Statistical theory of angular distributions and rotational orientation in chemical reactions

For A+BC→AB+C exchange reactions governed by a statistical collision complex, a large class of directional properties dependent on the rotational orientation of reactant or product molecules are shown to be determined by only two parameters, Λ=〈l/(l+j) 〉 and Λ′=〈l′/(l′+j′) 〉. Here l and l′ are the initial and final orbital angular momenta and j and j′ the rotational momenta of the reactant and product molecules. The angular distribution and the spatial orientation or polarization of the rotational momentum of product molecules are treated in detail. A classical form of statistical theory is used in which the directional properties are determined by Legendre moments involving averages over various unobserved angles between angular momentum vectors. Numerical formulas that give these averages in terms of Λ and Λ′ are derived from phase space calculations for a wide variety of reaction systems. Comparisons with previous treatments of product angular distributions involving other parameters show these can likewise be expressed in terms of Λ and Λ′. Methods are discussed for estimating these parameters and relating them to other reaction properties.