Franch--Condon factors in studies of 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'). For vibrational distributions linear surprisals are obtained for F + H2(D2), but not for H(D) + Cl2. 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. 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