On the Relation between Unimolecular Reaction and Predissociation

Attention is again directed to the analogy between unimolecular decomposition and predissociation. In the reverse of unimolecular decomposition two fragments recombine, and in the usual equilibrium theory it is assumed that the reaction coordinate passes freely over a potential‐energy hill (actually saddle point), regardless of energy. The analogous situation in predissociation must be sought by considering the equilibrium rate of transfer from a continuum state of fixed energy to a discrete state or states. For a model calculation there is first considered the case of a single continuum and an infinite number of uniformly spaced discrete states, with a uniform interaction matrix component, ${\upsilon }_{\mathrm{sd}}$ , between the continuous and the discrete states. The perturbed stationary states have been found in terms of the unperturbed states of the discrete set, with spacing ${\mathrm{\Delta E}}_d$ between energy levels, and the continuum, which has itself been converted into a close‐spaced set of discrete states with spacing ${\mathrm{\Delta \epsilon }}_s$ . This gives some very interesting relations between the perturbed and unperturbed energy levels. The results depend on a dimensionless invariant parameter ${\mathrm{f\hspace{0.17em}=\hspace{0.17em}\pi }}^2{\upsilon }_s{d}^2{\mathrm{\hspace{0.17em}/\hspace{0.17em}\Delta \epsilon }}_s{\mathrm{\Delta E}}_d$ . It is found that $\text{f\hspace{0.17em}=\hspace{0.17em}1}$ gives results analogous to the transition state theory of unimolecular reactions, with flux from the continuum being absorbed in the discrete states completely and uniformly at any energy. With any other value of $f$ , part of the flux is reflected, except at the center of the discrete line. The theory is extended to the case of many continua, and it is shown that the usual unimolecular rate theory can be described roughly as corresponding to a situation in which the discrete levels are divided into subsets, each subset connecting with a pair of continua, being independent of the other subsets, and having the average value of $f$ equal to $\frac{1}{2}$ rather than 1. Similar considerations apply to isomerizations.