Unitary group approach for effective potentials in 2D systems: Application to carbon suboxide C3O2

Highlights: • An algebraic approach is proposed to describe non-rigid triatomic molecules. • The approach keeps the connection with configuration space. • The quartic potential is analyzed to show the salient features of our model. • The application to the ro-vibrational spectroscopy of the C₃O₂ molecules is presented. A $U\left(3\right)$ algebraic approach is proposed to describe 2D systems for effective potentials. Our approach is based on the 2D vibron model where the addition of a scalar boson is introduced into the 2D harmonic oscillator space. As a crucial ingredient of our approach an algebraic realization of the coordinates and momenta is obtained. This feature provides the tools to obtain the algebraic representation of a 2D Hamiltonian in terms of similitude transformation of a diagonal matrix. As an application of our approach the rotation-bending energy levels of carbon suboxide C₃O₂ are described in good agreement with experimental data.