On the determination of C0 (or A0), D0K,H0K, and some dark states for symmetric-top molecules from infrared spectra without the need for localized perturbations

For symmetric-top molecules, the normal Δk = 0, Δl = 0 and Δk = ±1, Δl = ±1 selection rules for parallel and perpendicular bands, respectively, do not allow the determination of the K-dependent rotational constants, C0 (or A0), D0K, and H0K. However, we show here that several different combinations of allowed and apparently unperturbed rovibrational infrared transitions can give access to those constants. A necessary ingredient for the application of this technique is a band with selection rules Δk = ±1 (or Δk = 0), Δl = ∓2, such as an overtone or difference band, and appropriate other bands. Bands with selection rules Δk = ±2, Δl = ∓1 are also useful but are seldom found. As a general rule, more than one vibrational transition is needed. Examples are given for boron trifluoride (BF3), sulfur trioxide (SO3), and cyclopropane (C3H6) for which there are microwave measurements that provide a check on the derived constants. The technique is also extended to a D2d molecule, allene, even though we have no measurements to use as an example. Examples are also given for the determination of dark states from difference bands, and/or hot bands, and also whole forbidden bands that arise from mixing with distant energy levels.