Force field constants for Formaldehyde obtained from an algebraic approach

Abstract

Recently an accurate spectroscopic description of the vibrational excitations of the molecule of Formaldehyde was presented in the framework of an algebraic local model [R. Bernal, R. Lemus, J. Mol. Spectrosc. 235 (2006) 218]. In that description an effective Hamiltonian is expanded in terms of tensorial couplings among basic operator units associated with the fundamentals. The basic tensors are in turn given in terms of local operators associated with creation and annihilation operators of the Morse and Pöchl-Teller functions. In this description the most important Darling–Dennison and Fermi-like interactions were taken into account. Those interactions together with the diagonal anharmonic contributions provided a total of 43 interactions, which were considered to carried out a fit of 260 energy states up to 12 500 cm −1, obtaining an rms deviation of 2.39 cm −1. In this contribution we establish the connection of the algebraic Hamiltonian with the corresponding description in terms of coordinates and momenta, showing that a full approach carried out in configuration spaces is unable to provide a description of the same quality. The presented connection allows the force constants to be calculated, and consequently spectroscopic predictions for the vibrational spectrum of isotopomers are also possible.