The "old quantum theory" generates eigenvalues dependent entirely on the properties of classical orbits. Application of these old quantum theory ideas to diatomic molecules with one electron, such as H 2 + , is less successful than the corresponding application to one-electron atoms. Nonetheless, useful insight can be gleaned both from the successes and from the deficiencies of the application. Since obtaining correct values from quantum theory or accurate approximate values from uniform semiclassical theory provides quantitative results, the thrust of any old quantum theory formulation is to aide interpretation of results. The principal goals are then to show (i) the applicability of the method; (ii) the success of the method and its interpretation in terms of bonding in the ground state; and (iii) the fundamental failure of the classical approach and how that failure must influence bonding. The molecular orbits are less useful than their atomic analogues, but still deserve to be more widely known among chemists.