Microcanonical analysis of the kinetic method. the meaning of the "apparent entropy".

A rigorous analysis of the kinetic method is carried out using Rice-Ramsperger-Kassel-Marcus (RRKM) theory of microcanonical statistical unimolecular dissociation rates. The model employs a kinetics treatment appropriate for metastable ion dissociation. Proton-bound alkoxide dimer anions are used as model systems, with realistic vibrational and rotational parameters calculated by ab initio methods for the cluster ion and transition states leading to the competitive dissociation channels. The numerical simulations show that the kinetic method plots of ln(I2/I1) versus AAH are nearly linear but can exhibit significant curvature. The apparent entropy obtained in the extended kinetic method is not approximately equal to the thermodynamic entropy difference for dissociation, AAS(T), or for activation, deltadeltaS++(T), either at the effective temperature or at any fixed equilibrium temperature. Instead, the apparent entropy term can be related to the ratio of the microcanonical sum of states of the dissociation transition states for the kinetically selected internal energy of the dissociating ions.