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

Abstract

A simplified phase space theory (PST) of angular momentum-conserving microcanonical rate constant at specified total angular momentum J in unimolecular fragmentation under a central potential is proposed via the reverse association of fragments. Angular momentum-conserved rotational–translational sum/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 relatively simple numerical Laplace inversion routine of the product of Q_xi(J) and the vibrational partition function accomplishes in a single stroke the 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 (thermal) PST rate constant for dissociation. The procedure is checked against available more elaborate PST results and is illustrated on cases representing five different combinations of fragment symmetries: linear+atom, sphere+atom, linear+linear, sphere+linear and sphere+sphere. The method requires minimal computational effort and is particularly efficient for calculations involving large molecules and large angular momenta.