Can quantum transition state theory be defined as an exact t = 0+ limit?
Abstract
The definition of the classical transition state theory (TST) as a t → 0+ limit of the flux-side time correlation function relies on the assumption that simultaneous measurement of population and flux is a well defined physical process. However, the noncommutativity of the two measurements in quantum mechanics makes the extension of such a concept to the quantum regime impossible. For this reason, quantum TST (QTST) has been generally accepted as any kind of quantum rate theory reproducing the TST in the classical limit, and there has been a broad consensus that no unique QTST retaining all the properties of TST can be defined. Contrary to this widely held view, Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)] recently suggested that a true QTST can be defined as the exact t → 0+ limit of a certain kind of quantum flux-side time correlation function and that it is equivalent to the ring polymer molecular dynamics (RPMD) TST. This work seeks to question and clarify certain assumptions underlying these suggestions and their implications. First, the time correlation function used by HA as a starting expression is not related to the kinetic rate constant by virtue of linear response theory,more »
- Authors:
-
- City Univ. of New York, Queens, NY (United States); City Univ. of New York, New York, NY (United States)
- Univ. of Chicago, Chicago, IL (United States)
- Publication Date:
- Research Org.:
- City Univ. of New York, New York, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division; USDOE
- Contributing Org.:
- University of Chicago
- OSTI Identifier:
- 1469687
- Alternate Identifier(s):
- OSTI ID: 1239449; OSTI ID: 1755020
- Report Number(s):
- DOE-Queens-1393-16
Journal ID: ISSN 0021-9606; JCPSA6
- Grant/Contract Number:
- SC0001393
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 144; Journal Issue: 8; 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; Quantum transition state theory, RPMD transition state theory, Path integral
Citation Formats
Jang, Seogjoo, and Voth, Gregory A. Can quantum transition state theory be defined as an exact t = 0+ limit?. United States: N. p., 2016.
Web. doi:10.1063/1.4942482.
Jang, Seogjoo, & Voth, Gregory A. Can quantum transition state theory be defined as an exact t = 0+ limit?. United States. https://doi.org/10.1063/1.4942482
Jang, Seogjoo, and Voth, Gregory A. Thu .
"Can quantum transition state theory be defined as an exact t = 0+ limit?". United States. https://doi.org/10.1063/1.4942482. https://www.osti.gov/servlets/purl/1469687.
@article{osti_1469687,
title = {Can quantum transition state theory be defined as an exact t = 0+ limit?},
author = {Jang, Seogjoo and Voth, Gregory A.},
abstractNote = {The definition of the classical transition state theory (TST) as a t → 0+ limit of the flux-side time correlation function relies on the assumption that simultaneous measurement of population and flux is a well defined physical process. However, the noncommutativity of the two measurements in quantum mechanics makes the extension of such a concept to the quantum regime impossible. For this reason, quantum TST (QTST) has been generally accepted as any kind of quantum rate theory reproducing the TST in the classical limit, and there has been a broad consensus that no unique QTST retaining all the properties of TST can be defined. Contrary to this widely held view, Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)] recently suggested that a true QTST can be defined as the exact t → 0+ limit of a certain kind of quantum flux-side time correlation function and that it is equivalent to the ring polymer molecular dynamics (RPMD) TST. This work seeks to question and clarify certain assumptions underlying these suggestions and their implications. First, the time correlation function used by HA as a starting expression is not related to the kinetic rate constant by virtue of linear response theory, which is the first important step in relating a t = 0+ limit to a physically measurable rate. Second, a theoretical analysis calls into question a key step in HA’s proof which appears not to rely on an exact quantum mechanical identity. The correction of this makes the true t = 0+ limit of HA’s QTST different from the RPMD-TST rate expression, but rather equal to the well-known path integral quantum transition state theory rate expression for the case of centroid dividing surface. An alternative quantum rate expression is then formulated starting from the linear response theory and by applying a recently developed formalism of real time dynamics of imaginary time path integrals [S. Jang, A. V. Sinitskiy, and G. A. Voth, J. Chem. Phys. 140, 154103 (2014)]. It is shown that the t → 0+ limit of the new rate expression vanishes in the exact quantum limit.},
doi = {10.1063/1.4942482},
journal = {Journal of Chemical Physics},
number = 8,
volume = 144,
place = {United States},
year = {Thu Feb 25 00:00:00 EST 2016},
month = {Thu Feb 25 00:00:00 EST 2016}
}
Works referenced in this record:
Can the ring polymer molecular dynamics method be interpreted as real time quantum dynamics?
journal, April 2014
- Jang, Seogjoo; Sinitskiy, Anton V.; Voth, Gregory A.
