A Spectroscopic Description of Asymmetric Isotopologues of CO₂

A polyad-conserving algebraic model applied to vibrational excitations of asymmetric isotopologues of CO₂ is presented. First, the problem of vibrational excitations is studied by taking into account only the minimum subspace of states to characterize the Fermi interaction. This analysis allows an estimation of the force constants as well as the feasibility of describing the system in a local mode scheme, in terms of SU(2) operators associated with Morse ladder operators for the stretches. This description together with the algebraic U(3) for the bends establishes the dynamical group SU₁(2) × U(3) × SU₂(2) for a series of isotopologues. Six isotopologues are considered, namely, ¹⁶O¹²C¹⁸O, ¹⁶O¹²C¹⁷O, ¹⁶O¹³C¹⁸O, ¹⁶O¹³C¹⁷O, ¹⁷O¹³C¹⁸O, and ¹⁷O¹²C¹⁸O in their electronic ground states. For isotopologues ¹⁶O¹²C¹⁸O, ¹⁶O¹²C¹⁷O, ¹⁷O¹²C¹⁸O, and ¹⁶O¹³C¹⁸O, the vibrational description was carried out using a Hamiltonian involving 14 parameters. For this series of isotopologues with a number of energy terms 90, 57, 42, and 40, the deviations obtained were rms = 0.15, 0.10, 0.06, and 0.07 cm^-1, respectively. For ¹⁶O¹³C¹⁷O, with 28 experimental energies and involving 13 parameters, the deviation was rms = 0.05 cm^-1, while for ¹⁷O¹³C¹⁸O, a different strategy was proposed since only 12 experimental energy levels. In all cases, the polyad scheme P₂₁₂ = 2(ν₁ + ν₃) + ν₂ was considered. In addition, a new criterion of locality/normality degree is proposed, embracing the case of molecules with normal mode behavior, in particular, the isotopologues of CO₂.