1. INTEGRAL ENCOUNTER THEORY
2. UNIFIED THEORY OF IONIZATION AND RECOMBINATION
3. NON-LINEAR OPTICS
4. HOPPING THEORY OF TRANSFER REACTIONS
 

1. INTEGRAL ENCOUNTER THEORY

The most fundamental achievement of the last few years is a development of a new approach to bimolecular reactions in solutions based on the original ``integral encounter theory" (IET) which is actually a ``memory function formalism" first applied to the chemical kinetics. Within this formalism a number of problems of particular interest were solved that were inaccessible for a conventional rate approach. These are mainly the reactions of electron and/or energy transfer in liquids and solids.

Unlike other approaches of this kind the IET provides the microscopic recipe for the memory function calculation. The latter is defined via position dependent transition rates and the pair distribution functions of the reactants and products. The recipe is exact in binary approximation with respect to reactants participating in bimolecular transfer.

We demonstrated that the conventional (differential) methods of chemical kinetics fail to describe the reversible energy/electron transfer as well as the kinetics of geminate recombination following binary ionization. At least in these two cases there is no alternative to IET which provides us with a new, efficient and universal method of chemical kinetics beyond the rate concept.

The principle advantages of a new approach were illustrated by a number of important applications:

1. The intuitively established ``unified theory" of bimolecular ionization followed by geminate recombination (see below) was rigorously derived from the IET in a particular case of irreversible ionization.
2. If ionization is reversible such a reduction is impossible. Only the IET allows the charge separation quantum yield to be found at any free energy of ionization.
3. Only with IET the entire kinetics of charge accumulation followed by geminate and subsequent bimolecular recombination can be obtained. This has been done for photoionization after instantaneous photoexcitation of the solution and under permanent illumination of the system.
4. The light pumping of arbitrary shape can not be included into rate equations with time dependent constants, but is naturally incorporated into integral kinetic equations. Therefore the theory allows the permanent concentration of charge carriers to be found at stationary light pumping. This has been done for either impurity or biexciton ionization resulting in stationary photo-conductivity of the system.
5. The impurity and biexciton quenching of singlet and triplet excitations parallel to an inter-system crossing were studied as well as triplet-triplet annihilation after quenching. The triplet fusion results in delayed fluorescence through secondary singlet excitation and decay. It was justified that the shortage of near-contact excitations resulting from the preliminary energy quenching may be built into initial conditions for subsequent evolutions of triplets and leads to the ``anti-Smoluchowski " acceleration of diffusional or hopping triplet annihilation.
6. The IET was used to describe the photoconductivity of p-phenilene vinelene (PPV) accompanied by singlet oxygen generation in the polymer. Both singlet and triplet excitations of PPV react with triplet oxygen producing either ion pairs or singlet oxygen, respectively. The stationary concentration of the free carriers was obtained analytically as well as the stationary rate of singlet oxygen generation, suppressed by preliminary quenching of nearest excitations in the course of ionization.
7. The IET was used to calculate the quantum yield of fluorescence quenched by (a) impurity induced intramolecular inter-conversion , (b) itermolecular charge separation followed by their recombination and (c) irreversible intermolecular energy transfer. The conventional convolution recipe which expresses the quantum yield in arbitrary strong pumping light via the system response to d-pulse excitation was confirmed for case (a), but not for other two, although all of them are available for analytical study by means of IET. In cases b and c the qualitative violation of the classical Stern-Volmer law at high intensity of pumping light was discovered. The modified form of this law was proposed instead and the light dependence of the Stern-Volmer quenching constant was determined.

 

 
 
 

2. UNIFIED THEORY OF IONIZATION AND RECOMBINATION

An original ``Unified Theory" (UT) of photochemical ionization followed by their geminate recombination was used to study the Marcus ``Free Energy Gap" (FEG) law in charge separation quantum yield. The UT can be deduced from IET in a particular case of irreversible binary photoionization. The non-monotonous distance dependence of transfer rates in the inverted Marcus region was first included into consideration. It was established that the geminate recombination can be controlled by diffusion as well as bimolecular one,

provided the ions are generated not in the place where they recombine and reaction is limited by a delivery time. Diffusion control makes an essential distortion of the FEG law for recombination which is different in sign for the moderate and high free energies, because the spherical layers, where ions are produced and recombine, interchange their positions with increase of exergonicity of electron transfer..

