The vibration–rotation kinetic energy operator for sequentially bonded tetra-atomic molecules in internal coordinates

Abstract

An exact vibration–rotation kinetic energy operator for polyatomic molecules has been obtained. Using this Hamiltonian for sequentially bonded tetra-atomic molecules, all rovibrational terms have been derived with internal coordinates as the vibrational variables. The present approach is greatly simplified with less algebra compared with conventional methods. Also, simple and explicit expressions for the vibration–rotation coupling terms in internal coordinates are presented.

Keywords:

• Vibration–rotation coupling
• Tetra-atomic molecules
• Internal coordinates

Acknowledgement

We are grateful to the Ministry of Science, Research and Technology for financial support.

Notes

† 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 44.

† Details of the derivation of equation (26) are shown in appendix A.

† Details of the derivation of equation (B2) are shown in appendix C.