Three-Dimensional Master Equation (3DME) Approach.

The master equation technique is a standard tool to interpret gas-phase experimental kinetic results as well as to provide phenomenological rate coefficients for modeling. When there are significant changes of rotational constants along the reaction coordinate from a reactant through a transition state (TS) to product(s), including effects of angular momentum explicitly in a master equation model becomes vitally important. In this work, assuming that the K quantum number is adiabatic for both the TS and reactant, we developed an algorithm for pragmatic solutions of a three-dimensional master equation (3DME) that involves internal energy, total angular momentum ( J), and its projection K. Two examples (one is for a thermally activated isomerization of CHNC to CHCN via a tight TS, and the other is for a thermally activated dissociation of NH to H + NH via a loose, variational TS) are given. In addition, comparison of 3DME results with experiment as well as with those of 1DME and 2DME are documented.