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
 · 
71 Views
  • [Show abstract] [Hide abstract]
    ABSTRACT: The dynamical properties of liquid water play an important role in many processes in nature. In this paper, we focus on the infrared (IR) absorption spectrum of liquid water based on the linearized semiclassical initial value representation (LSC-IVR) with the local Gaussian approximation (LGA) [J. Liu and W. H. Miller, J. Chem. Phys. 131, 074113 (2009)] and an ab initio based, flexible, polarizable Thole-type model (TTM3-F) [G. S. Fanourgakis and S. S. Xantheas, J. Chem. Phys. 128, 074506 (2008)]. Although the LSC-IVR (LGA) gives the exact result for the isolated three-dimensional shifted harmonic stretching model, it yields a blueshifted peak position for the more realistic anharmonic stretching potential. By using the short-time information of the LSC-IVR correlation function; however, it is shown how one can obtain more accurate results for the position of the stretching peak. Due to the physical decay in the condensed phase system, the LSC-IVR (LGA) is a good and practical approximate quantum approach for the IR spectrum of liquid water. The present results offer valuable insight into future attempts to improve the accuracy of the TTM3-F potential or other ab initio-based models in reproducing the IR spectrum of liquid water.
    The Journal of Chemical Physics 12/2011; 135(24):244503. · 3.16 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: An efficient time-dependent (TD) Monte Carlo (MC) importance sampling method has recently been developed [G. Tao and W. H. Miller, J. Chem. Phys. 135, 024104 (2011)] for the evaluation of time correlation functions using the semiclassical (SC) initial value representation (IVR) methodology. In this TD-SC-IVR method, the MC sampling uses information from both time-evolved phase points as well as their initial values, and only the "important" trajectories are sampled frequently. Even though the TD-SC-IVR was shown in some benchmark examples to be much more efficient than the traditional time-independent sampling method (which uses only initial conditions), the calculation of the SC prefactor-which is computationally expensive, especially for large systems-is still required for accepted trajectories. In the present work, we present an approximate implementation of the TD-SC-IVR method that is completely prefactor-free; it gives the time correlation function as a classical-like magnitude function multiplied by a phase function. Application of this approach to flux-flux correlation functions (which yield reaction rate constants) for the benchmark H + H(2) system shows very good agreement with exact quantum results. Limitations of the approximate approach are also discussed.
    The Journal of Chemical Physics 09/2012; 137(12):124105. · 3.16 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper shows how a compact finite difference Hessian approximation scheme can be proficiently implemented into semiclassical initial value representation molecular dynamics. Effects of the approximation on the monodromy matrix calculation are tested by propagating initial sampling distributions to determine power spectra for analytic potential energy surfaces and for "on the fly" carbon dioxide direct dynamics. With the approximation scheme the computational cost is significantly reduced, making ab initio direct semiclassical dynamics computationally more feasible and, at the same time, properly reproducing important quantum effects inherent in the monodromy matrix and the pre-exponential factor of the semiclassical propagator.
    The Journal of Chemical Physics 02/2013; 138(5):054116. · 3.16 Impact Factor

Full-text (2 Sources)

View
15 Downloads
Available from
May 30, 2014