A number of important extension of the theory was made recently:

1. The role of excitation lifetime in electron transfer reactions was and proved to be very important when ionization is diffusional. The free energy dependencies of ionization and charge separation quantum yields were analyzed as well as the viscosity dependence of the Stern-Volmer constant.
2. The recombination which proceeds via backward proton transfer and results in the neutral radical production was studied. The kinetics of radical accumulation was shown to depend crucially on solvent which prevents the separation of ions (but not radicals) when the solvent polarity is low.
3. The spin states of reactants and ion-radical pairs were included into consideration of charge separation/recombination. It was shown that the kinetics of both stages can be controlled by spin-conversion and the reasonable fit to the real photoionization of Perylene in acetonitrile becomes only possible with the account of spin control of charge separation. This was actually an exit to the spin chemistry as a whole.
4. The UT was also applied to the reaction of photoexcited triplet Ru-trisbipyridine with methylviologen followed by spin conversion to a singlet state of radical ion pair and subsequent spin-allowed recombination which hinders the charge separation. At fast diffusion the spin conversion becomes a limiting stage if not completed during encounter and/or delivery time (from the initial distance to contact). The magnetic field effect on charge separation quantum yield was explained as well as its viscosity dependence which indicates the remote forward and backward electron transfer.
5. The model including creation of the exciplexes due to contact charge separation and their generation through association of solvent separated ion pairs was developed. The spin conversion of singlet ion pairs and their recombination to the ground state as well as the triplet ion pairs to the triplet excited state were included. Two alternative schemes of exciplex production were considered separately and analytical solutions for all the quantum yields were found provided the recombination is contact.

3. NON-LINEAR OPTICS

1. The saturation of the H-bond absorption spectra in a strong laser field was described as a level crossing problem with diffusional motion along the reaction coordinate. The full analogy with kinetics and rate of the intersystem electron transfer is emphasized when vibrational relaxation to the ground state is negligible. The stationary distributions in vibrational levels were found as well as the stationary absorption of the pumping light.
2. There is the loss in the center and gain in the red wing of the absorption spectra of the weak probe, as well as ``bleaching" and ``superabsorption" in the corresponding transmission spectra of probe field. The time evolution of these spectra, after switching the strong field on and off, was studied.

The theory was applied to pump-probe spectroscopy of intramolecular vibration of hydrogen bonded HDO molecules dissolved in H₂O. The parameters of the model extracted from experimental data show that the vibrational frequencies dependence on the hydrogen bridge length saturates, resulting in a suppression of superabsorption . The non-linearity of the frequency dependence may be attributed to either anharmonicity of the vibrational energy levels, or to different curvatures of parabolic levels. The calculated first moment of the ``bleaching" component shifts with time providing the information about the relaxation of H-bond to the equilibrium length. The limiting cases of long and short exciting pulses were investigated. At slow vibrational relaxation the kinetics of the first moment relaxation is similar to that obtained experimentally especially after short pumping. On the contrary, the kinetics of signal accumulation and dissipation is better to study at long pumping when it is closer to stationary response at any time. From this response the signal dependence on light power can be obtained.

4. HOPPING THEORY OF TRANSFER REACTIONS

The original hopping theory was developed further in a few directions:

• The hopping charge recombination was first considered with account for the Coulomb interaction between ions in solvent of low polarity. The rate constant of the process was corrected for the finite Onsager radius at either repulsion or attraction interaction between the reactants.
• The electric field effect on the hopping rate constant of recombination was estimated. It was shown to be different in sign with a similar effect in diffusional recombination. This difference can serve as a criterion for discrimination between alternative reaction mechanisms, hopping and diffusional.
• The impact of an external electric field on electron seizure by neutral traps was studied within the Torrey model of a solvated electron random walk. The step length of the random motion, determined by the free diffusion of a temporarily escaped electron, increases with electric field strength, changing the reaction mechanism from a diffusional to a hopping one.