Effect of High-Frequency Modes and Hot Transitions on Free Energy Gap Dependence of Charge Recombination Rate

Abstract

The charge recombination (CR) dynamics of geminate ion pairs formed by excitation of the ground-state donor-acceptor complexes in polar solvent have been investigated within the framework of stochastic approach. It is shown that for low exergonic reactions these dynamics critically depend on the reorganization energy of intramolecular high-frequency mode. Even moderate reorganization energies (0.1-0.2 eV) significantly accelerate the excited-state population decay making it nearly exponential. In the solvent-controlled regime, the majority of the excited donor-acceptor complexes recombine at nonthermal (hot) stage when the nonequilibrium initial wave packet passes through a number of term crossings corresponding to the transitions with creation of several vibrational quanta. Analysis of this mechanism allows to conclude (i) the CR in viscous solvents proceeds much faster than the diffusive relaxation of solvent, (ii) under certain conditions, the CR rate becomes practically independent of the diffusive component of solvent relaxation which is determined by solvent viscosity, (iii) in contrast to predictions of Marcus theory, the CR rate decreases monotonically with the rise of reaction exergonicity even at small free energy gaps, in accordance with experimental results. Two semiquantitative approaches providing rather simple analytical expressions for the hot charge recombination dynamics are suggested. These approximations give a good reproduction of the excited-state decay in the wide area of model parameters.

Charge recombination in excited donor-acceptor complexes with two absorption bands

“…In particular, for reactions in the normal Marcus region, the rate of recombination at the thermal stage can be much lower than at the nonthermal stage because of the higher energy barrier that separates the ionic and neutral states. Although this prediction of model A almost never finds support in experimental data, this by itself is not a strong argument against this model, because the overwhelming majority of transitions can occur at the nonthermal stage; as a result, the thermal stage can be unobservable [11,13].…”

“…This means that we ignore the difference in wave packet motion at the U e 1 and U e 2 terms at times of the radiationless transition between these states. This approximation reduces calculations of the dynamics of charge recombination in the three-level model under consideration to calculations in terms of the two-level model described in detail in [11,13].…”

“…It should, however, be borne in mind that the high-frequency vibrational mode decreases the effective electronic matrix element value at the expense of the Frank-Condon factor. It was shown in [11][12][13] that the overwhelming majority of hot transitions occurred into vibrational states with large quantum number n values, for which the condition of theory applicability V nj < k B T was fulfilled.…”

“…The original model [10] only included the reorganization of classical medium modes and predicted recombination to be strongly nonexponential, whereas an almost exponential kinetics was observed experimentally. It was shown in [11][12][13] that the inclusion of the reorganization of quantum high-frequency vibrational modes of complexes made the kinetics of recombination closer to exponential. It was in addition found that the nonadiabatic model (transitions between diabatic states induced by comparatively weak interactions between them) that took into account the nonequilibrium state of the medium and the reorganization of high-frequency modes (let us call it model A) gave a quantitative description not only of the kinetics of recombination but also of its dependence on the dynamic properties of solvents and the carrier frequency of exciting pulses [13].…”

Contact and Distant Luminescence Quenching in Solutions

“…Not only the reaction coordinate was included in this consideration but also the off-diagonal elements of transfer Hamiltonian instead of the rates of electron transfer. Quite recently, the charge transfer in the donoracceptor complex was studied, accounting for even two reaction coordinates: the fast and slow modes of the polar medium [116]. The implementation of this mechanism into the encounter theory will make it 5-dimensional, allowing one to correctly account for the biexponential dynamic solvent effect.…”