What Defines The Activation Energy of Electron Transfer: Reorganization Energy or Electron Coupling?

M.G. Kuzmin

XVIIth IUPAC Symposium on Photochemistry, Dresden, German, July 22-27, 2000, Book of Abstracts, p. 372.

ABSTRACT. Marcus theory of electron transfer implies rather weak (<0.05eV) electronic coupling between initial (locally excited, LE) and final (electron transfer, CT) states and presumes that the transition state is close to the crossing point of LE and CT terms. The value of electron transfer rate constant ket is controlled by the activation energy DG# which is a function of the reorganization energy (l/4) and electron transfer driving force DGet: ket = k0exp(-DG#/RT) and DG# = (l/4)(1+DGet/l)^2. For organic molecules reorganization energy was found to be in the range 0.1-0.3eV.

But electronic coupling of LE and CT states should decrease significantly the energy of the transition state since electronic coupling matrix element for excited charge transfer complexes (exciplexes) was found to be in the similar range 0.1-0.3eV. Therefore activation enthalpy of electron transfer should be considerably lower than the reorganization energy because of the stabilization of a transient with partial charge transfer.

Experimental data on activation energies of excited states quenching and radical ions formation confirm this concordant mechanism of excited-state electron transfer. The apparent excited-state quenching rate constant in the Marcus model is given by:

kq = kass/(1 + ket/ksep) = kass/[1 + (k0/ksep)exp(-DG#/RT)],

where kass and ksep are the diffusion association and separation rate constants, respectively. For transient exciplex formation (concordant electron transfer and reorganization) mechanism kq can be expressed as a function of Gibbs energies of electron transfer DGet and exciplex formation DGEx:

kq = 1/(1/k1 + t'/KEx) = k1/{1 + 1/[exp(-DGet/RT) + a*exp(-DGEx/RT)]}

Here KEx and k1=kass equilibrium constant and rate constant of exciplex formation, respectively, t' is the exciplex lifetime, and a = kd/k0 is the ratio of the exciplex deactivation (internal conversion and intersystem crossing) rate constants and preexponential factor for exciplex dissociation into free radical ions. In turn, DGEx depends on DGet, electronic coupling matrix element H12, and medium polarity.

Formally, the dependences of kq on DGet are similar in both models but the concordant reorganization model expects sufficiently lower (or even negative) apparent activation enthalpy (DHEx < DH# < l/4), slower decrease of excited state quenching rate constant in the region DGet > 0, enhanced triplet yield, and considerable decrease of radical ion yield at DGet > DGet > 0. Experimental data are consistent better with the concordant ion yield at DGet > reorganization model rather than with the Marcus model.

Laboratory of Photochemistry