Mulliken scale

There are a number of practical difficulties, however, in setting up a Mulliken scale of electronegativity. The quantity IA in the above analysis is not always the same as the readily-obtained /, the first ionisation potential. Consider as an example the HC1 molecule, where we might consider the resonance structures ... 

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. 

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

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,... 

The Mulliken scale of electronegativity (in volts) can be converted into the Pauling scale Xpa (Pauling units) by the empirical relation ... 

Electron-attracting power of an atom when it is part of a bond Mulliken scale = (/i + fea)... 

Figure 8.8 Plots of the Mulliken, scaled Pauling, and scaled Allen Rochow electronegativities of the elements versus the atomic number to illustrate the consistency and differences between the measures of electronegativity [41, 42].

Two scales of electronegativity are in common use the Pauling scale (proposed in 1932) and the Mulliken scale (proposed in 1934). Another proposal is the Allred-Rochow scale. 

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. 

The Mulliken scale may be more intuitive than the Pauling scale because we are used to thinking ionization eneigies and electron affinities as measures of the electron attracting powers of atoms. The choice of factor 1/2, however, is arbitrary, though reasonable, and no more arbitrary than the specific form of eqn 11.23 that defines the Pauling scale. 

Also the Mulliken scale presents an increasing complication of the electronegativity expression for the atoms involved in hybridizations, during their complexity. 

TABLE 4.19 The Mulliken Scale of Electronegativity Calculated for the First Four Periods of Periodical System, Based On the Relation (4.34), As the Semi-Sum of Ionization Potentials (IP) and of Corresponding Electronic Affinity (EA) ... 

The Mulliken scale considers electronegativity as a measure of the tendency of an atom to attract electrons (Mulliken 1934). Electronegativity is calculated as the arithmetic mean between the first ionization energy (IE) and the eleetron affinity (EA),... 

The Allred and Rochow and the Mulliken scales place the atoms of the periodic table in roughly the same order as the Pauling scale so, for our placement of the AOs in an MO diagram, the values in Table 7.4 will suffice. The other definitions help to highlight different approaches to the concept of electronegativity. 

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