Memory and temperature induced suppression of activated rate processes

Finite-barrier corrections for multidimensional barriers in colored noise

The usual identification of reactive trajectories for the calculation of reaction rates requires very time-consuming simulations, particularly if the environment presents memory effects. In this paper, we develop a method that permits the identification of reactive trajectories in a system under the action of a stochastic colored driving. This method is based on the perturbative computation of the invariant structures that act as separatrices for reactivity. Furthermore, using this perturbative scheme, we have obtained a formally exact expression for the reaction rate in multidimensional systems coupled to colored noisy environments.

Phase-space geometry of the generalized Langevin equation

The generalized Langevin equation is widely used to model the influence of a heat bath upon a reactive system. This equation will here be studied from a geometric point of view. A dynamical phase space that represents all possible states of the system will be constructed, the generalized Langevin equation will be formally rewritten as a pair of coupled ordinary differential equations, and the fundamental geometric structures in phase space will be described. It will be shown that the phase space itself and its geometric structure depend critically on the preparation of the system: A system that is assumed to have been in existence forever has a larger phase space with a simpler structure than a system that is prepared at a finite time. These differences persist even in the long-time limit, where one might expect the details of preparation to become irrelevant.

Chemical reaction dynamics within anisotropic solvents in time-dependent fields

The dynamics of low-dimensional Brownian particles coupled to time-dependent driven anisotropic heavy particles (mesogens) in a uniform bath (solvent) have been described through the use of a variant of the stochastic Langevin equation. The rotational motion of the mesogens is assumed to follow the motion of an external driving field in the linear response limit. Reaction dynamics have also been probed using a two-state model for the Brownian particles. Analytical expressions for diffusion and reaction rates have been developed and are found to be in good agreement with numerical calculations. When the external field driving the mesogens is held at constant rotational frequency, the model for reaction dynamics predicts that the applied field frequency can be used to control the product composition.

Self-similar renormalization approach to barrier crossing processes

An algebraic self-similar renormalization method developed recently for summation of divergent field-theoretical series is applied to the thermally activated escape of a Brownian particle over an arbitrarily shaped barrier. Based on the Mel'nikov-Meshkov result for the underdamped Brownian motion and the inverse friction expansion of the underlying Fokker-Planck equation for strong friction, an overall rate formula is constructed. This formula agrees in the weak friction regime with the rate obtained from a diffusion equation in energy variables and, in the limiting case of strong friction with the rate following from a Smoluchowski equation. Its validity is tested for Brownian motion in bistable potentials with parabolic, cusped, and quartic barriers of different heights. The proposed formula is found to give a reasonable description of activated rate processes even though the barrier is quite low. Our comparison also includes results from various different crossover theories. In most of the cases considered the present formula is in considerably better agreement with exact numerical rates than the other interpolation formulas.

Dynamics of chemical processes in polar solvents

Understanding solution-phase chemistry requires a microscopic description of the electronic structure of the reacting molecules, and of the complex influence of the solvent medium on the reaction energetics and dynamics. Processes involving reactant charge-transfer are of particular importance in chemistry and biochemistry, and are strongly influenced by polar media. Recent advances in experimental ultrafast laser spectroscopy and in computer simulation are working together to provide insight into the underlying molecular principles governing this class of processes in solution.