Collision Efficiency Parameter Influence on Pressure-Dependent Rate Constant Calculations Using the SS-QRRK Theory.

E Grajales-González,S Mani Sarathy,M Monge-Palacios

doi:10.1021/acs.jpca.0c02943

Abstract

The system-specific quantum Rice–Ramsperger–Kassel (SS-QRRK) theory (J. Am. Chem. Soc.2016, 138, 2690) is suitable to determine rate constants below the high-pressure limit. Its current implementation allows incorporating variational effects, multidimensional tunneling, and multistructural torsional anharmonicity in rate constant calculations. Master equation solvers offer a more rigorous approach to compute pressure-dependent rate constants, but several implementations available in the literature do not incorporate the aforementioned effects. However, the SS-QRRK theory coupled with a formulation of the modified strong collision model underestimates the value of unimolecular pressure-dependent rate constants in the high-temperature regime for reactions involving large molecules. This underestimation is a consequence of the definition for collision efficiency, which is part of the energy transfer model. Selection of the energy transfer model and its parameters constitutes a common issue in pressure-dependent calculations. To overcome this underestimation problem, we evaluated and implemented in a bespoke Python code two alternative definitions for the collision efficiency using the SS-QRRK theory and tested their performance by comparing the pressure-dependent rate constants with the Rice–Ramsperger–Kassel–Marcus/Master Equation (RRKM/ME) results. The modeled systems were the tautomerization of propen-2-ol and the decomposition of 1-propyl, 1-butyl, and 1-pentyl radicals. One of the tested definitions, which Dean et al. explicitly derived (Z. Phys. Chem.2000, 214, 1533), corrected the underestimation of the pressure-dependent rate constants and, in addition, qualitatively reproduced the trend of RRKM/ME data. Therefore, the used SS-QRRK theory with accurate definitions for the collision efficiency can yield results that are in agreement with those from more sophisticated methodologies such as RRKM/ME.

Highlights

Conventional theoretical kinetic studies cover temperaturedependent and pressure-dependent rate constants.[1]
The system-specific quantum Rice−Ramsperger−Kassel theory/modified strong collision model (SS-QRRK/ MSC)[13−15] approach was shown to underestimate the value of the pressure-dependent rate constants because of an inaccurate estimation of the collision efficiency, a parameter linked to the energy transfer model
This work explored the effect of two alternative definitions for the collision efficiency parameter using the SS-QRRK theory[13−15] in the calculation of pressure-dependent rate constants. These definitions for the collision efficiency parameter belong to the works of Gilbert et al.[21] and Dean et al.[12,20], which coupled with the SS-QRRK theory[13−15] were denoted as the SS-QRRK/MSC-Gilbert and SS-QRRK/

Summary

Introduction

Conventional theoretical kinetic studies cover temperaturedependent and pressure-dependent rate constants.[1] Lindemann described the pressure-dependent scheme as a sequence of two steps (reaction R1). The first step is an excitation process where the reactant molecule A collides with a molecule of the bath gas M to form the energized molecule A*. The second step is 2-fold: the energized molecule A* can deactivate by colliding with another molecule M or it can react to form the product P.2. Pressure-dependent reactions are common in a variety of chemical environments and applications,[3] such as combustion, atmospheric chemistry, and chemical vapor deposition, but an accurate theoretical treatment represents a challenge that has demanded comprehensive studies.[3] the rate constants k−1 and k2, which describes the relaxation and formation of the final product from the energized molecule, respectively.

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