Simulating Chemical Kinetics Without Differential Equations: A Quantitative Theory Based on Chemical Pathways.

Area of Science:

• Chemical kinetics
• Computational chemistry
• Reaction dynamics

Background:

• Conventional chemical kinetics modeling relies on solving differential equations for species concentrations.
• This approach can be computationally intensive and prone to numerical instability.
• An alternative method is needed for efficient and accurate simulation of reactive systems.

Purpose of the Study:

• To introduce a new method for simulating the time-evolution of chemically reactive systems.
• To provide an alternative to conventional mass-action kinetics modeling.
• To develop an iterative approach for generating time-dependent pathway probabilities.

Main Methods:

• The Sum Over Histories Representation (SOHR) method represents kinetic observables as a sum of pathway probabilities.
• An iterative algorithm is introduced to compute time-dependent pathway probabilities from elementary rate coefficients.
• The method avoids solving differential equations inherent in traditional kinetics models.

Main Results:

• The SOHR method successfully simulates the time-evolution of chemically reactive systems.
• The iterative approach effectively generates time-dependent pathway probabilities.
• The method was validated using the Lotka-Volterra system and a H2 combustion model.

Conclusions:

• The Sum Over Histories Representation (SOHR) offers a viable alternative to conventional differential equation-based kinetics.
• This pathway-based approach avoids numerical pitfalls associated with solving rate equations.
• The method demonstrates applicability to both simple and complex chemical systems.