Polyexponential kinetics of chemical reactions in condensed media within the quasiclassical approximation

The Journal of Chemical Physics (Impact Factor: 3.12). 01/1995; 102(4):1607-1618. DOI: 10.1063/1.468893

ABSTRACT Polyexponential kinetical behavior typical for condensed phase reactions in highly viscous media is studied on a simple example of one‐dimensional diffusion equation with a sink modeling a chemical conversion of reactants. The corresponding polyexponential regime is demonstrated to have a thorough analogy with the quasiclassical approximation of one‐dimensional quantum mechanics and a relevant approximation for the Green’s function is developed. The asymptotic short‐ and long‐time kinetics are examined at the analytical level. Contrary to the frozen medium approximation according to which the slow diffusion motion of the medium is entirely ignored, the present quasiclassical model is fit for a qualitative description of the total time interval covering the reaction events from the initial moment up to the ultimate steady‐state monoexponential evolution. The range of validity of the quasiclassical approach is discussed. Numerical tests expose some peculiarities of the present treatment for equilibrium and nonequilibrium initial distributions. The work presents a qualitative development of the theory of nonexponential kinetics pioneered by papers of Agmon and Hopfield, Sumi and Marcus, and Nadler and Marcus. © 1995 American Institute of Physics.

  • [Show abstract] [Hide abstract]
    ABSTRACT: New theoretical methods are developed to analyze dynamical effects on the position-dependent, non-localized reaction transitions. Both time-dependent kinetics and average survival times are evaluated. Predicated on the steady-state Green's function formalism introduced in Part I (Spirina and Doktorov, Chem. Phys., 203 (1995) 117), a consistent decoupling series approximation is introduced for the solution of dynamic equations. The conditions of its applicability are thoroughly analyzed. The approximation works well in the case of moderately narrow transition regions with weak-to-moderate electronic coupling. To compliment the decoupling procedure, the absorbing boundary approximation is introduced to cover the case of wider transition regions with strong electronic coupling. It is demonstrated that in the latter case, slow dynamics assure formation of the absorbing walls emerging from the center of the transition regions. Both methods require only straightforward evaluations as they successfully separate the surface dynamics from the reactive transitions. We present a consistent analysis of the major qualitative changes in the reaction rates induced by widening reaction regions. Special attention is paid to dynamic effects in reactions initiated by non-equilibrium distributions. A simple model for the description of dynamically smeared transition regions is also suggested and tested.
    Chemical Physics 08/1998; 234:121-151. · 1.96 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Smoluchowski equation with a sink term is widely used as a model of a rate process in a slowly relaxing environment. Two approximate solutions for the rate constant obtained for a steeply growing sink are tested numerically using an exponential sink. Both analytical solutions are in a good agreement with the numerical results over a wide range of the problem parameters (environment relaxation rate). They show how the rate constant Γ decreases when the viscosity η of the environment increases. If the dependence is approximated by the fractional power law, Γ∝η−α, the exponent α is always less than unity and depends on η. It tends to zero for fast relaxation of the environment (small η) and increases when the relaxation slows down (η grows). © 1998 American Institute of Physics.
    The Journal of Chemical Physics 09/1998; 109(11):4182-4189. · 3.12 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Dynamical effects of a solvent (environment) on an electron transfer (ET) reaction are investigated by using the Sumi–Marcus reaction–diffusion equation; this equation describes the time evolution of population distribution function of a reactant in a slow nuclear coordinate system. Assuming that viscosity of the solvent (environment) is proportional to a relaxation time scale of the slow nuclear mode, power dependence of a mean lifetime of ET on the relaxation time scale becomes the same as the one on the viscosity. Therefore, the former power dependence is investigated instead of the latter, and it is found that the power in the limit of the (infinitely) large relaxation time scale is 1−r when r<1, and 0 when 1 ⩽ r, where r is the ratio of the reorganization energy of fast nuclear modes to the slow nuclear mode. However, this limit cannot always be reached in a realistic situation. Therefore, the present theory is extended to a large but finite relaxation time scale. The values of the power obtained by the present theory are in reasonable agreement with the ones calculated numerically by W. Nadler and R. A. Marcus [J. Chem. Phys. 86, 3906 (1987)]. Finally, a difficulty in numerical calculations is shown. An expansion of the population distribution function in some basis set of functions is common in numerical calculations. However, the use of that finite basis set of functions which is independent of the relaxation time scale leads to a value of the power that is either zero or unity in the limit of the large relaxation time scale, and as such cannot reproduce the correct asymptotic behavior of the mean lifetime. © 1999 American Institute of Physics.
    The Journal of Chemical Physics 08/1999; 111(6):2665-2677. · 3.12 Impact Factor