Quantum instanton (QI) approximation is recently proposed for the evaluations of the chemical reaction rate constants with use of full dimensional potential energy surfaces. Its strategy is to use the instanton mechanism and to approximate time-dependent quantum dynamics to the imaginary time propagation of the quantities of partition function. It thus incorporates the properties of the instanton idea and the quantum effect of partition function and can be applied to chemical reactions of complex systems. In this paper, we present the QI approach and its applications to several complex systems mainly done by us. The concrete systems include, (1) the reaction of , (2) the reaction of , (3) H diffusion on Ni(100) surface; and (4) surface-subsurface transport and interior migration for H/Ni. Available experimental and other theoretical data are also presented for the purpose of comparison. 1. Introduction The accurate and efficient evaluation of chemical reaction rate constant is one of prime objectives of theoretical reaction dynamics. Since rigorous quantum mechanical approaches are limited to small molecular (several atoms) reactions, a variety of approximation approaches have been proposed. Benefited from the small recrossing dynamics at not-too-high temperatures, the transition state theories (TSTs), originally proposed by Eyring [1, 2] and Wigner [3],have become a possible and popular way to estimate rate constants. Due to their practical simplicity, they have been broadly applied to numerous reactions. The TST is inherently a classical theory and suitable at sufficiently high temperatures, where the classical description of nuclear motions may be adequate. At low temperatures, especially for the reactions involving the motions of light atoms (i.e., hydrogen), however, quantum effects become quite significant. To make the TST still valid for such low temperature reactions, many approaches have been proposed to quantize it [4–14]. However, there is no absolutely unambiguous way to do it. To develop a more accurate and less ad hoc quantum version of TST, with a specific focus on the tunneling regime, Miller et al. [15–17] have proposed a quantum instanton (QI) approach recently. The QI is based on an earlier semiclassical (SC) TST [18] that became known as the instanton [19, 20]. The similarity between the QI and SC instanton lies in using the steepest descent approximation to evaluate relevant integrals in the quantum rate formula, while the crucial difference is that the Boltzmann operator is evaluated by the quantum mechanics and semiclassical
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