Determination of Centrifugal-Distortion Coefficients of Asymmetric-Top Molecules. II. Dreizler, Dendl, and Rudolph's Results

Dreizler, Dendl, and Rudolph used the method of least squares to fit the equation of Kivelson and Wilson, which gives the rotational energy levels of an asymmetric top with first-order corrections for centrifugal distortion, to the observed rotational spectra of dimethyl sulfoxide and dimethyl sulfide. The normal equations obtained were found to be highly ill-conditioned, so that the centrifugal coefficients, A1to A6, were essentially indeterminate. It is shown here that the form of this indeterminacy can be understood quantitatively on the basis of a previously published linear relation between the average values in Kivelson and Wilson's equation. Explicit expressions are presented for the first-order centrifugal corrections to those energy levels that are given by linear or quadratic equations. These expressions suggest that there are no further linear relations of the above type.