The potential energy surface of CO₂ from an algebraic approach

Abstract

The potential energy surface for the ground state of the 12 C 16 O 2 molecule is estimated through an algebraic approach based on unitary groups. It is shown that a purely algebraic approach may lead to a unphysical surface even when the fit turns out to be of a remarkable high quality. The vibrational description is obtained in the framework of the U (2) × U (3) × U (2) model, where the U (2) algebras are associated with the CO bond stretching and the U (3) algebra with the OCO bending. The algebraic representation of the Hamiltonian is obtained through the connection between the coordinates and momenta and the generators of the dynamical algebra. It is shown that through this connection is possible to choose the appropriate set of spectroscopic parameters leading to the right Potential Energy Surface (PES). The fit from which the PES is estimated involves 101 energy levels with an standard deviation of rms = 0.53 cm −1 .

A study of the Raman spectrum of CO2 using an algebraic approach

“…1) we are confident to use the expansion (14) along with the model presented in Ref. [1,2] to simulate the Raman spectrum of CO 2 at high temperature. In Fig.…”

“…[2]. b Values obtained in this work by a fitting of experimental polarizability transition moments (see Table 1).…”

“…A convenient improvement is achieved with the introduction of the anharmonization procedure [1,2,10] …”

“…An algebraic description of the vibrational excitations of carbon dioxide (CO 2 ) in its ground electronic state has been recently reported [1,2]. The novel contribution of that work is the use of a polyad-preserving local-mode model to describe a molecule with a strong normal-mode behavior, taking advantage of the inclusion of anharmonic effects from the outset [3].…”

“…In Refs. [1,2] a set of 101 experimental vibrational energies were fitted with a root mean square deviation of 0.53 cm −1 . This description can be considered accurate for the standards of vibrational spectroscopy.…”