Unimolecular phase space theory rates by inversion of angular momentum-conserved partition function

A simplified phase space theory (PST) of angular momentum-conserving microc anonical rate constant at specified total angular momentum J in unimolecula r fragmentation under a central potential is proposed via the reverse assoc iation of fragments. Angular momentum-conserved rotational-translational su m/density of states of fragments is approximated by interpolation between " high-J" and "low-J" states (Chem. Phys. Lett., 1996, 262, 539), from which is obtained in closed form the corresponding J-conserved partition function Q(xi)(J); this represents the core result of this work [eqn. (20)]. A rela tively simple numerical Laplace inversion routine of the product of Q(xi)(J ) and the vibrational partition function accomplishes in a single stroke th e inversion that leads immediately to the microcanonical rate constant k(E) ,J)(PST). Averaging of Q(xi)(J) over J leads directly to the canonical (the rmal) PST rate constant for dissociation. The procedure is checked against available more elaborate PST results and is illustrated on cases representi ng five different combinations of fragment symmetries: linear + atom, spher e + atom, linear + linear, sphere + linear and sphere + sphere. The method requires minimal computational effort and is particularly efficient for cal culations involving large molecules and large angular momenta.