Impact of the dipole-moment representation on the intensity of high overtones

Abstract

Calculating intensities of ro-vibrational transitions is particularly challenging for transitions from a given vibrational state to all upper states up to the dissociation limit because their probabilities decrease exponentially with increasing Δn, the change in the vibrational quantum number. The experimental intensities available for low-Δn values are well reproduced by a variety of models but the models can greatly diverge in predicting the intensities of unobserved high-overtone transitions, the divergence rapidly increasing with the overtone number. In this paper, we investigate the impact of the dipole-moment function (DMF) representation on the high-overtone intensity simulation of the CO molecule. We tested various DMF forms including pointwise representation combined with cubic-spline interpolation, power and trigonometric expansions, and Padé approximants. Numerical calculations were performed with the highly accurate empirical potential-energy function (PEF) of Coxon and Hajigeorgiou (2004) using quadruple-precision arithmetic. Most calculated intensities fall off in the entire range of transitions according to the Normal Intensity Distribution Law (NIDL) (Medvedev, 2012). The slope of the NIDL trend line varies little between different analytical DMFs for a given PEF since the slope is basically associated with the PEF. Based on the NIDL, the limits within which the simulated intensities fall off up to the dissociation limit can be established. We claim that DMFs represented by analytical functions yield best results for all transitions. The pointwise functions (interpolated, in particular, by the conventional cubic splines) result in an unphysical flattening of the intensities at high-Δn transitions, Δn>7 for CO.