Bifurcation point, reaction coordinate

The potential (6.37) corresponds with the previously discussed projection of the three-dimensional PES V(p,p2,p3) onto the proton coordinate plane (pi,p3), shown in Figure 6.20b. As pointed out by Miller [1983], the bifurcation of reaction path and resulting existence of more than one transition state is a rather common event. This implies that at least one transverse vibration, q in the case at hand, turns into a double-well potential. The instanton analysis of the PES (6.37) was carried out by Benderskii et al. [1991b], The existence of the onedimensional optimum trajectory with q = 0, corresponding to the concerted transfer, is evident. On the other hand, it is clear that in the classical regime, T > Tcl (Tc] is the crossover temperature for stepwise transfer), the transition should be stepwise and occur through one of the saddle points. Therefore, there may exist another characteristic temperature, Tc2, above which there exists two other two-dimensional tunneling paths with smaller action than that of the one-dimensional instanton. It is these trajectories that collapse to the saddle points at T = Tcl. The existence of the second crossover temperature Tc2 for two-proton transfer was noted by Dakhnovskii and Semenov [1989]. 

As a conclusion it should be borne in mind that the simultaneous existence of the bifurcation point on the reaction coordinate and the Jahn-Teller effect imply most probably the impossibility of the formation of even slightly regular polymers in the free-radical polymerization of quasisymmetric monomers, at least at temperatures which are not very low. 

Care should be exercised in using both IRC and DRC calculations. Certain high-symmetry systems may have bifurcation points on the potential energy surface in which alternative paths are available. If such forks in the reaction coordinate exist, the final geometry resulting from two superficially similar calculations may be very different. 

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. 

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