The classical evaluation of the angularhyphen;momentumhyphen;resolved sum of states for the loosely hindered rotational degrees of freedom, i.e., the transitional modes, in loose transition states occurring in unimolecular dissociation, radicalndash;radical recombination, ionndash;molecule, and other collisionhyphen;complexhyphen;forming bimolecular reactions is considered. Exact analytic expressions are derived for the momentumhyphen;space volume available to the transitional modes at a given configurationqwith energyEand total angular momentum vectorJ. The results are completely general with respect to the type of fragment rotors involved and their relative orientation within the loose transition state, and constitute a dramatically simplified technique forJhyphen;resolved classical state counting. The utility of the expressions lies in the fact that they obviate the necessity of numerical integration over the systemrsquo;s momentum space, thus reducing substantially the computational effort involved in the exact evaluation of the transitionalhyphen;mode sum of states. The present results verify expressions which were postulated to apply to arbitrary configurations in our earlier work.
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