NDE (Near-dissociation expansion) including LeRoy-Bernstein formulas are improved by taking into account the multipole expansion coefficients and the nonasymptotic part of the potential curve. The theory is tested with the Rydberg-Klein-Rees (RKR) potential curve of the Cs-2(0(g)(-){6s+6p(3/2)}) state. Results indicate that the formula could be used to improve the determination of the asymptotic coefficient (within a 1% accuracy) and to extract relativistic correction from photoassociation spectra of long-range potential curve of diatomic molecules. (C) 2004 American Institute of Physics.