The Rydberg function describing the potential curves of diatomic molecules is used to 'derive' the α values in the Xα method for diatomic or linear molecules. The α value is expressed as a function of the internuclear separation for each molecule. Computations on Li2, N2, O2 and F2 molecules are carried out. Results for the calculated internuclear equilibrium distances, total energies and the dissociation energies from the present study are consistently better than those computed by the 'conventional' Xα method.