Examining the accuracy of methods for obtaining pressure dependent rate coefficients

Area of Science:

• Computational Chemistry
• Chemical Kinetics
• Applied Mathematics

Background:

• The full energy-grained master equation (ME) is computationally intensive for kinetic modeling.
• Reduced models using phenomenological rate coefficients are commonly employed as approximations.
• The accuracy of these reduced models is critical for reliable kinetic simulations.

Purpose of the Study:

• To evaluate the accuracy of methods for deriving pressure-dependent rate coefficients for reduced models.
• To compare the performance of existing methods against direct solutions of the full ME.
• To introduce and assess an alternative method, simulation least-squares (SLS).

Main Methods:

• Direct numerical solutions of the full energy-grained master equation (ME).
• Evaluation of the chemically-significant eigenvalue (CSE) method.
• Development and application of the simulation least-squares (SLS) method.
• Derivation of an algebraic error expression for the CSE method.

Main Results:

• Deviations between reduced models and the full ME can be substantial.
• The SLS method demonstrates comparable or superior accuracy to the CSE method.
• A variant of SLS using the matrix exponential is as fast as CSE and more robust.
• Existing methods, including CSE and SLS, exhibit inaccuracies under certain conditions.

Conclusions:

• Current methods for constructing reduced models from the ME have limitations and can fail.
• The SLS method presents a promising alternative for computing phenomenological rate coefficients.
• Further research is needed to develop more reliable methods for emulating the full ME solution.