- The Journal of Chemical Physics, Vol. 140, Issue 15
Properties of Quantum Transition State Theory and Its Corrections
journal, January 1996
- Hansen, Nancy Fisher; Andersen, Hans C.
- The Journal of Physical Chemistry, Vol. 100, Issue 4
A relationship between centroid dynamics and path integral quantum transition state theory
journal, May 2000
- Jang, Seogjoo; Voth, Gregory A.
- The Journal of Chemical Physics, Vol. 112, Issue 20
Centroid‐density quantum rate theory: Variational optimization of the dividing surface
journal, June 1993
- Messina, Michael; Schenter, Gregory K.; Garrett, Bruce C.
- The Journal of Chemical Physics, Vol. 98, Issue 11
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
A nonseparable quantum mechanical transition state theory
journal, June 1981
- Pollak, Eli
- The Journal of Chemical Physics, Vol. 74, Issue 12
Quantum Statistical Mechanical Theory of the Rate of Exchange Chemical Reactions in the Gas Phase
journal, July 1960
- Yamamoto, Tsunenobu
- The Journal of Chemical Physics, Vol. 33, Issue 1
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
Statistical-Mechanical Theory of Irreversible Processes. II. Response to Thermal Disturbance
journal, November 1957
- Kubo, Ryogo; Yokota, Mario; Nakajima, Sadao
- Journal of the Physical Society of Japan, Vol. 12, Issue 11
Quantum transition state theory
journal, August 1974
- McLafferty, Francis J.; Pechukas, Philip
- Chemical Physics Letters, Vol. 27, Issue 4
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
Consistent interpretations of quantum mechanics
journal, April 1992
- Omnès, Roland
- Reviews of Modern Physics, Vol. 64, Issue 2
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
Quantum-Statistical Metastability
journal, February 1981
- Affleck, Ian
- Physical Review Letters, Vol. 46, Issue 6
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
Short-time behavior of quantum correlation functions in rate theory
journal, October 1981
- Costley, Jennifer; Pechuka, Philip
- Chemical Physics Letters, Vol. 83, Issue 1
Roles of classical dynamics and quantum dynamics on activated processes occurring in liquids
journal, January 1986
- Chandler, David
- Journal of Statistical Physics, Vol. 42, Issue 1-2
Time correlation function and path integral analysis of quantum rate constants
journal, September 1989
- Voth, Gregory A.; Chandler, David; Miller, William H.
- The Journal of Physical Chemistry, Vol. 93, Issue 19
Reaction-rate theory: fifty years after Kramers
journal, April 1990
- Hänggi, Peter; Talkner, Peter; Borkovec, Michal
- Reviews of Modern Physics, Vol. 62, Issue 2
Generalized path integral based quantum transition state theory
journal, October 1997
- Mills, G.; Schenter, G. K.; Makarov, D. E.
- Chemical Physics Letters, Vol. 278, Issue 1-3
Green’s functions in quantum transition state theory
journal, September 1991
- Stuchebrukhov, A. A.
- The Journal of Chemical Physics, Vol. 95, Issue 6
Quantum-classical crossover of the transition rate in the damped double well
journal, August 1987
- Gillan, M. J.
- Journal of Physics C: Solid State Physics, Vol. 20, Issue 24
Feynman path integral formulation of quantum mechanical transition-state theory
journal, August 1993
- Voth, Gregory A.
- The Journal of Physical Chemistry, Vol. 97, Issue 32
Quantum activated rate theory: Variational optimization of planar dividing surfaces
journal, December 1993
- Messina, Michael; Schenter, Gregory K.; Garrett, Bruce C.
- The Journal of Chemical Physics, Vol. 99, Issue 11
Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems
journal, June 1957
- Kubo, Ryogo
- Journal of the Physical Society of Japan, Vol. 12, Issue 6
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
Beyond transition-state theory: a rigorous quantum theory of chemical reaction rates
journal, April 1993
- Miller, William H.
- Accounts of Chemical Research, Vol. 26, Issue 4
The symmetrized quantum thermal flux operator
journal, July 1997
- Pollak, Eli
- The Journal of Chemical Physics, Vol. 107, Issue 1
A new quantum transition state theory
journal, February 1998
- Pollak, Eli; Liao, Jie-Lou
- The Journal of Chemical Physics, Vol. 108, Issue 7
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
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
Works referencing / citing this record:
Multi-time formulation of Matsubara dynamics
journal, July 2019
- Jung, Kenneth A.; Videla, Pablo E.; Batista, Victor S.
- The Journal of Chemical Physics, Vol. 151, Issue 3