The Mulliken Electronegativity Scale

The chemical physicist, R. S. Mulliken, has shown that the average of the ionization potential (IP) and the electron affinity (EA) of an atom 

It may be noted that, in general, electron affinities are much smaller than ionization potentials. This being the case, the ionization potentials alone are rather good measures of electronegativities, particularly for electropositive elements. 

3 electron is distributed would determine whether these bonds have 70 percent, 80 percent, or 90 percent ionic character. 

This approach, which is certainly not exact, breaks down badly if extended to predominantly covalent bonds. To evaluate the degree of ionic character in such bonds if they occur in simple molecules, Pauling has used dipole moments. The term dipole has already been applied to the water molecule, a molecule in which there is a separation between the centers of positive and negative charge (Chap. 4). When the charges are equal in magnitude, the dipole moment, ju, is defined 

In addition to x-ray studies and dipole moments, there are other suggested ways of estimating the ionic character of bonds, but these involve more advanced considerations and none is really satisfactory. It follows then that any quantitative relationship between electronegativity and ionic character (and there are many of them that have been proposed) must be taken with reserve. 

---

While further details are left elsewhere (Magnasco, 2003), we shall content ourselves here to remark that the model atomic energy differences a2— i are seen to follow the Mulliken electronegativity scale (Coulson, 1961 McWeeny, 1979), an being the deepest atomic level for LiH,... 

The equation is valid for a given valence state. For instance, for trigonal boron compounds, a value of electronegativity can be defined for sp hybrid orbitals. Moreover, if the values of the ionization energy and electron affinity are expressed in MJ.moF , then the Mulliken electronegativity scale can be related to the Pauling scale by the relationship ... 

The problem has been resolved [69] by redefining electronegativity as the chemical potential of the valence state, calculated as the quantum potential of the valence electron, confined to its ionization sphere, i.e. x2 = h2/8mrl, expressed in eV. Whereas x corresponds to Pauling electronegativities, subject to simple periodic scaling, x2 corresponds to the Mulliken scale by the same type of operation. All of the many electronegativity scales in existence are simply related to the ionization radii, from which they ultimately derive. 

The Mulliken scale was proposed by Robert S. Mulliken in 1934. On the Mulliken scale, numbers are obtained by averaging ionization potential and electron affinity. Consequently, the Mulliken electronegativities are expressed directly in energy units, usually electron volts. 

At this point we need a criterion in order to properly control the re-scaling procedure. In order to unveil this criterion we are looking back on differential electronegativity formula (4.275) that should be seen as the kernel function for the Mulliken electronegativity functional (4.279). If we observe the analytical places the introduced chemical response indices a, b and the chemical action index appear, respectively, it can be easily seen that only the chemical action is coupled with the total number of electrons in the concerned state. 

It is clear from previous section that in order to derive the atomic radii it is necessary to solve the equations regarding the Mulliken electronegativity in the different scales presented. However, from the AUred-Rochow electronegativity scale is quite simple to get the atomic radii with the form (Putz, 2012b,e)... 

The second one regards both radii because in the different value scales of the Mulliken electronegativity it can be possible to obtain an imaginary component when the square root is performed for a given set N, In order to avoid both problems in one step we propose to take as the present atomic radii the combination between the two radii solutions in the form... 

TABLE 5.12 Electronegativities of selected elements using the revised Pauling scale, the Mulliken-Jaffe scale, and Allen s spectroscopic configuration energies. The iatter scales have been converted to the revised Pauling scale. The Mulliken-Jaffe values are listed for the sp valence hybridization, uniess otherwise indicated. 

Distinguish between the Pauling and Mulliken electronegativity scales. 

Based upon a scale developed by Mulliken, electronegativity is the average of the ionization energy and the electron affinity ... 

This was justified as follows. The energy required to take an electron from a neutral atom Y to a neutral atom Z is /Y — AZt whereas the energy cost to take an electron from a neutral atom Z to a neutral atom Y is Iz — Ay. Hence, the two atoms Y and Z would have an equal propensity for attracting electrons or equal electronegativity if /Y — Az = Iz — AY, that is if IY + Ay = Iz + Az. This is consistent with the Mulliken definition, eqn (3.35), the factor 1/2 being arbitrary. As can be seen by comparing the two different scales in Fig. 3.5, the Mulliken values are approximately 2.8 times the Pauling values. 

Fig. 3.5 The Pauling (left-hand panel) and Mulliken (right-hand panel) electronegativities for the sp-valent elements. Note that the electronegativities scales run vertically downwards in order to emphasize the similarity with the free-atom energy levels in Fig. 2.16 and negative inverse core sizes in Fig. 2.13.

Like the Mulliken method, the Allred-Rochow method defines electronegativities in terms of atomic rather than molecular properties. Another objection is that it fails in the case of hydrogen the above equation yields a value which would give H an electronegativity comparable with O. The value of 2.2 for hydrogen is rather arbitrarily chosen. Nevertheless, the Allred-Rochow scale has won widespread acceptance among inorganic chemists who find it consistent with many features of chemical periodicity. 

Moreover, Gordy s electronegativity differences are proportional to those on the Mulliken scale also. 

The electronegativity scale established by Pauling is not the only such scale, and the electronegativity of an atom A has been defined by Mulliken as... 

For example, fluorine has the Pauling electronegativity of 4.0 and a value of 3.91 on the Mulliken scale. A different approach was used by Allred and Rochow to establish an electronegativity scale. This scale is based on a consideration of the electrostatic force holding a valence shell electron in an atom of radius, r, by an effective nuclear charge,... 

---