Time-Dependent Behavior of Activated Molecules. High-Pressure Unimolecular Rate Constant and Mass Spectra

Abstract

A quantum-mechanical theory of the unimolecular decay of metastable or activated molecules is developed using Fano's treatment of resonance scattering. A resonance state is synonymous with the so-called activated molecule in unimolecular kinetics, and a set of widths is associated with each state which is a measure of the coupling to the various dissociation continuum channels (each channel designates an ``activated complex''). If the widths are small compared to the spacings between those neighboring states which are coupled to the same continua, then an ensemble of molecules prepared in a given activated state will decay exponentially in time, as a radiating or autoionizing excited atomic state does. However, unimolecular decay is fundamentally a problem in ``overlapping'' resonance widths, and is best considered using Fano's theory, which incorporates proper treatment of the overlap. This paper is particularly concerned with the implications of overlapping widths on the high-pressure rate constant, and on mass spectra. There are two effects of overlapping which are most striking. First, the time decay of an ensemble of metastable molecules is no longer a pure exponential, but for the special cases considered is represented by a sum of exponential, oscillatory, and/or linear terms; this can affect the interpretation of mass spectra. Second, the high-pressure rate constant is related to the initial rate of decay of a canonical ensemble of activated molecules, and proper consideration of overlap imposes an upper bound on the rate of dissociation without any artificially imposed restrictions on the widths. This bound yields the ``universal rate constant,'' kT/h times a transmission coefficient which is a function of the widths and spacings of the activated molecules, and has an upper limit of 1.