Reaction paths, potential energy surfaces bifurcations

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... 

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. 

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. 

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. 

Branching of the minimum energy reaction path into two different paths at a certain point (bifurcation point) on the potential energy surface. 

Carrington and Miller (235) developed a method called the reaction-surface Hamiltonian for reactions with large amplitudes perpendicular to the reaction path and for some types of reactions with bifurcation of the reaction path. In contrast to the reaction-path Hamiltonian method, in the reaction-surface Hamiltonian method two coordinates are extracted from the complete coordinate set. One coordinate describes motion along the reaction path and the second one describes the large-amplitude motion. Potential energy in space of the remaining 3JV — 8 coordinates perpendicular to the two-dimensional reaction surface is approximated by quadratic functions. It... 

A problem that sometimes occurs in reaction-path Hamiltonians, especially for bend potentia1s, is the bifurcation of the reaction path. This occurs when a harmonic frequency becomes imaginary, and for the Raff surface this occurs for bends on both sides of the saddle point. initio calculations can be helpful in determining if the bifurcation is an artifact of the form of the analytic potential function or if it is present in the actual system. When the MEP bifurcates it is probably best to base the RPH on a reference path centered on the ridge between two equivalent MEP s. l This requires extra effort when computing vibrational energy levels since the vibrational potential becomes a double-minimum one, but it probably reduces mode-mode coupling, which (see Sect. 2) is hard to treat accurately. 

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