Quantitative Calculation of Product Rovibrational Distributions from Atom−Diatom Exchange Reactions

Abstract

We describe a rapid, accurate method for calculating rovibrational distributions in diatomic products from elementary chemical reactions. The basis of the model is momentum interconversion at a critical configuration defined in terms of molecular dimensions of the species involved. This approach shares common elements with recent models of inelastic processes and the kinematic reactive model of Elsum and Gordon. We point out that these and related approaches represent a development of Newtonian mechanics equivalent to that followed in the conventional formulation of classical mechanics, but one in which motive force for change at the molecular level is attributed to dp/dt rather than to dV/dq. This leads to a particularly transparent form of mechanics that uses only familiar data such as bond length, mass, spectroscopic constants, and velocity, yet may be applied to the highly resolved single collision experiments of molecular reaction dynamics. We describe key aspects of the computational method, e.g., the definition of the critical configuration, the disposal of reaction enthalpy, the manner of assigning product vibrational states, and the way in which conservation of energy is ensured. Examples are chosen to illustrate the range of reactions to which the method may be applied. Each would represent a challenge to conventional theory. We show that velocity-angular momentum diagrams may be used to interpret data and to give physical insight into the origins of observed rotational distributions. Good agreement is obtained between experimental and calculated (v,j) distributions for a wide range of elementary reactions suggesting that our model, despite its simplicity, captures the principal physics of chemical change at the molecular level

A new approach to molecular collision dynamics

“…Thus the energy available for rotation decreases as vibrational level increases. 77 The principal features are seen in Fig. 11 where E-plots for transitions to v IF ¼ 9, 17, 19 from the reaction F þ I 2 !…”

“…Trajectories that meet these conditions are judged reactive while those that do not are nonreactive and are not counted. 77 Application of these conditions greatly increases the accuracy of calculations and permits state-to-state integral cross-sections, and hence total crosssections, to be calculated.…”

“…Calculations remain free of adjustable parameters and use only readily available spectroscopic, bond length and mass data. 77…”

“…Adapting these to encompass reactive collisions requires some changes but, as the previous section makes clear, the kinematics of reactive process consists of momentum inter-conversion (orbital-to-rotational) and therefore similar principles should apply. 77 In the case of a chemical reaction the product (v,j) states are those of the new species and hence final level spacings, and DE values must reflect this change. In addition, the array of product energy levels must be placed on an energy scale the zero of which is set by initial reactant levels.…”

Rotational distributions following van der Waals molecule dissociation: Comparison between experiment and theory for benzene–Ar

“…8 It has also been shown that angular momentum constraints determine cross sections for rotational transfer ͑RT͒ as well as vibrational-rotational transfer ͑VRT͒, 9,10 electronic energy transfer, 11 and atom-diatomic molecule exchange reactions. [12][13][14] Simple calculations based on a "torque arm" for the process are very successful in reproducing ex-perimental rotational distributions. Extension of this approach to the polyatomic case is quite challenging due to the fact that rotation may take place about more than one molecular axis.…”