For centuries, it has been known that vibrational and rotational degrees of freedom are in general not separable. Nevertheless, surprisingly little is known about the best strategies for approximately separating these degrees of freedom in practice—even in the case of semirigid molecules, where the separation is most meaningful. There is also some confusion in the literature about the proper way to quantify the magnitude of the Coriolis (i.e., rotation-vibration) coupling in rovibrational Hamiltonians or its effect on the rovibrational eigenenergies. In this study, a vibrational-coordinate-independent metric is proposed to quantify the magnitude of the Coriolis contribution to the rovibrational Hamiltonian. The impact of Coriolis coupling on the rovibrational eigenenergies is computed numerically exactly, using both full and various truncated Hamiltonians. The role played by the choice of the vibrational coordinate system—and especially by the choice of “embedding” or body-fixed frame—is examined extensively, both numerically and analytically. This investigation targets several molecular prototypes, all of which serve as important benchmarks for the high-resolution spectroscopic community. Most of these are triatomic molecules, including water (H216O), its deuterated isotopologues (D216O and HD16O), H3+, and ozone (16O3), but the tetratomic ammonia molecule (14NH3) is also investigated. These studies provide important insight into the nature of Coriolis coupling under various circumstances. The findings of this study also have significant practical ramifications, vis-à-vis the use of simplifying numerical approximation techniques in nuclear-motion computations.
|Journal||Spectrochimica Acta - Part A: Molecular and Biomolecular Spectroscopy|
|State||Published - Apr 5 2021|
- Coriolis coupling
- Eckart embedding
- Nuclear motion computations
- Optimal separation of rotations and vibrations
- Radau bisector embedding