Article

# Quantum instanton evaluation of the thermal rate constants and kinetic isotope effects for SiH4+H -> SiH3+H-2 reaction in full Cartesian space

Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.

The Journal of Chemical Physics (Impact Factor: 2.95). 04/2007; 126(11):114307. DOI: 10.1063/1.2714510 Source: PubMed

**ABSTRACT**

The quantum instanton calculations of thermal rate constants for the gas-phase reaction SiH4+H-->SiH3+H2 and its deuterated analogs are presented, using an analytical potential energy surface. The quantum instanton approximation is manipulated by full dimensionality in Cartesian coordinate path integral Monte Carlo approach, thereby taking explicitly into account the effects of the whole rotation, the vibrotational coupling, and anharmonicity of the reaction system. The rates and kinetic isotope effects obtained for the temperature range of 200-1000 K show good agreements with available experimental data, which give support to the accuracy of the underlying potential surface used. In order to investigate the sole quantum effect to the rates, the authors also derive the classical limit of the quantum instanton and find that it can be exactly expressed as the classical variation transition state theory. Comparing the quantum quantities with their classical analogs in the quantum instanton formula, the authors demonstrate that the quantum correction of the prefactor is more important than that of the activation energy at the transition state.

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**ABSTRACT:**The SiH(4)+H-->SiH(3)+H(2) reaction has been investigated by the quasiclassical trajectory (QCT) method on a recent global ab initio potential energy surface [M. Wang et al., J. Chem. Phys. 124, 234311 (2006)]. The integral cross section as a function of collision energy and thermal rate coefficient for the temperature range of 300-1600 K have been obtained. At the collision energy of 9.41 kcalmol, product energy distributions and rovibrational populations are explored in detail, and H(2) rotational state distributions show a clear evidence of two reaction mechanisms. One is the conventional rebound mechanism and the other is the stripping mechanism similar to what has recently been found in the reaction of CD(4)+H [J. P. Camden et al., J. Am. Chem. Soc. 127, 11898 (2005)]. The computed rate coefficients with the zero-point energy correction are in good agreement with the available experimental data. - [Show abstract] [Hide abstract]

**ABSTRACT:**The diffusion coefficients for hydrogen on Ni(100) surface are calculated by using the quantum instanton approximation, together with path integral Monte Carlo and adaptive umbrella sampling techniques. The model includes 163 atoms in which the motions of the hydrogen and 25 Ni atoms are treated quantum mechanically and the left Ni atoms are considered classically. At high temperature, the predicted diffusion coefficients are in good agreement with experiments. As temperature decreases to 80 K the hydrogen tunneling begins to dominate the diffusive process and the transition temperature is found to be 70 K under which the diffusion coefficient is nearly independent of temperature. The calculations also indicate that the quantum motions of surface atoms hinder the diffusive process compared to the rigid surface and purely classical motions of surface atoms. The underlying mechanisms are extensively investigated. -
##### Article: Frozen Gaussian series representation of the imaginary time propagator theory and numerical tests

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**ABSTRACT:**Thawed Gaussian wavepackets have been used in recent years to compute approximations to the thermal density matrix. From a numerical point of view, it is cheaper to employ frozen Gaussian wavepackets. In this paper, we provide the formalism for the computation of thermal densities using frozen Gaussian wavepackets. We show that the exact density may be given in terms of a series, in which the zeroth order term is the frozen Gaussian. A numerical test of the methodology is presented for deep tunneling in the quartic double well potential. In all cases, the series is observed to converge. The convergence of the diagonal density matrix element is much faster than that of the antidiagonal one, suggesting that the methodology should be especially useful for the computation of partition functions. As a by product of this study, we find that the density matrix in configuration space can have more than two saddle points at low temperatures. This has implications for the use of the quantum instanton theory.

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