We have previously established that, the vibration period T of a diatomic molecule, can be expressed as T = [4pi(2)/(rootninjh)]rootgM(0)m(e)r(2), where M-0 is the reduced mass of the nuclei, M-e the mass of the electron, r the internuclear distance of the molecule at the given electronic state, It the Planck Constant, and g a dimensionless and relativistically invariant coefficient, which appears to be a characteristic of the electronic configuration of the molecule. Herein we validate this relationship, chiefly on the basis of vibrational data of H-2 molecule's electronic states, and achieve its calibration, vis-a-vis the quantum numbers that it is to involve. This, basically yields, the elucidation of the complete set of H-2 spectroscopic data. Thus, the composite quantum number n(1)n(2) along our finding is nothing but the ratio of the internuclear distance r at the given electronic state, to the internuclear distance r(0) at the ground state. This makes that for electronic states configured alike, for which g is expected to remain the same, T-2 versus r(3), should exhibit a linear behavior. Our approach can well be applied to other molecules. (C) 2004 Published by Elsevier Ltd on behalf of the International Association for Hydrogen Energy.