Ab initio ro-vibrational Hamiltonian in irreducible tensor formalism: a method for computing energy levels from potential energy surfaces for symmetric-top molecules

Abstract

A theoretical approach to study ro-vibrational molecular states from a full nuclear Hamiltonian expressed in terms of normal-mode irreducible tensor operators is presented for the first time. Each term of the Hamiltonian expansion can thus be cast in the tensor form in a systematic way using the formalism of ladder operators. Pyramidal XY₃ molecules appear to be good candidates to validate this approach which allows taking advantage of the symmetry properties when doubly degenerate vibrational modes are considered. Examples of applications will be given for PH₃ where variational calculations have been carried out from our recent potential energy surface [Nikitin et al., J. Chem. Phys. 130, 244312 (2009)].

Keywords:

• irreducible tensor operators
• variational calculations
• vibration–rotation energy levels
• symmetric-top molecules

Acknowledgements

We acknowledge the support from GDRI SAMIA program, from ANR CH4@Titan grant, from IDRIS computer centre of CNRS France and of the computer centre Reims-Champagne-Ardenne. A.N. thanks the University of Reims for the invitation to work on this project.