A. I. Shushin

Effect of state-selective reactive decay on the evolution of quantum systems

The effect of state-selective reactive decay on the relaxation kinetics of quantum multistate systems is studied in detail in the Bloch-Redfield approach (BRA). The results are applied to the analysis of this effect in radical pair recombination kinetics. The BRA is shown to be able to describe quantitatively most important specific features of the recombination kinetics including those predicted by phenomenological treatment and by recently proposed approaches based on quantum measurement theories.

Manifestation of anisotropic reactivity and molecular interactions in chemical reaction kinetics

The effect of highly anisotropic reactivity and interaction between molecules on kinetics of diffusion-influenced liquid-phase reactions is analyzed in detail. The Smoluchowski equation (SE) that describes the space/time evolution of pairs of reacting molecules is solved analytically by the method proposed earlier [A. I. Shushin, Chem. Phys. Lett. 130, 452 (1986); Chem. Phys. 120, 91 (1988)]. The method allows for reducing the original SE in curvilinear translational/rotational coordinates of reacting molecules to the SE in the local Cartesian coordinates in the vicinity of reactive relative orientations. Many formulas for the reaction rate are derived in the realistic models of reactivity using this method. Analysis demonstrates high accuracy of these formulas. The model of reactive patches is shown to give reaction rates that are considerably smaller than those predicted here. Peculiarities of reaction kinetics for molecules with anisotropic reactivity and interaction potential are analyzed in detail. P...

Influence of hydrodynamic interaction on the diffusion-controlled reaction kinetics of molecules with highly anisotropic reactivity

In this work we analyze the effect of hydrodynamic interaction (HI) on diffusion-controlled reaction rate of molecules with highly anisotropic reactivity, modeled by small reactive hemispheres around the reactive centers (RCs) on the surfaces of molecules. The effect of the HI (that manifests itself in the coordinate dependence of relative diffusion coefficients) is shown to be mainly determined by the HI at short distances between molecules (where the traditional long distance analysis of the HI is irrelevant) and very sensitive to the local shape of molecules near the RCs. The effect is analyzed within three models of the shape: spherical, non-spherical spheroidal, and non-spherical of truncated-sphere type, with the use of the method of local analysis based on the approximation of the general curvilinear coordinates of pairs of reacting molecules by the Cartesian ones in the region close to the reactive orientations. Simple analytical expressions for the reaction rate are derived, which show that the H...

The effect of anisotropic reactivity and interaction potential on the kinetics of diffusion controlled reactions

The manifestation of strongly anisotropic reactivity and interaction potential in the kinetics of diffusion controlled reaction is thoroughly investigated using the method of local analysis (MLA) proposed earlier. The MLA enables one to simplify the problem reducing it to the analysis of the stochastic relative motion of molecules in the vicinity of the reactive orientations. Simple analytical expressions for the reaction rate are derived within the realistic model of reactive hemispheres (MRH) assuming that the reaction occurs upon the overlap of the small reactive hemispheres on the surfaces of molecules. Unlike the conventional model of reactive patches (MRP) the MRH takes into account the “thickness” of the reactive region, which is found to lead to the strong (up to two orders of magnitude) increase of the rate. Within the proposed model of ellipsoidal reactive patch the unified formula for the rate is derived that reproduces the results of both the MRP and the MRH. It is shown that the peculiarities...

The stationary non-Poissonian collision model of energy relaxation and stochastic motion in condensed phase processes

The effect of energy dissipation on transport and activated rate processes in condensed phase is analyzed in detail within the non-Poissonian collision model (NPCM). The NPCM is a generalized variant of the collision model (CM) describing the instantaneous change of the velocity of probe particles induced by random collisions with particles of a medium. Unlike the conventional CM, the NPCM assumes the non-Poissonian collision statistics. In this work we concentrate on the stationary variant of the NPCM (SNPCM), which differs from the nonstationary NPCM (NNPCM) discussed in previous studies by the proper treatment of the collision statistics ensuring the time homogeneity of the process. The SNPCM is shown to be free of inconsistencies inherent in the NNPCM. In particular, the SNPCM reproduces the physically natural relations between the average parameters (the average displacement and velocity, correlation functions, etc.) well known in the transport theory. The SNPCM describes properly the specific featur...

