# Semiclassical calculation of thermal rate constants in full Cartesian space: The benchmark reaction D+H2→DH+H

**Abstract**

Semiclassical (SC) initial-value representation (IVR) methods are used to calculate the thermal rate constant for the benchmark gas-phase reaction D+H2→DH+H. In addition to several technical improvements in the SC-IVR methodology, the most novel aspect of the present work is use of Cartesian coordinates in the full space (six degrees of freedom once the overall center-of-mass translation is removed) to carry out the calculation; i.e., we do not invoke the conservation of total angular momentum J to reduce the problem to fewer degrees of freedom and solve the problem separately for each value of J, as is customary in quantum mechanical treatments. With regard to the SC-IVR methodology, we first present a simple and straightforward derivation of the semiclassical coherent-state propagator of Herman and Kluk (HK). This is achieved by defining an interpolation operator between the Van Vleck propagators in coordinate and momentum representations in an a priori manner with the help of the modified Filinov filtering method. In light of this derivation, we examine the systematic and statistical errors of the HK propagator to fully understand the role of the coherent-state parameter γ. Second, the Boltzmannized flux operator that appears in the rate expression is generalized to a form that can be tuned continuously between the traditional half-split and Kubo forms. In particular, an intermediate form of the Boltzmannized flux operator is shown to have the desirable features of both the traditional forms; i.e., it is easy to evaluate via path integrals and at the same time it gives a numerically well-behaved flux correlation function at low temperatures. Finally, we demonstrate that the normalization integral required in evaluating the rate constant can be expressed in terms of simple constrained partition functions, which allows the use of well-established techniques of statistical mechanics.

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- "Semiclassical (SC) calculations were carried out using the Initial Value Representation (IVR) method of W. H. Miller and coworkers [14]. The method reconducts the evaluation of the vibrational state to state rate coefficients to the calculation of the flux-flux correlation function. "

[Show abstract] [Hide abstract]**ABSTRACT:**The thermal rate constants for the N +N 2 gas-phase reaction have been calculated using the quasiclassical semiclassical and reduced dimensionality quantum methods. The improvement of semiclassical over quasiclassical calculations (with respect to quantum ones) is significant.- "R f (t) is a " dynamical " factor that can be evaluated approximately through the combined use of semiclassical initial value and path integrals techniques. The " static " factor C f (0) is formulated as (see ref. [14]) "

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**ABSTRACT:**A dynamical perspective of tunneling is obtained in the time domain. In particular, the time evolution of individual wave packets reveals details of the tunneling process that cannot be gained from energy dependent transmission probabilities alone.

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