Bifurcating energy surface

After 28 years the perepoxide quasi-intermediate was supported by a two-step no intermediate mechanism [71, 72]. The minimum energy path on the potential energy surface of the reaction between singlet molecular oxygen ( A and dg-teramethylethylene reaches a vaUey-ridge inflection point and then bifurcates leading to the two final products [73]. 

The potential energy surfaces of the reactions in equations 10 and 11 are more complex than that of equation 14 and involve reaction path bifurcation and low symmetry structures in each channel. The salient features of structures of these complexes and TSs are shown... 

Siebert, M. R. Zhang, J. Addepalli, S. V. TantiUo, D. J. Hase, W. L. The need for enzymatic steering in abietic acid biosynthesis Gas-phase chemical dynamics simulations of carbocation rearrangements on a bifurcating potential energy surface, J. Am. Chem. Soc. 2011,133, 8335-8343. 

The HjO HP-HF complex was reexamined more recently in conjunction with a comparison with H O H O -HF. The focus of this work was an exploration of the potential energy surface to identify all the local minima. In addition to the cyclic structure of Fig. 5.27, a bifurcated geometry, in which the water serves as double proton acceptor, was also located as a minimum of the PES of H O -HF—HF. In the complex containing a pair of water molecules and one HF, the only minimum located was of cyclic type. Both of these structures are illustrated in Fig. 5.28. 

The failure to achieve selectivity in this model system can be traced to the dynamics on the anharmonic excited-state surface, and, in particular, the wavepacket bifurcation. This observation motivated us to explore more systematically the features of the excited-state potential energy surface and excited-state wavepacket dynamics that are compatible with the proposed selectivity scheme. 

Whereas the equilibrium structure itself is pretty much agreed on for the water dimer, there are a number of other geometries that one might suppose should be comparable in energy. For example, the notion of a cyclic structure has been advanced over the years as have various types of bifurcated geometries. Smith et al. recently completed the most comprehensive survey of the ab initio potential energy surface of the water dimer to date. They examined the question of a number of possible minima on the surface and potential transition states that connect them. 

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. 

Figure 9. Energy surface for two degrees of freedom which exhibits a bifurcation of a single valley. The data were produced using a modified form of model functions presented by Valtazanos and Ruedenberg [67].

At E = 0, the formerly disconnected components merge (the energy surface bifurcates), and for E > 0, the energy surface has locally the structure of... 

---