Electronegativities from Kimball atoms He ... Mn (ES April 2015/1963)

This is a non empirical electronegativity scale, with one proportionality constant, adjusted to Allred-Rochow’s value for

The physicochemical idea is very simple: A Kimball sphere of radius Ri has the size of the expected radius of the electron(s) it represents in conjunction with the nucleus or nuclei near its center. Hence, the ratio of net nuclear charge over radius Ri of an atoms core is the potential energy a negative probe charge “feels” at the spheres surface. This is certainly a measure of the “power of an atom to attract electrons to itself when it is part of a compound” (definition of EN, e.g. in D.F.Shriver, P.W.Atkins, C.H.Langford, Inorganic Chemistry, 2nd ed. Oxford University Press, 1994, page 43) . Pauling’s original EN has dimension Sqrt(energy), since he measured the gain in energy of a polar bond between atom1-atom2 in regard to a nonpolar bond with ΔEN=0 by constant*(EN1-EN2)^2. Then we have simply to compute the noble gas cores, form the ratio of net charge/Ri, i.e. He-core:(Z-2), Ne-core:(Z-10), and Ar-core:(Z-18), ..., resp., divided by the computed core ion radius and take the square root. Adjusting these numbers such that EN(Fluorine) = 4.1 (Allred -Rochow version of EN) produces our EN scale, whith proportionality constant 0.414 under the square root. This is all done transparently below for Li to Mn and compared to Allred-Rochow’s and Pauling’s scale. It takes less than 1 sec to compute this notebook.

The third series, K+ to Mn+7, or Z=19 to 25, is not totally comparable, because the Allred-Rochow and Pauling values pertain to the divalent ions Ti+2, V+2, Cr+2, and Mn+2, not to the highest valent cores Ti+4...Mn+7 as the Kimball EN’s do. The values from K+ to Sc+3, only, are similarly defined in all scales.

Allred-Rochow's and Pauling's scales are empirical. The first is a slight correction of the original first Pauling EN scale and is better understandable. There are several other proposals for EN-scales, Mulliken's (splendidly simple!), Sanderson's and more. Our scale on the basis of Kimball's model is a non empirical scale. The values are almost identical to the empirical scales and have a simple explanation! Since the Kimball radii correlate well with Hartree-Fock atomic radial density maxima (to be elaborated in a forthcoming tutorial), our EN scale can also be deduced with Hartree-Fock radii (for those who don't like Kimball's model!).

However, there are important, non empirical, developments in the field of electronegativity. They are much more sophisticated than ours (and harder to understand!), based on DFT. See especially *R.Parr & W.Yang*, "Density-Functional Theory of Atoms and Molecules", Oxford University Press 1989, pages 90ff., and newer publications of Parr and collaborators.

Part of the code in this notebook has been contributed by Willy Heinzelmann (Diplomathesis, 1963, Univ. of Zürich), and by Markus Hehlen (1989, Univ. of Bern).