Anomalous features of the kinetics of subdiffusion-assisted bimolecular reactions

Some specific features of the kinetics of subdiffusion-assisted bimolecular reactions are analyzed in detail with the use of the non-Markovian stochastic Liouville equation (SLE) recently derived within the continuous time random walk approach. The SLE allows for describing important peculiarities of the reactions: Slow long time behavior of the kinetics, nonanalytical dependence of the reaction rate on the reactivity of particles, the onset of quasistatic regime independently of particle mobility in the case long-range reactivity, strong manifestation of fluctuation kinetics showing itself in very slow reaction kinetics at long times, etc.

The theory of chemically induced dynamic electron polarization for radical pair recombination in low dimensional space

The kinetics of multiplet chemically induced dynamic electron polarization (CIDEP) generation for radical pair (RP) recombination in low dimensional media (the dimensionality n⩽3) is theoretically analyzed in detail. Simple analytical expressions for the time dependent amplitude Pe(t) of the multiplet CIDEP are derived. These expressions show that Pe(t) is sensitive to the dimensionality only in the limit of weak spin dependent interaction Q and large diffusion coefficient D, when ξ=Qd2/D≪1, where d is the distance of closest approach. In the opposite limit ξ>1, the dependence Pe(Q) is universal Pe(Q)∼Q/(1+ΛQ/D), where Λ∼d.

Effect of interparticle interaction on kinetics of geminate recombination of subdiffusing particles.

The kinetics of geminate subdiffusion-assisted reactions (SDARs) of interacting particles is analyzed in detail with the use of the non-Markovian fractional Smoluchowki equation (FSE). It is suggested that the interparticle interaction potential is of the shape of potential well and reactivity is located within the well. The reaction kinetics is studied in the limit of deep well, in which the FSE can be solved analytically. This solution enables one to obtain the kinetics in a simple analytical form. The analytical expression shows that the SDAR kinetics fairly substantially depends on the mechanism of reactivity within the well. Specific features of the kinetics are thoroughly analyzed in two models of reactivity: the subdiffusion assisted activated rate model and the first order reaction model. The theory developed is applied to the interpretation of experimental kinetics of photoluminescence decay in amorphous a-Si:H semiconductors governed by geminate recombination of electrons and holes that are recently found to undergo subdiffusive relative motion. Analysis of results demonstrates that the subdiffusion assisted activated rate mechanism of reaction is closer to reality as applied to amorphous a-Si:H semiconductors. Comparison of experimental and theoretical kinetics allowed us to obtain some kinetic parameters of the systems under study: the rate of escaping from the well and the parameter characterizing the deviation of the subdiffusive motion from the conventional one.

The non-Poissonian collision model for the condensed phase activated rate processes

The non-Poissonian collision model (CM) of energy dissipation (friction) in condensed phase activated rate processes is proposed and analyzed in detail. This model describes the instantaneous change of the velocity distribution of a probe particle caused by the collisions with particles of a medium. In the considered CM the statistics of collisions is assumed to be non-Poissonian. The efficiency of collisions is determined by the transition kernel K(v,v′) in the velocity space which can model both the weak and the strong collision limits including the cases of complete velocity randomization and backscattering (v≈−v′). In the proposed CM simple formulas for the diffusion coefficient D and the rate kr of passage over a barrier are derived in the moderate-to-strong friction limit. They accurately reproduce the known analytical and numerical results. The non-Poissonian CM predicts the interesting phenomenon, the kinetic cage effect, which is observed for the special type of the collision distribution functio...

The Green's function for multistate schrödinger-type equation. Magnetic-field effects in radical pair recombination in the presence of interaction potential

The recently proposed expression for the Green’s function (GF) of the multistate Schrodinger-type equation is applied to obtaining the GF for the stochastic Liouville equation which describes the chemically induced dynamic electron polarization (CIDEP) generation in diffusion assisted radical pair recombination in liquids in the presence of interrradical interaction (for example, the Coulomb interaction). The analytical formulas for CIDEP amplitude are derived with the use of the sudden perturbation approximation, properly treating the effect of the spin exchange interaction, and two approaches, the cage and interpolation ones, which allow for the accurate description of diffusive motion of radicals in the potential. The accuracy of these two approaches and specific features of CIDEP generation in the presence of the interaction potential are discussed in detail.