We investigate two forms of macroscopic kinetic equations for evaluation of different reaction rate constants for irreversible unimolecular reactions in liquids. The steady-state differential and integral equations for calculation of the rate constants were formulated. New forms of the Green's function, the steady-state Green's functions, convenient for calculation of the rate constant, were introduced and their physical meaning was established. The concept of the mean first passage time (MFPT) was generalized from the ''MFPT to a point'' to the definition of the ''effective MFPT''. The effective MFPT was defined as the average time for particles to reach a region on the surface, rather than a point. Applications of the steady-state Green's function method as well as the effective MFPT concept are shown for one- and two-dimensional potential surface reactions. The rate constant for the one- and two-dimensional harmonic oscillator and bistable potentials are presented for all barrier heights.

The effect of solvent and intramolecular dynamics on the rate of a bond breaking electron transfer reaction is investigated. The reaction takes place on a two-dimensional potential energy surface with one coordinate the solvent’s polarization and the other the breaking bond’s displacement. The dynamics are governed by overdamped spatial diffusion along the polarization coordinate and by energy diffusion along the bond coordinate. A scheme is presented that treats the transition from rate control by the equilibrium rate constant kr (as evaluated by, e.g., a Golden Rule calculation) to dynamical control, where the rate is controlled by diffusion on the surface, with rate constant kd, that accounts for the different character of the dynamics in the two directions. The overall rate constant has the form appropriate to a consecutive reaction mechanism: k−1=k−1d+k−1r. The kd rate constant is analyzed numerically and the results compared with a number of approximation schemes. A method of analysis is developed for situations where one dynamics is fast/slow compared with the other. Which time controls kd depends strongly on the relation between the fast diffusion rate and kr.

A theoretical model based on the assumption about different rates of electron tunneling from different spin states is suggested to explain the experimentally observed low temperature inversion of OD ESR spectra of radical–ion pairs. Mathematical background of the model based on the conception of the effective tunneling spheres of different radii is given. The model suggested is in excellent agreement with the qualitative picture of OD ESR signal formation at the required conditions. On the basis of the model the inversion point of spectra is found and the behavior of the OD ESR signal intensity in the neighborhood of the inversion point depending on various physical parameters is predicted. The dependencies obtained may serve as a basis for experimental identification of the suggested mechanism.

The effects of solvent and intramolecular dynamics on the rates of bond-breaking electron transfer (BBET) reactions is investigated. In the model we adopt, suggested by Saveant [J. Am. Chem. Soc. 109, 6788 (1987)], electron transfer and bond breaking are considered to occur as a concerted process. Thermal equilibrium rate constants kie [i=1(2) denoting the forward (reverse) reaction] are derived and exhibit a characteristic Marcus form, with the reorganization energy equal to the sum of contributions from the solvent, intramolecular vibrational and bond-breaking coordinates. The effect of dynamics on the BBET rate constants is studied by using diffusion-reaction equations. We assume that the intramolecular vibrational coordinate is in equilibrium and the solvent and the bond-breaking coordinates can be out of equilibrium. The survival probabilities are derived analytically with the use of a decoupling approximation. The single exponential decay of the survival probabilities leads to nonthermal-equilibrium rate constants ki that interpolate between the thermal equilibrium kie and diffusion controlled kid rate constants (where motion along the nonequilibrium coordinates control the rate) according to k−1i=k−1ie+k−1id. The diffusion controlled rate constants kid depend on the relaxation times along both the bond-breaking and solvent coordinates. For large activation energies, the fast relaxation will dominate the rate, while for small activation energies, the slow relaxation time will dominate the rate. We also discuss the case of the dynamics along the bond-breaking coordinate being characterized by an energy diffusion process. The rate constant is evaluated for high activation barrier reactions and still has the form given above, with a suitably redefined relaxation time for energy diffusion.

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.

A semiempirical approach in terms of the ZDO method is suggested to described potential energy surface (PES) of some radical reactions with a bounded basis including only frontier (single-filled) molecular orbitals of radicals depending on the geometric parameters with allowance for all the possible configuration. The methods for a choice of parameters are analyzed. The developed approach has been used to calculate the PES of CH4 + CH.3 --> CH.3 + CH4 reaction some points of which are checked up by the nonempiric method allowing for correlation energy according to perturbation theory. Relaxation energies are calculated. One-site parameters are found from the nonempiric consideration of CH3+, CH3 and CH3- energy, two-site ones - from simulation of CH4 --> -CH3 + H and C2H6 --> 2CH3 reactions in terms of the same one-orbital approximation. Energy parameters of the considered reactions are over-estimated by 10% while geometric ones - by 15%. The Hartree-Fock solutions and the solutions allowing for Cl have been also comparatively analyzed; the changes in spin and charge densities on the reaction centres have been considered.

A semiempirical approach is suggested to describe potential-energy surfaces (PESs) of some radical reactions in the zero-differential overlap (ZDO) approximation. An incomplete basis set is used including only frontier (single-filled) radical molecular orbitals (MOs) depending on geometrical parameters. All possible configurations are taken into account. The parameter selection techniques are analyzed. The approach is applied to PES calculation of the CH4 + CH3 · → CH3 · + CH4 reaction. Some points of the PES are verified by a nonempirical method using the perturbation theory and taking into account the correlation energy. The relaxation energies are calculated. The one-center parameters are determined nonempirically from the CH3 + CH3 ·, and CH3− energetics. The two-center parameters are found by modeling the CH4 → CH3 · + H and C2H6 → 2CH3 reactions in the same single-orbital approximation. The energy parameters of the reactions considered are overestimated by 10%, whereas the geometrical parameters are under-estimated by 15%. Further, a comparative analysis of the Hartree-Fock solutions and those including correlation interactions (CIs) is given. The variations in the spin and charge densities on the reaction centers are considered.