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

Authors:
ORCiD logo [1]; ORCiD logo [2]
  1. Department of Chemistry and Biochemistry, Queens College, City University of New York, 65-30 Kissena Boulevard, Queens, New York 11367, USA and Ph.D. Programs in Chemistry and Physics, and Initiative for the Theoretical Sciences, Graduate Center, City University of New York, 365 Fifth Avenue, New York, New York 10016, USA
  2. Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, 5735 S. Ellis Avenue, Chicago, Illinois 60637, USA
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1361846
Grant/Contract Number:
SC0001393
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 146; Journal Issue: 17; Related Information: CHORUS Timestamp: 2018-02-14 20:10:53; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics
Country of Publication:
United States
Language:
English

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.
Jang, Seogjoo, & Voth, Gregory A. Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space. United States. doi:10.1063/1.4982053.
Jang, Seogjoo, and Voth, Gregory A. 2017. "Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space". United States. doi:10.1063/1.4982053.
@article{osti_1361846,
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 = {},
doi = {10.1063/1.4982053},
journal = {Journal of Chemical Physics},
number = 17,
volume = 146,
place = {United States},
year = 2017,
month = 5
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on May 2, 2018
Publisher's Accepted Manuscript

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  • Feynman's path integral representation of the Boltzmann operator e/sup - $beta$H/ is used to express the rate constant of a recently formulated quantum mechanical version of transition state theory. By evaluating the path integral in two separate stages, one is able to interpret the result as a generalization of a model suggested several years ago by Johnston and Rapp for handling the nonseparable aspect of tunneling in transition state theory. A Fourier series expansion of the path integral is also developed and this approach has promise for direct numerical evaluation of the quantum rate expression. (auth)
  • The authors have used canonical variational transition-state theory with multidimensional tunneling contributions (CVT/MT) to calculate 21 kinetic isotope effects (KIE) for the addition of hydrogen atom to ethylene. The potential energies are obtained by variable scaling of external correlation (VSEC). The reorientation of the dividing surface (RODS) algorithm is employed so that the same reaction path can be used for every isotopic substitution. The results show the importance of the tunneling effect for explaining the trends in the KIEs in this almost barrierless reaction. The authors have predicted the regioselectivity for three different isotopically substituted substrates and have shown howmore » the addition to the most substituted carbon is kinetically favored, especially at low temperature. However, their calculations show no cis/trans selectivity for the isotopically substituted ethylene substrate.« less
  • We consider a triatomic system with zero total angular momentum and demonstrate that, no matter how complicated the anharmonic part of the potential energy function, classical dynamics in the vicinity of a saddle point is constrained by symmetry properties. At short times and at not too high energies, recrossing dynamics is largely determined by elementary local structural parameters and thus can be described in configuration space only. Conditions for recrossing are given in the form of inequalities involving structural parameters only. Explicit expressions for recrossing times, valid for microcanonical ensembles, are shown to obey interesting regularities. In a forward reaction,more » when the transition state is nonlinear and tight enough, one-fourth of the trajectories are expected to recross the plane R = R{sub *} (where R{sub *} denotes the position of the saddle point) within a short time. Another fourth of them are expected to have previously recrossed at a short negative time, i.e., close to the saddle point. These trajectories do not contribute to the reaction rate. The reactive trajectories that obey the transition state model are to be found in the remaining half. However, no conclusion can be derived for them, except that if recrossings occur, then they must either take place in the distant future or already have taken place in the remote past, i.e., far away from the saddle point. Trajectories that all cross the plane R = R{sub *} at time t = 0, with the same positive translational momentum P{sub R{sub *}} can be partitioned into two sets, distinguished by the parity of their initial conditions; both sets have the same average equation of motion up to and including terms cubic in time. Coordination is excellent in the vicinity of the saddle point but fades out at long (positive or negative) times, i.e., far away from the transition state.« less
  • The purpose of the present work is to determine initial conditions that generate reacting, recrossing-free trajectories that cross the conventional dividing surface of transition state theory (i.e., the plane in configuration space passing through a saddle point of the potential energy surface and perpendicular to the reaction coordinate) without ever returning to it. Local analytical equations of motion valid in the neighborhood of this planar surface have been derived as an expansion in Poisson brackets. We show that the mere presence of a saddle point implies that reactivity criteria can be quite simply formulated in terms of elements of thismore » series, irrespective of the shape of the potential energy function. Some of these elements are demonstrated to be equal to a sum of squares and thus to be necessarily positive, which has a profound impact on the dynamics. The method is then applied to a three-dimensional model describing an atom-diatom interaction. A particular relation between initial conditions is shown to generate a bundle of reactive trajectories that form reactive cylinders (or conduits) in phase space. This relation considerably reduces the phase space volume of initial conditions that generate recrossing-free trajectories. Loci in phase space of reactive initial conditions are presented. Reactivity is influenced by symmetry, as shown by a comparative study of collinear and bent transition states. Finally, it is argued that the rules that have been derived to generate reactive trajectories in classical mechanics are also useful to build up a reactive wave packet.« less
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