The molecular Hamiltonian

The molecular Hamiltonian represents one of the most basic concepts in spectroscopy and molecular reaction dynamics. Its derivation is notoriously difficult owing to the use of a rotating reference frame which, in turn, is necessary to define the concept of vibration and rotation. In this article, we review the construction of the molecular Hamiltonian in normal mode and in internal coordinates. For normal mode coordinates, the Watson Hamiltonian including its modification for linear molecules is derived using an approach based on classical mechanics and the Podolsky transformation. The method is subsequently used to derive the molecular Hamiltonian in terms of Jacobi and valence coordinates. Results are presented for the triatomic system and for the extension toward N-atom systems with N greater than or equal to 3.