Orbital Electronegativity and Electrical Potential

The energy of an atom, E(q), is a function of its charge q. This function, the same as any function, can be expressed as a Taylor series, i.e. 

The drawback of this definition was, that it had been restricted to the atomic ground states and that it ignored the atomic shell structure, i.e. that large jumps in E(N) are expected, when atomic shells identified by their (n, l) quantum numbers are transgressed. 

About at the same time, though published somewhat later, we were concerned with the calculation of valence state electronegativities following the original definition of Mulliken[23,24] and in turn we expressed the energy of an atom as a function of the charge q in a valence orbital, i.e. a hybrid orbital ready for bonding as 

Defining the ionisation energy for the orbital of the system (atom) as 

substituting b and c into eq. (4.5) yield for the normally singly occupied orbital ready for bonding the orbital electronegativity 

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