The challenge of excited state proton transfer

What is excited state proton transfer (ESPT)?
Consider a hydrogen bond A-H...B in a molecular system.
Suppose the system absorbs a photon (usually in the visible to near UV range) and undergoes a transition to an electronic excited state. In most cases A-H is an organic molecule containing conjugated bonds and the transition is a pi to pi* transition. Then on the time scale of picoseconds [within a factor of one thousand] the proton transfers from the donor A to the acceptor B,
i.e. (A-H)*...B evolves to something like (A-)*...(H-B)+.
If A and B are part of the same molecule then this is intramolecular ESPT.
If A and B are distinct molecules then this is intermolecular ESPT.
If A-H is dissolved in water, and significant ESPT occurs then A-H is called a photoacid.

I have started to work on this rich and diverse subject.

My goal is to develop several simple diabatic state models that might give a more unified picture of the phenomena and provide some physical insight. Given the chemical complexity, this may be a mistake, reflecting a physicists naivety and/or hubris. But I am encouraged by the "success" of the simple two diabatic state model that I have promoted for hydrogen bonding (and proton) transfer in the ground state.

I am working my way through the extensive chemical literature and so here is my attempt to organise some of what I have learnt. Comments and corrections are particularly welcome.

In a short review [focusing mostly on solvent effects] from 1986 Michael Kasha presented the following picture. It shows the energy of the ground state (S_0) and the excited state (S_1) as a function of the hydrogen co-ordinate Q_H. For example this might be an OH stretch.

One can clearly see that in the excited state proton transfer is both energetically and kinetically more favourable. What might a diabatic state model look like?
The ground state surface could be described in terms of the usual two diabatic states: A-H,B-  and
A-,H-B.   Similarily the excited state surface could be described in terms of a separate but analogous model involving two diabatic states that differ by transfer of a proton.
The difference between the two models is simply the relative energy of the two diabatic states, i.e. the relative proton affinity of the donor and acceptor is reversed between the ground and excited states.
Furthermore, the barrier to proton transfer could be reduced, or even removed, if the coupling of the two diabatic states increases in the excited electronic state. This could happen if the donor-acceptor distance is reduced in the excited state.

This natural "explanation" of ESPT was widely promoted for a long time, probably going back to Weller in 1952. The basic idea is that in the excited state there is charge redistribution leading to weakening of the O-H bond, making it easy for the H to "pop off". A related claim is that in a photoacid the pKa of the excited state is much less than that of the ground state.

However, there are multiple problems with the picture presented above.

A. It is arguably not really an explanation but a description. It almost says "ESPT happens because ESPT happens." Specifically, it does not really explain why the relative energy of the donor and acceptor diabatic states reverses upon photo excitation.

B. It assumes there is no relationship (or interaction) between the ground and excited electronic states. In reality they can be intimately connected. Striking examples include that of twin states or resonance assisted H-bonds, such as in malonaldehyde.

C. Based on the energy surfaces above Forster presented a simple equation relating the S0-S1 energy difference (and the associated absorption and emission frequencies) between the two tautomers [i.e. molecules differing in the location of the proton] and the pKa's [a measure of acidity] in the ground and excited states.

However, Tolbert and Solntsev report many violations of this equation.

D. Actual high level quantum chemistry calculations for specific molecules that do exhibit ESPT do find that for some there is little charge redistribution in the excited state relative to the ground state; or more importantly, the proton affinity does not necessarily change significantly.

E. It may be omitting a role for different excited states (e.g. charge transfer states or n-pi* states) and conical intersections.

D. and E. are emphasised this calculation by Grannuci, Hynes, Milli, and Tran-Thi.

E. is emphasised by Sobolewski and Domcke who present the diabatic state picture below for cases where the proton transfer is coupled to an electron transfer.

A particularly interesting and widely studied case of ESPT is in the green fluorescent protein (GFP). More on that later...

I thank Seth Olsen for introducing me to some of the literature. If some of the above is not as coherent as it might be that is because of my limited reading and understanding. But, I think it also reflects the diversity of the subject and the lack of a comprehensive picture.

I welcome comments.