Conical intersections formulation

The radical anion dissociation conical intersection formulation described here seems reasonably complete for a solution environment, at least for the molecule considered. Naturally, refinements of the treatments of the electronic structure and the cavities could be considered, as was mentioned near the conclusion of the Introduction. However, as was noted in the Introduction to Section 3.7.2, other environments, e.g. DNA, are also of interest. Here one could pursue the development of a Poisson-Boltzmann type of description [100] for the inhomogeneous environment. 

The reverse reaction, closure of butadiene to cyclobutene, has also been explored computationally, using CAS-SCF calculations. The distrotatory pathway is found to be favored, although the interpretation is somewhat more complex than the simplest Woodward-Hoffinann formulation. It is found that as disrotatory motion occurs, the singly excited state crosses the doubly excited state, which eventually leads to the ground state via a conical intersection. A conrotatory pathway also exists, but it requires an activation energy. 

The initial systematic introduction of the model into photochemistry is now nearly two decades old [2-5]. More recently, the model has been elaborated [1,6,7] and its utility for the prediction and rationalization of geometries at which Sq - conical intersections occur has been recognized [1,6-8]. While most of the standard expositions have concentrated on the orbital and configuration (in this case, geminal) space as opposed to the spin space part of the electronic problem, one of the two early reviews treated spin-orbit coupling as well and formulated useful general rules [2] which have since found support in ab initio calculations [9]. 

Minimization of Vi subject to the geometric constraints, Eq. (16), and requirement that the point lies on the seam of conical intersection, Eq. (18), can be formulated using Lagrange mulipliers. The desired point of conical intersection is an extremum of the following Lagrangian ° ... 

Another important topological feature, which is obviously absent from the above single-valued formulations, is the conical intersection between the two lowest " A adiabatic potential energy surfaces. A two-valued potential energy surface, which describes such a conical intersection is due to Hirsch et It is obtained by diagonalizing a 2 x 2 potential matrix, with... 

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