An essential approach to the architecture of diatomic molecules. 1. Basic theory

Abstract

We consider the quantum mechanical description of a diatomic molecule of "electronic mass" m0e, "internuclear distance" R0, and "total electronic energy" E0e. We apply to it the Born-Oppenheimer approximation, together with the cast E 0em0eR02 ∼ h2 (we established previously), written for the electronic description (with fixed nuclei). Our approach yields an essential relationship for T0, the classical vibration period, at the total electronic energy E0e, i.e., T0 = [4π2/(√n1n2h)] √gM0meR02; M0 is the reduced mass of the nuclei; me is the mass of the electron; g is a dimensionless and relativistically invariant coefficient, roughly around unity; this is a quantity associated with just the electronic structure in consideration; thus, it remains practically the same for bonds bearing similar electronic configurations; n1 and n2 are the principal quantum numbers of electrons making up the bond(s) of the diatomic molecule in hand; because of quantum defects, they are not integer numbers. The above relationship holds generally, although the quantum numbers n1 and n2 need to be refined. The related task is undertaken in our next article, yielding a whole new systematization regarding all diatomic molecules.