Potential Energy Surface Crossings in Organic Photochemistry is a nice introductory review article from 1996 by Bernardi, Olivucci, and Robb. It is particularly helpful because it was only at that time that both experimental and computational evidence that

**conical intersections**are quite ubiquitous in large molecules and key to understanding mechanisms of non-radiative decay.

They stress how originally it was thought that photochemistry proceeded via coupling of vibrational states rather than via coupling of electronic states.

How do conical intersections arise? The review points out that often conical intersections occur when a molecule relaxes to a geometry that has a local triangular symmetry (i.e. there is an equal coupling between three electronic states). This means there is a C_3 symmetry and the two degenerate eigenstates belong to the two-dimensional E representation.

I find very helpful a J. Phys. Chem. A paper Locating Electronic Degeneracies of Polyatomic Molecules: A General Method for Nonsymmetric Molecules by Zilberg and Haas. A paragraph is below

It is not clearly stated, but the matrix has a C_3 symmetry and the eigenstates are in the A and E representations. The latter are two-fold degenerate.

The figure above is taken from a review by Klessinger.

...but the coupling between electronic states is zero at intersection! I thought the coupling was neither electronic nor vibrational but VIBRONIC. Doesn't the coupling also vanish between the purely vibrational states (by energy conservation, a zero gap in on both sides of the bipartition would be needed, right)? The coherence leading to transfer should be carried by the electron-nuclear entanglement, and vanish in the observable algebras defined on the separate, disjoint subsystems...

ReplyDeleteHi Seth,

ReplyDeleteI wonder if I should have been more precise and whether it as complicated as you suggest.

I agree the coupling between the two (diabatic) electronic states is zero at the intersection. But I thought the point was that system just "sails through" the intersection staying on the same diabatic state surface. That is the key dynamics not coupling of vibrational states on different adiabatic potential energy surfaces.