Kier-Hall electronegativity

Kier and Hall noticed that the quantity (S -S) jn, where n is the principal quantum number and 5 is computed with Eq. (2), correlates with the Mulliken-Jaffe electronegativities [19, 20]. This correlation suggested an application of the valence delta index to the computation of the electronic state of an atom. The index (5 -5)/n defines the Kier-Hall electronegativity KHE and it is used also to define the hydrogen E-state (HE-state) index. 

The E-state indices are atomic descriptors composed of an intrinsic state value I and a perturbation AI that measures the interactions with all other atoms in a molecule. The Kier-Hall electronegativity is the starting point in the definition of the intrinsic state of an atom, which encodes its potential for electronic interactions and its connectivity with adjacent atoms. The intrinsic state of an atom i is [19, 21] ... 

The Kier-Hall electronegativity is used to define the HE-state index HS [19] ... 

Table E-7. Valence vertex degrees 6, vertex degrees 6, their differences, and Kier-Hall electronegativity values for different atoms.

Therefore, the Kier-Hall electronegativity was proposed based on the difference between valence and simple vertex degree, as ... 

Z, atomic number b", valence vertex degree 8, vertex degree VSI, valence state indicator Iar, aromatic indicator I, intrinsic state KHE, Kier-Hall electronegativity. Data from [Kier and Hall, 1999b]. 

Moreover, the following relationship between Li valence vertex degree and Kier-Hall electronegativity KHE holds ... 

Six different weighting schemes are proposed (1) the unweighted case u (yvi = 1 i —, n, where A is the number of atoms for each compound), (2) atomic mass m, (3) the - van der Waals volume v, (4) the Sanderson - atomic electronegativity e, (5) the - atomic polarizability p and (6) the - electrotopological state indices of Kier and Hall 5. All the weights are also scaled with respect to the carbon atom, and their values are shown in Table W-5 moreover, as all the weights must be positive, the electrotopological indices are scaled thus ... 

Further, in the same paper, Kier and Hall demonstrated for the first time a simple and direct relation between electron counts and valence state electronegativity. ... 

---