Statistical phase space theory of polyatomic systems: Rigorous energy and angular momentum conservation in reactions involving symmetric polyatomic species

Abstract

Classical formulas for the sum and density of rotational and rotational–orbital states pairs of polyatomic molecules are derived using a geometrical approach that rigorously conserves energy and angular momentum. The pair combinations considered include a spherical top in combination with either a linear, spherical, or symmetric top molecule. With the formulas presented here it is possible to perform exact classical statistical phase space theory calculations for bimolecular reactions involving polyatomic molecules. In suitable limits our results reduce to well-known classical expressions for rotational state densities and sums or to equations previously derived by Klots using an aprroximate phase space approach. Calculations are given that demonstrate the distortions produced in the system phase space by molecular oblateness and prolateness are usually small.