Transition metal dimer internuclear distances from measured force constants

Several empirical rules, which correlate force constants and equilibrium internuclear distances, have been extended to the transition metal dimers to test which one gives the most accurate fit. It is also of interest to determine to what extent their use can accurately predict internuclear distances for dimers for which there are no available experimental values. Pauling showed by using crystallographic data that internuclear distance can be correlated with the logarithm of the bond order, which itself is closely related to the force constant. Another empirical rule, due to Badger, indicates an inverse correlation between the force constant and the third power of the internuclear distance. Badger's relationship is the most widely used; therefore, it has found considerable application in various branches of chemistry. Guggenheimer proposed a correlation between force constant and the inverse of the internuclear distance raised to the power 2.46. We find that Pauling's rule provides a considerably better fit to existing data than Badger's and Guggenheimer's for the transition metal dimers. Although Pauling's rule gives the best results, the remarkable accuracy of Guggenheimer's relation is of considerable theoretical interest.