An essential approach to the architecture of diatomic molecules: 1.Basic theory
Yarman, Nuh Tolga
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We consider the quantum-mechanical description of a diatomic molecule of electronic mass m(0e), internuclear distance R-0, and total electronic energy E-0e. We apply to it the Born-Oppenheimer approximation, together with the relation E(0e)m(0e)R(0)(2) similar to h(2) (which we established previously), written for the electronic description (with fixed nuclei). Our approach yields an essential relationship for T-0,T- the classical vibration period, at the total electronic energy E-0e; i.e., T-0 = [4pi(2)/(rootn(1)n(2)h)] rootgM(0)m(e) R-0(2). Here, At,0 is the reduced mass of the nuclei; m(e) is the mass of the electron; g is a dimensionless and relativistically invariant coefficient. roughly around unity (this quantity is associated with the particular electronic structure under consideration; thus, it remains practically the same for bonds bearing similar electronic configurations); and n(1) and n(2) 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 n(1) and n(2) need to be refined. This task is undertaken in our next article, yielding a whole new systematization regarding all diatomic molecules.