Bifurcation point, dimers

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 PES of the water dimer system is characterised by three main stationary points the "quasi-linear" structure, representing the global minimum (Fig. 11), and the cyclic and bifurcated configurations (saddle points). 

Figure 4.19 Bifurcating PES for the dimerization of cyclopentadiene. Heavy black lines are two trajectories that lead from the Diels-Alder bispericyclic TS 77 to the valley-ridge inflection (VRI) point and then diverge, one into the well of product 76a and one into the well of product 76b.

Gas-phase spectroscopic measurements [115] had been unable to clearly determine the structure of the H2S dimer, but had offered the suggestion of a linear or bifurcated geometry. Frisch et al. [94] compared these two theoretically and found indications that the bifurcated structure represents a transition state on the surface, about 1 kJ/mol higher in energy than the linear structure. The dimer is only very weakly bound, by less than 6 kJ/mol and by an even smaller amount (3.3 kJ/mol) when zero-point vibrational energies are considered. Accentuating the weakness of the interaction, the S S distance was calculated to be quite long at 451.4 pm. 

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