 EST 2016 · Journal of Chemical Physics · OSTI ID:1465983

Jang, Seogjoo; Voth, Gregory A.

An alternative derivation of ring-polymer molecular dynamics transition-state theory

Journal Article · Sat May 07 00:00:00 EDT 2016 · Journal of Chemical Physics · OSTI ID:1465983

Hele, Timothy J. H.

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

Journal Article · Mon Apr 21 00:00:00 EDT 2014 · Journal of Chemical Physics · OSTI ID:1465983

Jang, Seogjoo; Sinitskiy, Anton V.; Voth, Gregory A.

Related Subjects

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

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

Citation Formats

References (25)

Similar Records

Related Subjects