The potential energy surface of CO₂ from an algebraic approach

The potential energy surface (PES) 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 it is possible to choose the appropriate set of spectroscopic parameters leading to the right PES. The fit from which the PES is estimated involves 101 energy levels with an standard deviation of RMS = 0.53 cm −1 .