Quantitative Correlations between Rotational and Vibrational Spectroscopic Constants in Diatomic Molecules Available to Purchase

The rotational constants $Be$⁠, the vibrational frequencies $ωe$⁠, the vibration–rotation interaction constants $αe$⁠, and the anharmonic constants $xe$ of 160 diatomic molecules are examined in order to determine whether or not there exist consistent relationships between them. Basing the investigation on the Dunham analysis the following correlations are found to be valid within about 5%: (1) The Dunham constants $a1$ and $a2$ are identical for almost all the molecules examined. (2) For diatomics formed from atoms belonging to the ith and jth columns of the periodic table the following monotonic relations exist: $Be / ωe = Kijωe1 / 2 + Lij$⁠, $αe/Be = Kij′ωe1 / 2 + Lij′$⁠, $xe = Kij″ωe1 / 2 + Lij″$⁠. These equations are shown to be interrelated by virtue of the constancy of $a1$ and $a2$⁠. The scope and limitations of the correlations are discussed and several examples are given pertaining to their use for the resolution of incorrect or ambiguous spectroscopic information.