The global potential energy surface of a many-body system often reduces in dimensionality at the dissociation limit. For example, when O is separated from O2, an O3 global adiabatic potential energy surface, which depends on three internal coordinates, should reduce to a onedimensional diatomic potential energy surface of O2 (that depends on the electronic state of O2) plus a constant (which is the energy of a given state of O). To treat dissociation, we assume the entire system Z is composed of subsystems X and Y, and we considering the reaction