Born–Oppenheimer breakdown in the ground state of carbon monoxide: A direct reduction of spectroscopic line positions to analytical radial Hamiltonian operators

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Abstract
A collection of 10 866 of the most precise ground-state (X1Σ+) vibration–rotational and pure rotational line positions of four carbon monoxide isptopomers (12C16O, 12C18O, 13C16O, and 13C18O) is employed simultaneously in a direct determination of the radial Hamiltonian operator in compact analytical form. The 22-parameter isotopically self-consistent operator takes full account of the Born–Oppenheimer breakdown and its quantum-mechanical eigenvalues represent all the available spectroscopic line positions of CO isotopomers to within the experimental uncertainties. Rayleigh–Schrödinger perturbation theory is employed to calculate quantum-mechanical molecular constants of rotation (Bν – Mν) for nine common isotopomeric forms of CO. Together with the quantum-mechanical vibrational eigenvalues these are fully consistent with the exact eigenvalues obtained by direct solution of the radial wave equation. The set of constants is expected to provide an accurate prediction of line positions of CO isotopomers that have not yet been experimentally observed.

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