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Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes

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Eigenvalue methods for unimolecular rate calculations with several products.

Huw O Pritchard¹

¹Department of Chemistry, York University, Toronto, Canada. huw@yorku.ca

The Journal of Physical Chemistry. A

|October 5, 2007

Summary

Calculating unimolecular reaction rates using master equation eigenvalue problems can yield results smaller than numerical errors. This study extends a prior method to handle multiple reaction products and analyzes eigenvalue behavior.

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Area of Science:

Chemical Kinetics
Computational Chemistry
Theoretical Chemistry

Background:

Master equation eigenvalue problems are used to calculate unimolecular reaction rate constants.
Numerical precision issues can arise, where calculated rates are smaller than the trace of the reaction matrix's rounding error.
A previous method addressed this for single product reactions.

Purpose of the Study:

To extend a previously published procedure for solving master equation eigenvalue problems to cases with multiple reaction products.
To analyze the occurrence of avoided crossings between eigenvalues in various unimolecular reaction scenarios.

Main Methods:

Extension of a previously published numerical procedure for master equation eigenvalue problems.
Analysis of eigenvalue behavior in the context of unimolecular reactions with multiple products.
Investigation of avoided crossings in reversible, mixed, and multiwell systems.

Main Results:

The previously published procedure was successfully extended to handle unimolecular reactions with more than one product.
The study identified and noted the occurrence of avoided crossings between master equation eigenvalues.
These avoided crossings were observed in reversible, mixed reversible-irreversible, and multiwell unimolecular reaction systems.

Conclusions:

The extended method provides a robust approach for calculating accurate unimolecular reaction rate constants, even with multiple products.
Understanding avoided crossings is crucial for accurately interpreting the dynamics of complex unimolecular reactions.
This work enhances the computational toolkit for theoretical chemical kinetics.