Diffusion-model for a reactive coordinate coupled to a solvent variable of different timescale

A Smoluchowsky stochastic equation for a system made by a reactive coordinate x coupled to a solvent coordinate y is used to investigate the effect of additional degrees of freedom on the dynamics of reactive events. The eigenvalue spectrum is evaluated by representing the time evolution operator over basis sets of both orthonormal and optimized nonorthogonal functions, and the advantage of the latter choice in terms of computation time and memory requirement is demonstrated. Correlation functions for the observable f(x, y) = x, sensitive to the kinetic process, are evaluated over a large range of diffusional anisotropies, i.e., ratios of the principal values of the diffusion tensor of the system. A rationalization is made of the different physical regimes observed by varying both hydrodynamic and energy parameters of the model. Only in asymptotic cases of very slow solvent motions do adiabatic approximations lead to monodimensional diffusion equations with a sink term.