Isotope shifts and band progressions in SO₂ rovibrational energy levels: using quantum theory to extract rotational constants

We report the isotope shifts of the rotational constants and vibrational band progressions of the sulfur dioxide molecule (SO₂), for all four stable sulfur isotopes³²S,³³S,³⁴S, and³⁶S. These are extracted from exact quantum theoretical calculations of the SO₂ rovibrational energy levels, as reported in Chem. Phys.450–451, 59 (2015) and Chem. Phys.461, 34 (2015) and by fitting these levels to a J-shifting (JS)-type scheme, applied to a representative set of total angular momentum (J) values. The approach used to obtain the rotational constants is unusual in that it is derived directly from the quantum theoretical framework used for the earlier calculation, which gives rise to a flexible (i.e., vibrational- and rotational-state-dependent) but symmetric rotor description. The usual (K_a, K_c) rotational quantum numbers are thus replaced with a single body-fixed azimuthal rotation quantum number, K, with various strategies introduced a posteriori to address rotor asymmetry. The new model fits the numerically computed rovibrational levels well, over a fairly broad range of vibrational (v) and rotational (J) excitations. The computed rotational constants agree well with previously reported experimental values [J. Chem. Phys.58, 265 (1973)]. The explicitly v- and J-dependent approach used here should thus prove valuable in broader contexts—e.g., for an analysis of self-shielding in sulfur mass-independent fractionation, even though the rovibrational levels themselves exhibit mass-dependent fractionation.