Free-Energy-Gap Law for Ultrafast Charge Recombination of Ion Pairs Formed by Intramolecular Photoinduced Electron Transfer

Abstract

In this article, regularities of ultrafast charge recombination (CR) kinetics in photoinduced intramolecular electron transfer in polar solvents are studied. The kinetics of charge separation and ensuing ultrafast CR are simulated within the framework of the multichannel stochastic model. This model accounts for the reorganization of both the solvent and a number of intramolecular high-frequency vibrational modes. The solvent relaxation is described in terms of two relaxation modes. For ultrafast CR, the free-energy-gap law strongly depends on the parameters: the electronic coupling, reorganization energy of intramolecular high-frequency vibrational modes, and the vibrational and solvent relaxation times. The semilog dependence of the CR rate constant on the free-energy gap varies from a parabolic shape to a nearly linear one with increasing the electronic coupling and decreasing the vibrational relaxation time. The dynamic solvent effect in CR is predicted to be large in the area of strong exergonicity and small in the area of weak exergonicity. This regularity is opposite to that observed for the thermal reactions.

Equivalence between inverted regions of the energy gap law and inverted regions of donor–acceptor distances in photoinduced electron transfer processes in flavoproteins

“…Reliability of our method of ET analyses in flavoproteins is discussed in the previous work. 36 EXDL profiles often show a parabolic behavior when ET rates are faster than ca. 1 ps −1 .…”

“…However, it is also known that the ln Rate vs. standard free energy gap (SFEG) relationship displays parabolic functions, which is called the energy gap law (SEGL). [33][34][35][36] The region of ÀSFEG (negative value of SFEG) greater than that at the maximum value of ln Rate is called the inverted region of SEGL (E-inverted region). It is evident that both the parabolic relationships originated from the Marcus ET theory.…”

The Efficiency of Photoinduced Intramolecular Charge Separation from the Second Excited State: What Factors Can Control It?

“…As a result, the cross-point of G CSS and G LES1 here lies to the left of the G CSS FES minimum so that the CSS wave packet undergoes charge recombination to LES1 before its thermalization. Such non-equilibrium CT in the Marcus normal region is generally ultrafast and occurs on timescales of several picoseconds and even faster. − …”

Modeling Kinetics of Ultrafast Photoinduced Intramolecular Proton-Coupled Electron Transfer

“…The theories describing proton/electron transfer in terms of the thermal rate constant are applicable for the description of the reactions which are significantly slower than the vibrational and solvent relaxations. Ultrafast reactions proceed on timescale of nuclear relaxation and nonequilibrium of the solvent and intramolecular vibrational modes can be of paramount importance. − Thus, theoretical treatment of ultrafast reactions has to include nonequilibrium of the nuclear subsystem formed by an excitation pulse and specific stages of a complex reaction. Ultrafast stages of the reactions proceed in parallel with the relaxation of the nonequilibrium state created at the previous stage, and hence, the memory about it is preserved.…”