Reaction dynamics symmetry approach

However, we need to go beyond the simpler ideas. Chemical reactions are more complex than the first few sections of this article would suggest. For example, there may be multiple reaction paths (or mechanisms, if you like) for a single reaction there may be multiple symmetry related paths (versions of the same mechanism) for a reaction there may be different reaction paths for different reactions in close proximity on the PES (competing reactions). These macroscopic difficulties for the reaction path concept have echoes even in the simple case of a single reaction path when we consider in detail the shape of the valley walls. In later sections we explore a way in which the reaction path approach forms the nucleus of a more general approach to interfacing ab initio quantum chemistry and reaction dynamics in these more complex scenarios. 

The import of diabatic electronic states for dynamical treatments of conical intersecting BO potential energy surfaces is well acknowledged. This intersection is characterized by the non-existence of symmetry element determining its location in nuclear space [25]. This problem is absent in the GED approach. Because the symmetries of the cis and trans conformer are irreducible to each other, a regularization method without a correct reaction coordinate does not make sense. The slope at the (conic) intersection is well defined in the GED scheme. Observe, however, that for closed shell structures, the direct coupling of both states is zero. A configuration interaction is necessary to obtain an appropriate description in other words, correlation states such as diradical ones and the full excited BB state in the AA local minimum cannot be left out the scheme. 

The descriptions of molecular dynamics and the theory of chemical reactions in gas and condensed phases are based on the concept of potential energy function (hypersurface) [1,2] rooted in the Bom-Oppenheimer (BO) approach [3]. The parametric dependance of the electronic wave function with respect to nuclear coordinates is the basic idea on which the BO framework rest. In this paper, a different approach is taken. The electronic state functions are taken to be independent from the instantaneous nuclear positions. As a first step, we consider molecular systems which are characterized by stationary nuclear configurations belonging to particular symmetry groups. The corresponding electronic stationary states must always transform according to given irreduci-... 

Let us mention some very basic problems to illustrate this point. Consider two ethylene molecules approaching each other for a [2 -F 2] reaction. The answer to the question of whether that reaction is allowed thermally or photo-chemically, or whether a suprafacial or antarafacial process will take place, or whether the reaction will take place at all, is very much dependent on the symmetry of alignment of the two reacting molecules or moieties. The extremes are D2h for a parallel approach and C2 for an orthogonal approach, and it has been predicted successfully that the former is needed for a suprafacial photochemical formation of cyclobutane. Most of the time, however, the two ethylenes are not in an ideal Djh arrangement. This may be due to an intramolecular frozen conformation of the two double bonds, to non-symmetric sterical hindrance caused by substituents on the double bond, and to the dynamical nature of the system (rotations and translations, especially in viscous media). 

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