Reaction paths bifurcation regions

Figure 6.20. (a) Projection of a three-dimensional PES K(p,p2,p3) for two-proton transfer in formic acid dimer onto the (p, p,) and (p, p3) planes. In contrast with points A and B, in points C and D the potential along the p3 coordinate is a double well resulting in bifurcation of the reaction path [from Shida et al., 1991b]. (b) The contour lines correspond to equilibrium value of p3 and potential (6.37) when V(Q) = V0(Q4 - 2Q2), V0 = 21 kcal/ mol, C = 5.()9V0, A = 5.351/, Qn = 0.5. When Q > Qc, two-dimensional tunneling trajectories exist in the shaded region between curves 1 and 2. Curve 3 corresponds to synchronous transfer. 

The recent application of hyperspherical and related coordinates to treat the dynamics on a reactive potential energy surface offers, in fact, the possibility of exploring also those regions where reaction paths present sharp curvatures or bifurcations, taking into account of dynamical quantum effects like tunneling and resonances. Several reviews available [4-10] provide a useful introduction to various aspects of the hyperspherical approach. 

However, the restrictions on the dynamics posed by the inclusion of only quadratic terms in the expansion of the perpendicular vibrational motions, the fact that the reaction path itself may be poorly deflned in certain regions, bifurcations of the path should not be overlooked. In such cases it is possible to switch to the reaction surface or the reaction volume methods. These methods are more demanding from the point of view of the potential energy surface and also as far as the dynamical requirements are concerned. But they nevertheless reduce the problem considerably by demanding only the full information in a 2 or 3D space and the harmonic displacement of the spectator atoms connected to the reaction center. 

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