We present a method for evaluating the distribution of products in chemical reactions which proceed by complex formation. The method consists of separating the degrees of freedom into strong modes, which are correlated directly with the reaction dynamics and weak modes. We then treat the dynamics of the strong modes explicitly and perform a statistical averaging over the weak degrees of freedom. Our final result [Eq. (5)] for the distribution of products is in the form of a product of three matrices whose sizes are determined by the number of relevant strong modes. The first matrix accounts for the preparation of the complex, the second for the energy redistribution within the complex, and the third for the dissociation of the complex. As one possible course of procedure we evaluate the first and third matrices by applying a normal coordinate transformation of the strong modes from reactants to complex and then to products and then use Franck–Condon factors between the strong states of the complex and fragments (reactants and products); the second matrix is evaluated using a step ladder model. We then apply the formulation to the system F+C2H4 for which deviations from statistical behavior were observed. Nonstatistical behavior may occur in our model from two distinct sources: (1) the Franck–Condon factors which are associated with the dynamics and (2) the finite energy redistribution rate within the complex (relative to the dissociation rate). We discuss the influence of these two effects in F+C2H4 and conclude that the first one is dominant in this case.
We investigate the application of the Franck–Condon approach to nonadiabatic molecular scattering processes. Computationally simple, analytic formulas are developed to describe the energy dependence of quenching of electronically excited atoms by atoms and molecules. These formulas include the dependence of the Franck–Condon factors on the translational wavefunctions as well as the wavefunctions for the internal degrees of freedom. We use these formulas to evaluate the translational energy dependence of the fine structure transition cross sections for F(2P3/2)+X→F(2P1/2)+X, where X= Xe, H+, and H2. The cross sections generally increase as the initial translational energy increases. Our results agree semiquantiatively (or better) with those obtained from other theoretical techniques. In the case of F+H+ we find that the absolute cross section is sensitive to the analytic form used for the nonadiabatic coupling but our model gives the correct energy dependence. At the energies of our calculations we find only a small amount of vibrational excitation of H2. Finally, we use our expressions to interpret some trends of available experimental results on the quenching of Hg (3P2→3P1) by several molecules. We find that collisional excitation of the internal modes of the molecule becomes more important as the initial translational energy increases. However, these modes do not contribute to the quenching cross section in a statistical fashion.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.