Relation between State-Selected or State-Averaged Cross Sections of Endothermic Reactions and Rate Constants of Exothermic Reactions. Application of Bimolecular Microcanonical Activated Complex Theory*

INTRODUCTION In a previous paper1 a microcanonical ensemble of reacting pairs of molecules in bimolecular reactions was considered and a quasiequilibrium assumed between the pairs and activated complexes moving in a positive direction along the reaction coordinate. As noted previously, this microcanonical version of activated complex theory is related to the usual version by means of a Laplace transform.3 Recently, in an interesting and most stimulating Communication, Anlauf, Maylotte, Polanyi, and Bernstein4 have calculated rates of formation of a particular vibrational-rotational-translational state (some most probable state) of products of an endothermic reaction, as a function of initial quantum state of reactants at fixed total energy. They used infrared chemiluminescence data on the (inverse) exothermic reaction, plus microscopic reversibility and two approximations, including one to describe the most probable state. In the present paper we employ one of their assumptions, together with microcanonical activated complex theory, to calculate molecular beam reaction total cross sections of an endothermic reaction, as a function of the initial vibrational-rotational-translational state in the incident beam, using rate constants of the (inverse) exothermic reaction [Eq. (11)]. An expression is also given for a velocity-selected internal state-averaged cross section [Eq. (11')] since in practice the beams are not usually state-selected. The relation of Eq. ( 11) to the results of Ref. 4 is described in a subsequent section. Previously, bimolecular microcanonical activated complex theory! was used to formulate a reaction crosssection theory5 (as a function of initial quantum state) for a different class of reactions, "nearly vibrationally adiabatic" ones. It was also used,! in conjunction with available computer data, to test certain aspects of activated complex theory. In both cases the theory was in good agreement with the computer results without introducing adjustable parameters.1•6 The results in Ref. 1 have been illustrated by application to specific cases recently .7 THEORY