Multidimensional tunneling corrections

The rate of hydrogen transfer can be calculated using the direct dynamics approach of Truhlar and co-workers which combines canonical variational transition state theory (CVT) [82, 83] with semi-classical multidimensional tunnelling corrections [84], The rate constant is calculated using [83] ... 

Alternative corrections are Eckart tunneling, multidimensional zero-curvature tunneling, and multidimensional small-curvature tunneling (Truhlar et al. 1982), in increasing order of accuracy. The last two involve points on the PES other than the first order saddle point and have more sophisticated calculations. 

If accurate tunneling corrections are required, the situation rapidly becomes more complicated. Issues related to separability of motion along the reaction coordinate, curvature of the reaction coordinate, and multidimensional tunneling arise and must be dealt with. Marcus and Coltrin [51] found that reaction path curvature forces the reaction to cut... 

Multidimensional Tunneling Corrections Based on the Adiabatic Approximation... 

Fortunately, it is relatively simple to estimate from harmonic transition-state theory whether quantum tunneling is important or not. Applying multidimensional transition-state theory, Eq. (6.15), requires finding the vibrational frequencies of the system of interest at energy minimum A (v, V2,. . . , vN) and transition state (vj,. v, , ). Using these frequencies, we can define the zero-point energy corrected activation energy ... 

In particular, the high-temperature regime T>TC, where the trivial trajectory jc(t) = x is the only solution contributing to Im F, is correctly described by the instanton formalism. Furthermore, the equivalence of (2.6) (at T = 0) and (3.68) for the cubic parabola is demonstrated in Appendix B. Although at first the infinite determinants in (3.67) might look less attractive than simple formulas (2.6) and (2.7) or the direct WKB solution by Schmid, it is the instanton approach that permits direct generalization to dissipative tunneling and to the multidimensional problem. 

The AG value deduced from the PMF is corrected by replacing classical vibrational partition functions by their quantum homolog. Recrossing, tunnelling and non-classical reflection effects can be included in the transmission coefficient by various procedures. This ensemble-average variational transition state theory with multidimensional tunnelling (EA-VTST/MT) method was applied to proton and hydride transfers in various enzymes such as yeast enolase, liver alcohol dehydrogenase and triosephosphate isomerase. For a review, see ref. 3 and the chapter by J. Gao in this book. 

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