Nonlinear dynamical effects on reaction rates in thermally fluctuating environments

Area of Science:

• Chemical Physics
• Theoretical Chemistry
• Computational Chemistry

Background:

• Calculating reaction rate constants in condensed phases is crucial for understanding chemical processes.
• Traditional methods often rely on the transition state theory, which has limitations.
• Understanding the role of solvent fluctuations and dissipation is key.

Purpose of the Study:

• To present a novel theoretical framework for calculating rate constants of condensed phase reactions.
• To avoid the reliance on the concept of transition states.
• To provide a rigorous mathematical foundation for reactivity in fluctuating media.

Main Methods:

• Utilizing a multidimensional underdamped Langevin equation in the vicinity of a rank-one saddle.
• Defining a reaction coordinate as a nonlinear functional of system and environment variables.
• Analytically deriving reaction probability and integrating with the Boltzmann distribution.

Main Results:

• The sign of the reaction coordinate predicts reaction outcome in fluctuating environments.
• Reaction probability is analytically derived as the probability of the reaction coordinate being positive.
• The method yields exact reaction rate constants under conditions of local equilibrium and negligible quantum effects.

Conclusions:

• The developed theory offers a robust, analytical approach to reaction rate calculations.
• It inherently accounts for nonlinear effects, fluctuation, and dissipation.
• Provides a fundamental understanding of reactivity origins in condensed phase systems.