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

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.

A theoretical study of the Ḣ- and HOȮ-assisted propen-2-ol tautomerizations: Reactive systems to evaluate collision efficiency definitions on chemically activated reactions using SS-QRRK theory

“…Initial calculations for the chemically activated Ḣ-assisted tautomerization using the original SS-QRRK/MSC approach [18,19] displayed an underestimation of the bimolecular stabilization rate constant , similar to the underestimation of pressure-dependent rate constants of thermally activated reactions previously corrected [21]. The following paragraphs provide a brief description of such correction; for a more detailed discussion of the topic, the reader is referred to the original publication [21].…”

“…Because of the usefulness of the collision efficiency definition given by Eqs. (3) and (4) when estimating pressure effects for thermally activated reactions [21,37], we tested in this work the same relations to alleviate the underestimation of pressure-dependent rate constants in chemically activated processes. Two methods were tested, which resulted from the SS-QRRK theory [18,19] combined with the MSC model adopting the collision efficiency definitions of Eqs.…”

“…1(b)) entails thermally activated processes. Therefore, their low pressure rate constants were computed following the indications given in our previous work [21], that is, with the implementation of a modified version of the original SS-QRRK/MSC approach, referred to as SS-QRRK/MSC-Dean, where the collision efficiency definition of Dean et al [23,24] (Eq. (4)) is used.…”

“…Despite the advantages of the SS-QRRK/MSC method, its original formulation underpredicts the values of pressure-dependent rate constants for reactive systems involving large molecules and at high temperatures. In our previous work [21], we reduced these underestimations of pressure effects when dealing with thermally activated reactions (reaction type AB) by implementing two alternative definitions for the collision efficiency, which refer to the work of Gilbert et al [22] and Dean et al [23,24]. However, chemically activated reactions (reaction type A+BAB*P)…”

“…Since the first step of each tautomerization entails a bimolecular reaction, they offered a suitable scenario to also address the underestimation of chemically activated rate constants derived from the original SS-QRRK/MSC formulation. To achieve this goal, we tested the same collision efficiency definitions that were successfully implemented for thermally activated reactions in our previous work [21].…”