Symmetry-required conical intersections

For the s Tnmetry allowed conical intersection and the symmetry required conical intersection as well (the definition due to Yarkony, see Ref. [117]), the mechanism of converting conical intersection to avoided crossing and the role of the laser have been thus evident. Yet, even for other types of conical intersection, the conversion of conical intersection by an appropriate choice of VE(i2, t) may be possible depending on the electronic-state origin [316] of the appearance of the degeneracy. Therefore the idea of laser conversion of conical intersection is worth further investigation both experimentally and theoretically. 

Symmetry-Required Conical Intersections The Jahn-Teller Effect... 

The Sx and Sy, Agh and Sgh describe the tilt, asymmetry and pitch of the double cone, and Sy describe the tilt of the principal axis of the cone. Agh describes the asymmetry in the pitch of the cone, which is measured by 6gh- The electronic state symmetry classification of the conical intersection is reflected in these topographical parameters. The syirmietry required double cone characteristic of the extensively studied Jahn Teller problem " has Sx = Sy = 0, and g = hhy symmetry so that q = g and Agh = 0. It is therefore a vertical (non-tilted) symmetric, Agh = 0) cone. For the accidental symmetry-allowed conical intersection only Sy... 

The prompt dissociation of the fast H atom in the pathway, for which character change and collapse of the 3s Rydberg orbital on the ethyl radical to the Is orbital of the H product are required,121-123 could be assisted by the conical intersection. Also, relaxation and internal conversion from the 3s state to the ground state ethyl can be facilitated by this conical intersection, in addition to other possible vibronic couplings in the A symmetry.39... 

The expression avoided state touching (crossing) can refer to one of two situations (Salem et al., 1975). First, an avoided touching can be encountered along paths that pass close to a real state touching but miss the tip of the cones and do not quite reach the required values of Xy and Xj to enter the (F - 2)-dimensional intersection coordinate subspace. An example would be a path that does not quite preserve the high symmetry that is characteristic of some conical intersections. Second, it can be encountered upon improvement of a simpler quantum mechanical approximation in which a... 

The search for conical intersections, avoided crossings and seams of intersection between two PESs are also tasks involving optimization [115-123]. If the two surfaces represent different spin states or have different spatial symmetry, they can cross. If they are the same symmetry and spin, they can interact and the crossing is avoided. Where the matrix element coupling the two surfaces is zero, they touch and give rise to a conical intersection, as illustrated in Eig. 10.3. To study the mechanisms of photochemical reactions, we often wish to hnd the lowest energy point on a seam or conical intersection. For a seam of intersection between two adiabatic surfaces and E2, we require ] = Ei-Since a (non-linear) molecule has 6 internal degrees of freedom, a seam of... 

Intersections are symmetry-required when the two electronic states form the components of a degenerate irreducible representation. The Jahn-Teller intersection of the two lowest electronic states in Nas which correspond to the components of an E irreducible representation of the point group Csv, provides an example of this class of conical intersection. Conical intersections which are not required by symmetry are accidental intersections. Accidental symmetry-allowed different symmetry) intersections correspond... 

Prom Table 1, it is seen that there is more than one type of conical intersection. For molecules with even (odd) / = 2 (77 = 3 or 5). The origin of the differences is, as explained by Mead, time reversal symmetry. For odd (even) and are (are not) linearly independent. Here T is the time reversal operator. See appendix A. Thus for odd (even) electron systems, the intersection of two potential energy surfaces requires the degeneracy of four (two) electronic states. As discussed below, this leads to the values of 77 reported in Table 1. 

Here the nonrelativistic (Coulomb, r] = 2) and relativistic (Coulomb - -spin-orbit, = 3) seams of conical intersection are compared. In Cg symmetry, there are 5 symmetry preserving internal coordinates. The seam conditions, the conditions that require X to be a point of conical intersection, define r] internal coordinates. Thus there is a many-to-one association of nonrelativistic and relativistic seam points. This many-to-one association can be reduced to one-to-one association by comparing the lowest energy point of conical intersection for a fixed-value of the H -H distance, — H ), see Fig. 8(a) for atom labelling. Below we show that this approach results in meaningful comparisons. 

---