Knowledge Bank

In this work we present some new calculations of vibrational energy spectra and infrared transition intensities within the framework of the vibron $model(1)$. This is an alternative approach to the usual techniques based on the solution of the Schr""{o}dinger equation or on the inclusion of higher order terms in a Dunham expansion. In the vibron model one replaces each interatomic bond with a Lie-algebraic structure. The Hamiltonian is then written in terms of generators of these algebras and, making use of group theory, one obtains energy levels and wave functions. We present here results for several triatomic molecules, both linear and bent, including $CO2,H2S,OCS,N2O,HCN$ and some isotopic species. Depending on the number of terms included in the algebraic expansion, r.m.s. errors in the vibrational energy levels fall in the $1-10cm-1$ range. The vibron model allows also one to compute the expectation values of any operator. We have computed intensities of IR transitions for some of the listed molecules, obtaining results in reasonable agreement with the most recent observations. Possible developments of this approach to the systematic study of tetra-and poly-atomic molecules will be also presented.