Algebraic local vibrational spectroscopic description of formaldehyde

The spectroscopic description of vibrational excitations of the molecule of formaldehyde is presented in the framework of a local model, where Morse potentials are associated with the stretching and bending modes, while a Pöschl-Teller potential is considered for the out-of-plane mode. An effective Hamiltonian in constructed in terms of tensorial couplings among basic operator units associated with the fundamentals. This approach is equivalent to take a linear approximation for the expansion of the coordinates and momenta in terms of creation and annihilation operators of the Morse (Pöschl-Teller) potential. Most of Darling-Dennison and Fermi-like interactions consistent with the preservation of the polyad are taken into account. These interactions, together with the anharmonic contributions provides a total of 43 interactions, which were considered to carried out a fit of 260 energy states, obtaining an rms deviation of 2.39 cm−1.