A. I. Burshtein

Non-markovian theory of diffusion-controlled excitation transfer

Abstract The non-markovian encounter theory is extended to kinetic calculations of an exciton (electron) contact transfer between an energy (charge) donor and acceptor. This process is shown to be non-stationary from the beginning to the end if the donor state relaxation time is shorter than the encounter time. The theory is applied to calculations of hot luminescence quantum yield in liquid solutions with a quenching impurity.

Geminate recombination after binary photoionization

Abstract A kinetic law is derived for geminate recombination which results from binary encounters of photoexcited donor with electron acceptors in liquid solution. The initial distribution over ion pair separation is found for both slow and fast ionization. When ionization is controlled by diffusion, the spherical reaction layer, where ions are mainly born, is shown to have a greater radius than the closest-approach distance.

Hot recombination of photogenerated ion pairs

The recombination dynamics of ion pairs generated upon electron transfer quenching of perylene in the first singlet excited state by tetracyanoethylene in acetonitrile is quantitatively described by the extended unified theory of photoionization/recombination. The extension incorporates the hot recombination of the ion pair passing through the level-crossing point during its diffusive motion along the reaction coordinate down to the equilibrium state. The ultrafast hot recombination vastly reduces the yield of equilibrated ion pairs subjected to subsequent thermal charge recombination and separation into free ions. The relatively successful fit of the theory to the experimentally measured kinetics of ion accumulation/recombination and free ion yield represents a firm justification of hot recombination of about 90% of primary generated ion pairs.

Integral encounter theories of multistage reactions. I. Kinetic equations

The matrix kinetic equations for multi-stage reactions in liquid solutions are derived using a newly developed original method based on a many-particle master equation. The method leads to an infinite hierarchy for vector correlation patterns that can be truncated two different ways. The simplest one reproduces the conventional Integral Encounter Theory (IET), while the other allows a general modification of the kernel, resulting in the matrix formulation of so called Modified Encounter Theory (MET). Unlike IET, MET accounts for all binary contributions and correctly restores the long-time asymptotics of bimolecular reactions. The matrix MET, applied in Part II to reversible reactions of inter-molecular energy transfer, significantly improves the results obtained with other methods.

Universal binary theory of photochemical charge separation and distribution

Using integral formalism we developed the encounter theory of reversible photoionization followed by charge recombination. This is a problem that can not be approached with conventional (differential) formalism, unless ionization is highly exothermic and thus irreversible. In this limit, the integral theory supplemented by the recipe for calculating the ion distribution may be successfully reduced to the differential theory used in our previous work. However, there is no alternative to integral theory when ionization is quasiresonant and the back electron transfer to the excited state should be accounted for. Using the contact approximation we calculated the free-energy dependence of the Stern-Volmer constant of reversible photoionization accompanied by charge recombination.

Inter-system crossing catalyzed by solute encounters

We studied the reversible transitions between two levels of excited molecule stimulated by encounters with other solutes. The inter-system crossing results in either quenching or trapping of excitation depending on the relationship between the lifetimes of the levels. In the particular case of an immobile excited molecule and equal lifetimes, an exact solution of the problem was given which is valid for arbitrary concentration of solutes. We compared the fluorescence quantum yield obtained with this solution, superposition approximation and integral encounter theory. Our main conclusion is that for equal lifetimes the latter has an advantage, even in small concentration limits and is out of competition when the lifetime of the primary excited level is shorter than another.

Kinetic and diffusional control of geminate recombination

A study is presented of geminate recombination and separation kinetics and their rates in liquid solutions. Applicability limits are proposed for the ‘‘exponential model’’ of this process, which is widely used for interpreting experimental data on back‐electron transfer following photoionization. It is proved that this model qualitatively contradicts an analytical description of the process in polar media. A numerical experiment shows that the exponential model may be used only for nonpolar media of moderate viscosity. In this case the separation rate is linearly connected with the recombination constant and may be used to check the energy gap law characteristic for electron transfer.

Spatial dispersion of electron transfer probability

Abstract Recombination and ionization rate constants were calculated taking into account the spatial dispersion of reaction free and reorganization energies. The conditions were found under which the reactions are contact and the contact estimation of their rate is invalid. The spatial dispersion of transfer probability was shown to be responsible for the smoothing of the multichannel structure of the free energy “gap” dependence of the rate constant.

Accumulation and distribution of energy quenching products

Abstract The quantum yield of irreversible energy quenching, as well as the accumulation and distribution of its products, were studied by means of differential and integral encounter theories and a competing approach based on the superposition approximation. The lower-order concentration corrections to the Stern–Volmer constant are found, but only the non-binary contributions to them are different. Such a difference between the theories was shown to have an impact on the accumulation and final distribution of the charged products, especially at short distances. This effect is of principle importance but does not affect significantly the main results of any encounter theory.

Diffusional distortion of the free‐energy gap law

The free‐energy gap law in back electron transfer reactions is shown to be affected by encounter diffusion in photogenerated ion pairs. The ion separation quantum yield increases when initial separation of ions is large compared to the radius of the reaction layer and decreases in the opposite situation when ions are created in contact but recombine outside. The effect changes the sign with free energy when passing from the normal region of recombination to the inverted one. As a result, the top of a bell‐shaped curve representing the free‐energy gap law is subjected to qualitative distortion, which is stronger when diffusion is slower.