Revisited LeRoy-Bernstein formula for weakly bound molecules

The energy law giving the eigen energies of a -cn/Rn-cm/Rm potential (studied by LeRoy in 1980 [1]) is revisited. For n=3, m=6, an analytical law giving the density of states is deduced. In the context of weakly bound levels an energy law giving the vibrational number v versus the binding energy is given. We show that the well-known LeRoy-Bernstein formula [2] [3] has to be corrected by additional terms, with the first one varying as the binding energy , the second one as its square and the third as a power to 7/6. The use of such a law is discussed in the context of the photo-association spectroscopy of long range molecular levels. References [1] Theory of deviations from the limiting near-dissociation behaviour of diatomic molecules, R. J. LeRoy, J. Chem. Phys. 73, 6003 (1980). [2] Dissociation energy and long-range potential of diatomic molecules from vibrational spacings of higher levels, R. J. LeRoy and R. B. Bernstein, J. Chem. Phys. 52, 3869 (1970). [3] The Dissociation Energy of the Hydrogen Molecule Using Long-Range Forces, W. C. Stwalley, Chem. Phys. Lett. 6, 241,1970.