Derivation of the rovibrational Hamiltonian based on the tensor form: a new approach to generalized internal coordinates depending on the external parameters

Abstract

The transformation of the complete (non-relativistic) molecular Hamiltonian from Cartesian to generalized coordinates based on the tensor form has been obtained. By taking generalized internal coordinates depending on two parameters we present an exact derivation of the molecular Hamiltonian that has simple and explicit expressions for general triatomic molecules, and all rovibrational couplings are determined. Our approach is applicable to various kinds of internal coordinates in a straightforward way. In this derivation, no approximations and no restrictions are imposed on the nature of the vibrational variables. We also introduce a straightforward method with minimum equations to obtain , which is the key vector in our approach compared with the methods used in our previous works.

Keywords:

• rovibrational Hamiltonian
• internal coordinates
• large-amplitude motions

Notes

Note

1. The notation used throughout this paper, as in previous work, is as follows: the indices i, j refer to the nuclei, s, t refer to the electrons, k, l refer to the vibrational variables, f, g, h refer to a general direction of the LF frame axes, α, β, γ refer to a general direction of the BF frame axes, and e _f and ϵ _α are the orthogonal unit vectors along the LF and the BF frame axes, respectively. Also, M is the total mass of the molecule, m is the mass of the electron, and m_N is the total mass of the nuclei.