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k 0 2 R ω g M 4 E min min | | π = . Where 0 M is the reduced mass of the molecule, min R the “internuclear distance” associated with ω , and k g a Lorentz invariant dimensionless coefficient, insuring the equality; it depends only on the electronic structure of the molecule; therefore for electronic states configured similarly, we expect the coefficient k g , to remain practically the same; it takes values, roughly around unity. The framework in question is interesting, given that, for alike electronic states of a given molecule, min E versus 2min 2 0 R ω M , should behave linearly. This further, should allow the determination of k g , for the states in consideration. The expression is anyway valid for any diatomic molecule, along with a given k g . On the other hand, the “ground states” of bonds delineating chemical similarities, display “alike electronic configurations”. This means that, k g for such bonds, should remain practically the same. Thus, regarding the ground states of such molecules, min E versus 2min 2 0 R ω M should further be expected to behave linearly (the quantities of concern, now being exclusively assigned to the ground states of the molecules in question). We check this prediction successfully for the entire body of diatomic molecules and calculate k g , for different “chemical families”. The relationship we discover has got as much predictive power as that provided by the classical quantum mechanical tools; it is though incomparably simpler and faster.

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The interdependence of electronic energy, period of time, mass and internuclear distance displayed by any object, Part 2: Molecular derivation and application to chemically alike molecules