Abstract
This study, based on mere considerations induced by the Special Theory of Relativity, has previously established the following relationship between the “minimum electronic energy” , and the related “classical vibration frequency” , in regards to electronic states of a given diatomic molecule: . Where is the reduced mass of the molecule, the “internuclear distance” associated with , and 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 , 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, versus , should behave linearly. This further, should allow the determination of, for the states in consideration. The expression is anyway valid for any diatomic molecule, along with a given . On the other hand, the “ground states” of bonds delineating chemical similarities, display “alike electronic configurations”. This means that, for such bonds, should remain practically the same. Thus, regarding the ground states of such molecules, versus 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 , 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. Key words: Special theory of relativity, quantum mechanics.
Highlights
In this study, it has been shown earlier that the special theory of relativity (STR) imposes the following
It can be checked that the proportionality constant, coming into play, is dimensionless; the somewhat new denominations introduced here, have been defined earlier
Equation (1) outlines the architecture delineated by any given entity with respect to “period of time” T0, “characteristic length” R 0, “clock mass” M 0, and “total energy“ E0, one can associate with the “internal dynamics” of an atomistic or molecular quantum mechanical object
Summary
It has been shown earlier that the special theory of relativity (STR) imposes the following. (Relationship we derived quantum mechanically and we consider for the ground states of molecules belonging to a given chemical family, where the electronic configurations of the bonds can be considered to remain the same) where T0 is the inverse of π 0 ; this is obviously Equation (8), where though the proportionality constant is displayed. We suggest that, for chemically alike molecules, the period of vibration T0 , should behave as proportionally to M0 | E0 | R 0. For each chemical family of concern, g k is calculated and presented in
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