Franck-Condon factors in studies of the dynamics of chemical reactions. III. Analysis of information theory for vibration-rotation distributions and isotopic branching ratios

A previously developed approximate theory of chemical dynamics based on generalized Franck-Condon factors is used to study the information theoretic analysis of vibration-rotation distributions and of isotopic branching ratios. We begin by examining the surprisal function I obtained from the Franck-Condon factors for rotational and vibrational distributions. For rotational distributions we find linear surprisal behavior for low rotational excitation in the limit of strong potential and weak kinematic coupling, but nonlinear surprisals for high rotational excitation in that limit. In addition, nonlinear rotational surprisals are generally obtained for any degree of rotational excitation in the limit of strong kinematic and weak potential coupling. We find these generalizations from the Franck-Condon factors and their applications to the H+H₂, F+H₂(D₂), and H+Cl₂ reactions. For F+H₂(D₂), nearly microcanonical rotational distributions are obtained (for low j′), due to the cancellation of contributions from the angular coordinate overlap factor [which leads to a positive slope (temperature) parameter θ] and centrifugal stretching effects (which lead to negative θ). For vibrational distributions linear surprisals are obtained for F+H₂(D₂), where little of the reaction exoergicity is released in the exit channel and the region of maximum overlap of reagent and product wavefunctions is highly localized, but not for H(D)+Cl₂, which has a higher repulsive energy release (in the terminology of Polanyi and co-workers) and a more delocalized overlap. For both rotational and vibrational surprisals, we find that linearity occurs when the potential constrains the reaction to occur through a highly localized set of nuclear configurations (and hence in the limit of strong potential coupling and of highly localized overlaps). In our study of branching ratios, we consider the isotopic branching in F+HD→FH(FD)+D(H). We first show that the purely dynamical Franck-Condon factor provides a correct qualitative description of the branching ratio (especially its dependence on reagent rotational excitation). We then use information theory to predict the same ratio, and find some points of similarity to the purely dynamical result (such as the dependence on parameters of the product state distributions), but also certain important points of difference (such as dependence on degree of reagent rotational excitation). These points of similarity and difference may be reinterpreted in terms of the relative contribution of strongly coupled potential and kinematic effects, respectively, and the success of simple information theoretic branching ratio predictions depends on the relative importance of these factors.