Semi-classical reaction probability

G.C. Schatz, J.M. Bowman, A. Kuppermann, Exact quantum, quasiclassical, and semi-classical reaction probabilities for the collinear F+TL -HF+F reaction, J. Chem. Phys. 63 (1975) 674. 

R. I. Altkorn and G. C. Schatz, A method for determining semi-classical tunneling probabilities in atom-diatom reactions,... 

The flux-flux expression and its extensions have been used to calculate reaction probabilities for several important reactions, including H2+02 H + H2O, by explicit calculation of the action of G in a grid representation with absorbmg potentials. The main power of the flux-flux fomuila over the long mn will be the natural way in which approximations and semi-classical expressions can be inserted into it to treat larger systems. 

Some authors have described the time evolution of the system by more general methods than time-dependent perturbation theory. For example, War-shel and co-workers have attempted to calculate the evolution of the function /(r, Q, t) defined by Eq. (3) by a semi-classical method [44, 96] the probability for the system to occupy state v]/, is obtained by considering the fluctuations of the energy gap between and 11, which are induced by the trajectories of all the atoms of the system. These trajectories are generated through molecular dynamics models based on classical equations of motion. This method was in particular applied to simulate the kinetics of the primary electron transfer process in the bacterial reaction center [97]. Mikkelsen and Ratner have recently proposed a very different approach to the electron transfer problem, in which the time evolution of the system is described by a time-dependent statistical density operator [98, 99]. 

Semi-classical correction to the reaction probability is given by the following formula ... 

In the current understanding of PCET reactions, both electron and proton are treated quantum-mechanically, and therefore the tunnelling probability must be accounted for both particles. In fact, concerted processes can be described as double tunnelling (proton and electron), with a single transition state. " For a description of the reaction coordinate, four adiabatic states (reactants, products and intermediates) described by paraboloids, are usually considered. The expression for the semi-classical rate constant in this case incorporates elements derived from electron and proton transfer theories... 

Avery accurate method to calculate tunnelling correction along a unidimensional reaction pafli involves the semi-classical approximation [4]. The transmission coefficient and the transmission probabilities are... 

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