Article

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

J. Chem. Phys 01/2003; 118:2135. DOI: 10.1063/1.1533081

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.

0 Bookmarks
 · 
85 Views
  • Source
    Molecular Physics 05/2012; 110(9-10):497-510. · 1.64 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: The Herman Kluk (HK) approximation for the propagator is derived semiclassically for a multidimensional system as an asymptotic solution of the Schrödinger equation. The propagator is obtained in the form of an expansion in ℏ, in which the lowest-order term is the HK formula. Thus, the result extends the HK approximation to higher orders in ℏ. Examination of the various terms shows that the expansion is a uniform asymptotic series and establishes the HK formula as a uniform semiclassical approximation. Successive terms in the series should allow one to improve the accuracy of the HK approximation for small ℏ in a systematic and purely semiclassical manner, analogous to a higher-order WKB treatment of time-independent wave functions.
    Chemical Physics 01/2006; 322:3-12. · 2.03 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: In the early days of quantum mechanics - before the concept of matter waves had been introduced - the understanding of atomic spectra was based on classical mechanics combined with conditions for discreteness.

Full-text (2 Sources)

Download
88 Downloads
Available from
May 30, 2014