Determining phenomenological rate coefficients from a time-dependent, multiple-well master equation: species reduction at high temperatures

In this article we discuss at length the determination of phenomenological rate coefficients from the solution to a time-dependent, multiple-well master equation. Both conservative and non-conservative formulations are considered. The emphasis is placed on how to handle the situation when a CSE (chemically significant eigenvalue of the transition matrix) merges with the quasi-continuum of IEREs (internal energy relaxation eigenvalues), indicating that one or more chemical reactions begin to take place on vibrational-rotational relaxation time scales. The methodology is illustrated with four examples.