Hamiltonian dynamics of chemical reactions. Consecutive first-order reactions and reactions possessing one autocatalytic intermediate

A recently proposed Hamiltonian approach to phenomenological chemical kinetics [T. Georgian and G.L. Findley, Int. J. Quantum Chem., Quantum Biol. Symp. 10 , 331 (1983); T. Georgian, J.M. Halpin, and G.L. Findley, Int. J. Quantum Chem., Quantum Biol. Symp. 11 , 347 (1984)] is applied to all consecutive first-order, single-step reactions, and to all reactions possessing one autocatalytic intermediate. The reaction Hamiltonians presented are shown to be consistent with the phenomenological rate equations and the relationship between reaction form and the form of the reaction potential is discussed. In particular, we show: (1) that the interaction between consecutive reactions manifests itself as a coupling term in the reaction potential, a term which may be eliminated via transition to “normal reaction coordinates” for the chemical system; and (2) that coupled sets of autocatalytic reactions give rise to coupling terms in the reaction Hamiltonian which are characteristic of the reaction mechanism.