CORRELATIONS WITHOUT COINCIDENCE MEASUREMENTS - DECIDING BETWEEN STEPWISE AND CONCERTED DISSOCIATION MECHANISMS FOR ABC-]A + B + C

A method is presented for deciding the degree to which a dissociation of the form ABC → A + B + C is synchronous and/or concerted based on measurement of the dynamical properties of the fragments. The method considers the joint probability distribution, P, giving the coincidental occurrence for each possible set of the dynamical variables. Information theory is used to obtain the most probable joint probability distribution that is consistent with the experimental measurements available, each of which is simply a projection of P. Once this "maximum-entropy" P is found, it can be used to predict the outcome of measurements that are less experimentally accessible; an important prediction is the angular distribution describing the fragmentation. A "concertedness" parameter is defined, which ranges from a value of zero for the stepwise limit of dissociation to a value of unity for the concerted limit. This parameter can be directly calculated from the angular distribution provided by P and can be used to estimate to what degree a reaction is concerted based on the experimental data used to calculate P. An exact prior distribution based on conservation of both energy and linear momentum is derived for a dissociation producing three atoms. Algorithms for calculating P are discussed. © 1990 American Chemical Society.