Sanderson electronegativity scale

The current chemistry of the Group IV elements has been reviewed in the second volume of the MTP series. In an analysis of the i.r. band intensities of a number of MHCI3 and MX4 (M = C, Si, or Ge X = F, Cl, Br, or I) molecules, the electronegativities of the Group IV elements have been shown not to vary smoothly as deduced by Pauling, but to vary erratically, as indicated by the Allred-Rochow and Sanderson Electronegativity scales (Table 1). 

The Mulliken, Allred-Richow, Gordy and Sanderson electronegativity scales are all different but they all characterize an atom in a combination, and hence it is possible to convert one scale into another. The absolute electronegativity characterizes isolated atoms and their ability to react (electronic chemical potential). It does not take into account the changes in size and shape of the electron density and external potential to which electrons are subjected when the atoms combine. 

Table W-5. Mass, van der Waals volume, Sanderson electronegativity, and polarizability (atomic original and scaled values).

Besides Pauling s electronegativity scale, estimated on the basis of the energies of bond rupture, there exist some other electronegativity scales based on various assumptions. Among these, the scales obtained by Mulliken, Allred and Rochow and Sanderson, should be mentioned. All these scales, together with the principles of their construction and the values of the electronegativities, can be found in handbooks. 

Sanderson calls his electronegativity stability ratio SR. The electronegativity in this scale is x(SR) = n/(4.19 r ), in which n is the number of valence electrons and r the covalent atomic radius. It also expresses the influence that atomic volume has on electronegativity. Sanderson was the first to point out the electronegativity equalization principle. Although the -values are different in the various scales as is clear from Table 2.4, all the electronegativity scales correlate strongly with one another. 

Tempted by the interpretation of the Kullback-Leibler expression (9.78) as a tool to distinguish two probability distributions, the possibility of using it to compare atomic density functions is explored. To make a physically motivated choice of the reference density Po x) we consider the construction of Sanderson s electronegativity scale [63], which is based on the compactness of the electron cloud. Sanderson introduced a hypothetical noble gas atom with an average density scaled by the number of electrons. This gives us the argument to use renormalized noble gas densities as reference in expression (9.78). This gives us the quantity... 

For the construction of the functional in the above section, the choice to set the reference (the prior) density to that of a hypothetical noble gas atom, in analogy to Sanderson s electronegativity scale, was motivated and the particular choice lead to results which could be interpreted chemically. Following these findings one can see that it would be interesting to compare the information entropy, evaluated locally as... 

TABLE 1.1 Electronegativities of Some Atoms on the Pauling" and Sanderson Scales... 

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 ... 

Sanderson defined a scale of electronegativity [21] based on the assumption that the reactivity of an atom, i.e. its propensity to retain its own electrons and attract others, is linked to its compactness. The most inert elements, the rare gases, are the most compact. Therefore, a chemical combination is the result of the tendency of the atoms to attain the configuration of the most chemically inert elements. Sanderson s electronegativity is characterized by the stability ratio S, which is defined as the ratio of the compactness of an atom to that of the most inert (or compact) element / of its period—the rare gas S = D/D, with D = ZjV = 3Z/47rr. Here Z is the atomic number of the atom and r is the covalent radius. Sanderson s electronegativity is a dimensionless number. 

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