Exact and constrained kinetic energy operators for polyatomic molecules: The polyspherical approach

A review of the polyspherical approach to the kinetic operators for polyatomic molecules is given. This approach provides general and correct forms of the kinetic energy operator (KEO) expressed in terms of curvilinear coordinates. These forms are well adapted to the physical description of molecular systems and to the numerical methods used to solve the Schrِdinger equation. The approach derives its name, polyspherical, from the fact that the operators are expressed in terms of spherical coordinates eventually. These kinetic energy operators can be exploited to treat a large variety of problems such as the calculation of infrared or photo-absorption spectra or the study of reactive scattering systems. Special emphasis is placed on concrete examples.