REACTIVE SCATTERING WITH ROW-ORTHONORMAL HYPERSPHERICAL COORDINATES .1. TRANSFORMATION PROPERTIES AND HAMILTONIAN FOR TRIATOMIC SYSTEMS

The formalism for triatomic reactive scattering using row-orthonormal hyperspherical coordinates is presented. The transformation properties of these coordinates under kinematic rotations and symmetry operation s are derived, as is the Hamiltonian of the system. This formalism is compared with the one using symmetrized principal moment of inertia hy perspherical coordinates. Continuity conditions appropriate for the ab sence and presence of the geometric phase effect associated with conic al intersections are considered. The potential application of these tw o sets of coordinates to tetraatomic systems is discussed. It is shown that the row-orthonormal coordinates are well suited for the treatmen t of systems of four or more atoms.