An important except is benzene. In the lowest excited state the b2u vibrational mode increases in frequency by about 20 per cent. This has a natural explanation in terms of valence bond theory (see figure below) and is discussed in a Accounts of Chemical Research paper by Shaik, Zilberg, and Haas.
The ground state (which has A1g symmetry) can be described as a linear superposition of two valence bond structures, Kr + Kl.The lowest excited state (which has B2u symmetry) can be described as the antisymmetric superposition, Kr - Kl.
The b2u distortion couples linearly to the energy of Kr and Kl near the degeneracy point. This leads to the curves shown above.
It is clear that the b2u vibrational mode will have a higher frequency in the excited state than the ground state.
High-level quantum chemistry calculations support this simple picture, which underscores the importance of using the appropriate Hilbert space to describe strongly correlated systems.
I have been thinking a lot recently of the two-state VB crossing models put forward by these authors, particularly as relates to theories of activated chemical processes (for example, Shaik & Reddy's "Avoided Crossing State" model). In particular, it is interesting to contrast these with models advocated by Levine & Agmon (e.g. Chem. Phys. Lett. 52 (1977) 197-201, and subsequent works by both authors).
ReplyDeleteIn the latter model, the states are not wavefunctions (VB or otherwise), but are the vertices of a convex set. The set can be modelled with numbers, but in principle could be commuting density matrices. The barrier arises in these models as a term that is the mixing entropy along the interpolation between the vertices.
Interestingly, both the Shaik/Reddy VB model and the Levine/Agmon mixing coordinate model can explain the Hammond-Leffler postulate relating the total change in free energy to the "position" of the activated state. But, it is clear that they are very different because in the Levine/Agmon model the barrier arises from entropy (i.e. an information lack), whereas the Shaik/Reddy model explains the barrier by postulating new information, in the form of an interacting VB state.