Rate constants in spatially inhomogeneous systems.

Area of Science:

• Chemical Physics
• Computational Chemistry
• Statistical Mechanics

Background:

• Calculating reaction rate constants in spatially inhomogeneous systems is computationally challenging.
• Existing methods often struggle with complex environments and rare events.
• Understanding the factors influencing reaction rates is crucial for many chemical processes.

Purpose of the Study:

• To present a novel theory and computational method for determining rate constants in spatially inhomogeneous systems.
• To establish a connection between rate constants and free energy differences in trajectory ensembles.
• To provide a framework for interpreting and analyzing rare chemical events in complex environments.

Main Methods:

• Developed a theory linking rate constants to path space partition functions.
• Employed importance sampling techniques, analogous to equilibrium free energy calculations.
• Extended transition path sampling by combining biased path ensembles and weighted histogram analysis.

Main Results:

• Demonstrated that relative changes in rate constants are isomorphic to free energy differences in a trajectory ensemble.
• Successfully estimated relative rate constants using importance sampling.
• Showed that rate constants can be decomposed into contributions from stability, barrier height, and flux.

Conclusions:

• The proposed method offers a robust approach for computing rate constants in complex, spatially varying systems.
• The decomposition of rate constants provides valuable mechanistic insights into rare processes.
• The theory and methods were validated using models of diffusion and ion pair dissociation near interfaces.