Conical Intersections Topography

Conical intersections are characterized by their topography.The topography of the PESs in the vicinity of a conical intersection plays a significant role in the efficacy of a conical intersection s ability to promote a nona-diabatic transition. This topography is described to first order by the 

The topography of the cone affects the system s dynamics. Simple classic arguments can rationalize the way topography affects a trajectory Vertical cones facilitate transitions from the upper surface to the lower surface whereas tilted cones are less efficient. Actual quantum mechanical calculations have confirmed these generalizations. The efficacy of a conical intersection in promoting a nonadiabatic transition reflects the topography in the vicinity of a conical intersection.  

The g and h vectors represent nuclear displacements similar to the normal modes of a molecule. As the wavefunctions of the degenerate states can mix arbitrarily, these vectors are not unique. A unitary transformation can be used to rotate them in a way that makes them orthogonal to each other without changing the form of the Hamiltonian. The two vectors then span 

After a system on the higher surface encoimters a conical intersection, it can emerge through the conical intersection to the lower surface. The conical intersection tends to orient the molecular motion in the directions defined by the branching plane. Accordingly, the outcome of a photochemical reaction 

This expression shows that the derivative coupling is inversely proportional to the energy difference between the two states, so when the two states approach each other, the derivative coupling becomes large. At the conical intersection, the energy difference is zero and the derivative coupling becomes infinity. 

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The topography of a conical intersection affects the propensity for a nonadiabatic transition. Here, we focus on the essential linear tenns. Higher order effects are described in [10]. The local topography can be detennined from Eq. (13). For T] = 3, Eq. (13) becomes, in orthgonal intersection adapted coordinates... 

The conical parameters describe the topography of the conical intersection. The directions for g, h, and h relate the abstract x, y, z directions to actual molecular... 

In the nonrelativistic case much has been, and continues to be, learned about the outcome of nonadiabatic processes from the locus and topography of seams of conical intersection. It will now be possible to describe nonadiabatic processes driven by conical intersections, for which the spin-orbit interaction cannot be neglected, on the same footing that has been so useful in the nonrelativistic case. This fully adiabatic approach offers both conceptual and potential computational... 

Yarkony DR (2001) Nuclear dynamics near conical intersections in the adiabatic representation. I. The effects of local topography on interstate transition. J Chem Phys 114 2601... 

The topography of the potential energy surfaces in the vicinity of a conical intersection can also be characterized by the relative orientation of the two potential surfaces, as discussed by Ruedenberg et al.46 In this review we use... 

One important point about photochemical reactions is that state switches between excited states occur in the region of topographies such as the peaked intersection region sketched above (Figure 2.4b). To understand the role of conical intersections in state switches, it is useful to compare the two-dimensional picture of Figure 2.6 with the simple one-dimensional model that is normally used to describe this phenomenon, with the help of an avoided crossing. (One dimensional means here that only one nuclear coordinate, the reaction coordinate, is considered.)... 

S Tnmetric character of i ioa)- In a qualitative sense the phenomenon is generic, however, reflecting the topography of the adiabatic PE surfaces. The wave packet is focused into the conical intersection when moving on the upper part of the cone, while it is pushed away from the intersection when moving on the lower part of the cone. This explains the unidirectionality of the internal-conversion process on the femtosecond time scale. 

Nevertheless, although the characterization of the topography of potential energy surfaces using electronic structure calculations often provides a qualitative understanding of the mechanisms of photochemical transformations, a deeper insight into such processes often requires simulating the dynamics of the nuclei. For instance, it is known that the existence of conical intersections is often reflected in the absorption... 

The diabatic representation can now be used to characterize the topography of the PESs at the vicinity of conical intersections. We first expand the diabatic potential energy matrix elements as Taylor expansions around a reference geometry Jlo... 

Fig. 7.S Classification of conical intersections according to their local topography (from [27,39])...

Fig. 7.6 Different topographies of conical intersections along a reaction coordinate (extended version adapted from [39])...

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