A Spectroscopic Description of Asymmetric Isotopologues of CO2

A polyad-conserving algebraic model applied to vibrationalexcitationsof asymmetric isotopologues of CO2 is presented. First,the problem of vibrational excitations is studied by taking into accountonly the minimum subspace of states to characterize the Fermi interaction.This analysis allows an estimation of the force constants as wellas the feasibility of describing the system in a local mode scheme,in terms of SU(2) operators associated with Morseladder operators for the stretches. This description together withthe algebraic U(3) for the bends establishes thedynamical group SU (1)(2) x U(3) x SU (2)(2) for a seriesof isotopologues. Six isotopologues are considered, namely, (OCO)-O-16-C-12-O-18, (OCO)-O-16-C-12-O-17, (OCO)-O-16-C-13-O-18, (OCO)-O-16-C-13-O-17, (OCO)-O-17-C-13-O-18, and (OCO)-O-17-C-12-O-18 in their electronicground states. For isotopologues (OCO)-O-16-C-12-O-18, (OCO)-O-16-C-12-O-17, (OCO)-O-17-C-12-O-18, and (OCO)-O-16-C-13-O-18, the vibrational description was carried out using a Hamiltonianinvolving 14 parameters. For this series of isotopologues with a numberof 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 (OCO)-O-16-C-13-O-17, with 28 experimentalenergies and involving 13 parameters, the deviation was rms = 0.05cm(-1), while for (OCO)-O-17-C-13-O-18, a different strategy was proposed since only 12 experimentalenergy levels. In all cases, the polyad scheme P (212) = 2(& nu;(1) + & nu;(3)) + & nu;(2) was considered. In addition, a new criterion of locality/normalitydegree is proposed, embracing the case of molecules with normal modebehavior, in particular, the isotopologues of CO2.