Abstract

We consider the quantum mechanical description of a diatomic molecule. We apply to it, the Born & Oppenheimer approximation, together with the cast [total energy x mass x size**2 ~h²] (we established previously), written for the electronic description (with fixed nuclei); here, "mass" is the electron mass.

Our approach yields an essential relationship for the classical vibration period, in terms of the [square root of the reduced mass of the nuclei] x [the square of the internuclear distance], at the given total electronic energy. The quantum multiplier that comes into play, next to the Planck Constant, in this latter expression, is determined in the subsequent part. The approach yields a whole new systematization regarding all diatomic molecules.

We draw the classical vibration periodversus [the square root of the reduced mass of the nuclei] x [the square of the internuclear distance], for different chemical families, yielding indeed a smooth behavior. The plots are further bettered, along the determination of the quantum multiplier of concern, throughout the subsequent articles.