Is energy transfer nonadiabatic or adiabatic?

[HAYAO]

Many textbook, particularly Forster Resonance Energy Transfer shows a diagram where transition of a donor nonradiatively excites an acceptor in the dipole interaction scheme. When considering spectral overlap, they explain the overlap of the phonon-sidebands of the two species. This seems to me like an adiabatic representation.

However, there is also another picture, the initial state transitions to the final states through the PES. Most likely at the intersection of two states, the PES is going to have nonadiabatic contribution because BO or BH approx fails. This seems to me like an nonadiabatic representation.Both seems reasonable to me, and I cannot judge which is the correct picture (or perhaps both is right). I feel that the both pictures include different levels of approximation. Fundamentally speaking, FRET or Dexter (and also dipole-quadrupole, magnetic dipole-electric dipole, anything) is an approximated picture. FRET and Dexter mechanism comes from direct Coulomb and exchange matrix element. So which is right? Are both right? At what circumstances are each of them right?

 

[jim mcnamara]

It might help if you can post the exact place the diagram (a page number) occurs and the title and edition of your text. Really clear questions get better answers.
As an aside, I once had a second-hand chemistry text that turned out to have out-of-date information and caused me to become really confused. So, knowing exactly what you are looking at, in both of your examples, will help. Thanks.

 

[TeethWhitener]

However, there is also another picture, the initial state transitions to the final states through the PES. Most likely at the intersection of two states, the PES is going to have nonadiabatic contribution because BO or BH approx fails. This seems to me like an nonadiabatic representation.

Do you have a reference for this picture? I'm more familiar with the first picture. Basically the wavefunctions (excited donor/ground acceptor) and (excited acceptor/ground donor) are coupled by a dipole-dipole interaction matrix element. (Once again, Tokmakoff to the rescue):
http://home.uchicago.edu/~tokmakoff/TDQMS/Notes/12.1. Forster.pdf
I'm not sure where there would be a non-adiabatic intersection of states in this picture.

Edit: I think we're going to get into the definition of "what is adiabatic/non-adiabatic" as we've done before, so best to clarify what exactly you mean by that at the outset. My "non-adiabatic" above would refer to nonzero coupling of electronic and vibrational states.

 

[DrDu]

Fundamentally, FRET involves the coupling of the states of two molecules by the long range Coulomb interaction. The coupling is quite small so that a transition will only be possible, when the nuclear configuration is such that the BO adiabatic states of the isolated molecules are degenerate. If there were no coupling, the PES corresponding now to the electronic states of the isolated molecules would intersect and the nuclear motion would follow the diabatic PES, not the adiabatic ones. I.e. without coupling the dynamics is non-adiabatic. When the coupling is included, we get an avoided intersection and the process has a small probability to remain on the adiabatic PES. That's when FRET takes place. Hence FRET is an adiabatic process. A description in terms of phonon sidebands uses a crude adiabatic picture, i.e. the electronic wavefunctions do not depend on the nuclear coordinates but are evaluated at only one definite position of the nuclei (usually the equilibrium position of e.g. the initial state). Whether a process is adiabatic or non-adiabatic is not clear in this picture.

 

[HAYAO]

First of all, I am extremely sorry for the late reply. I got my Ph.D. and I was moving to a different college and had no (good) access to the internet.

I am sure most of the people here is familiar with the first picture (i.e. dipole-dipole interaction scheme), but the latter picture is used for example in this paper:
M. Hatanaka and K. Morokuma, J. Chem. Theory Comput. 2014, 10, 4184–4188.

Basically the wavefunctions (excited donor/ground acceptor) and (excited acceptor/ground donor) are coupled by a dipole-dipole interaction matrix element. (Once again, Tokmakoff to the rescue):
http://home.uchicago.edu/~tokmakoff/TDQMS/Notes/12.1. Forster.pdf
I'm not sure where there would be a non-adiabatic intersection of states in this picture.

The two dimensional potential energy curve figure in that text contain two different x-axis (i.e. Q_D and Q_A), so we cannot judge from that picture whether there is an intersection(s) or not. The entire (multi-dimensional) PES may have intersection when the x-axis is taken as the reaction coordinate. I was not very sure whether this intersection may be the place where BO fails and the non-adiabatic transition occurs (meaning electronic and vibrational states are coupled around that intersection and produces nonadiabatic PES).DrDu's reply seems to answer my question, though. I am extremely grateful for your answers.

 

[DrDu]

You got your PhD? Congratulations then!

 

[TeethWhitener]

I got my Ph.D.

Congratulations!

 

[jim mcnamara]

Yes, definitely - congratulations!