Approximate instanton method

Computational methods now exist that include contributions from all vibrational modes to the H/D-transfer process, thus eliminating the need to introduce any empirical parameters, e.g., variational transition state theory with semiclassical tunneling corrections (Truhlar, D. G. Garett, B. C. Klippen-stein, S. J.J. Phys. Chem. 1996, 100, 12771) and the approximate instanton method (Siebrand, W Smedarchina, Z. Zgierski, M. Z. Femandez-Ramos, A. Int. Rev. Chem. Phys. 1999, 18, 5). 

The parameter controlling the concertedness is the proton-proton correlation represented by a term that is bilinear in the local proton coordinates. The model is combined with a previously developed approach to single proton transfer based on an approximate instanton method. This leads to the recognition of three coupling regimes governing the mechanism of nondassical double proton transfer. 

The integral in (4.33) may be evaluated by the steepest descent method, which leads to an optimum value of Q = Q. This amounts to minimization of the total action 5, + S2 over the positions of the bend point Q. In fact, in the sudden approximation one looks for the minimum of the barrier action taken on a certain class of paths, each consisting of two straightforward segments. If the actual extremal path is close to one of the paths from this class—and this is indeed the case for low enough ft—then the sudden approximation provides accurate results. In particular, the sudden approximation permits calculation of the rate constant to an accuracy of 10% at V /co0 = 3, ft = 0.1, C 0.05 [Hon-tscha et al., 1990], For the cubic parabola (n = 1 in (4.29)) at small coupling parameter the rate constant in the sudden approximation may be evaluated analytically by using the one-dimensional instanton result (3.68) for k D ... 

Methods used Arrhenius law, transition state theory, Wigner tunneling correction, quanrnm instanton approximation, and exact analytical solution... 

Methods used transition state theory and quantum instanton approximation... 

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