RRKM–ME for unimolecular reactions involving intermediates with multiple conformers

Abstract

In the RRKM–ME calculations of gas-phase unimolecular reactions, reactants and intermediates are first uniformly partitioned into energy grains. The unimolecular rate coefficient k(E) within each grain is calculated using RRKM theory, while the master equation (ME) is employed to account for energy transfer between different grains due to collisions. Solving the RRKM–ME yields the time-dependent population and energy distributions of all species during the reaction. However, when reactants or intermediates have multiple conformers arising from internal rotations or ring puckering, inclusion of all conformers leads to an excessively high matrix order in RRKM–ME calculations, rendering them infeasible or computationally prohibitive. To address this challenge, this study developed a multi-conformer RRKM–ME (MC–RRKM–ME) method. By recognizing that multiple conformers of the same species have low interconversion barriers and rapid transition rates, the densities of states of these conformers are included in the k(E) calculation. Treating multiple conformers as a single species by combining their densities of states significantly reduces the matrix order of the ME, thereby maintaining kinetic accuracy while substantially lowering computational costs. After validating the algorithm with simple reaction systems, the MC–RRKM–ME method was applied to investigate the ozonolysis of cyclopentene, in which the Criegee intermediate (CI) possesses 100 conformations and a ME order of 98 456. Merging the 100 CIs with two CIs reduces the ME order down to 7244, resulting in a ∼2500-fold decrease in matrix-solving computational efforts. MC–RRKM–ME calculations identified vinyl hydroperoxide and dioxirane as the primary products in cyclopentene ozonolysis, with negligible secondary ozonide formation. The results are consistent with experimental observations.