Rovibrational interactions in linear triatomic molecules: a theoretical study in curvilinear vibrational coordinates

TL;DR

This study develops a variational approach using curvilinear vibrational coordinates to analyze rovibrational interactions in linear triatomic molecules, providing accurate energy levels and new insights into l-doubling phenomena.

Contribution

It introduces a novel variational method in curvilinear coordinates for rovibrational analysis and explains l-doubling as an effect of rotational constant inequivalency.

Findings

Fifth-order potential truncation yields high-accuracy vibrational energies.

L-doubling explained by inequivalent average rotational constants.

Theoretical results agree well with experimental and ab initio data.

Abstract

A variational solution to the rovibrational problem in curvilinear vibrational coordinates has been implemented and used to investigate the nuclear motions in several linear triatomic molecules, like HCN, OCS, and HCP. The dependence of the rovibrational energy levels on the rotational quantum numbers and the l-doubling has been studied. Two approximations to the rovibrational Hamiltonian have been examined, depending on the level of truncation of the potential energy operator. It turns out that truncation after the fifth order in the potential is sufficient to produce vibrational energies of high accuracy. An interesting feature of the present formulation of the problem in terms of the curvilinear vibrational coordinates is the explanation for the l-doubling of the rovibrational levels, which in this picture is interpreted as the result of the inequivalency of the average rotational constants in mutually perpendicular planes, rather than as the effect of the Coriolis-type interactions between the vibrational and rotational motions. The present theoretical results are compared with the available experimental data from high-resolution spectroscopy, as well as with other ab initio calculations.