Eigenvalue methods for unimolecular rate calculations with several products

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.