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

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, multi-dimensional tunneling, and multi-structural torsional anharmonicity in rate constant calculations. Master equation solvers offer more rigorous approach to compute pressure-dependent rate constant, but several implementations available in the literature do not incorporate the aforementioned effects. However, 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. The selection of the energy transfer model and its parameters constitute 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 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.