An essential approach to the architecture of diatomic molecules: 2. How are size, vibrational period of time, and mass interrelated?

In our previous article, we arrived at an essential relationship for T, the classical vibrational period of a given diatomic molecule, at the total electronic energy E; i.e., T = [4π ² /(√n₁ n₂ h)]√gM₀ mₑ R₀² , where ℳ0 is the reduced mass of the nuclei; m e is the mass of the electron; R is the internuclear distance; g is a dimensionless and relativistically invariant coefficient, roughly around unity; and n 1 and n 2 are the principal quantum numbers of electrons making up the bond(s) of the diatomic molecule, which, because of quantum defects, are not integer numbers. The above relationship holds generally. It essentially yields T ∼ R 2, for the classical vibrational period versus the square of the internuclear distance in different electronic states of a given molecule, which happens to be an approximate relationship known since 1925 but not understood until now. For similarly configured electronic states, we determine n 1 n 2 to be R/R 0, where R is the internuclear distance in the given electronic state and R 0 is the internuclear distance in the ground state. Furthermore, from the analysis of H2 spectroscopic data, we found out that the ambiguous states of this molecule are configured like alkali hydrides and Li2. This suggests that, quantum mechanically, on the basis of an equivalent H2 excited state, we can describe well, for example, the ground state of Li2. On the basis of this interesting finding, herein we propose to associate the quantum numbers n 1 and n 2 with the bond electrons of the ground state of any diatomic molecule belonging to a given chemical family in reference to the ground state of a diatomic molecule still belonging to this family but bearing, say, the lowest classical vibrational period, since g, depending only on the electronic configuration, will stay nearly constant throughout. This allows us to draw up a complete systematization of diatomic molecules given that g (appearing to be dependent purely on the electronic structure of the molecule) stays constant for chemically alike molecules and n 1 n 2 can be identified to be R 0/R 00 for diatomic molecules whose bonds are electronically configured in the same way, R 00 then being the internuclear distance of the ground state of the molecule chosen as the reference molecule within the chemical family under consideration. Our approach discloses the simple architecture of diatomic molecules, otherwise hidden behind a much too cumbersome quantum-mechanical description. This architecture, telling how the vibrational period of time, size, and mass are determined, is Lorentz-invariant and can be considered as the mechanism of the behavior of the quantities in question in interrelation with each other when the molecule is brought into uniform translational motion or transplanted into a gravitational field or, in fact, any field with which it can interact.