Pauling and Mulliken Scales

In 1932 Pauling formulated the first idea referring to the explanation of the chemical bond nature by introdueing the electronegativity (Pauling, 1932)  

Quantum Nanochemistry Volume II Quantum Atoms and Periodicity 

PRINCIPLE EN9 of Pauling) (a) The normal covalent character between two atoms A and B is transposed by the bond energies additivity of involved atoms  

Using thermochemical data for the bonds formation and based on the principle just expressed, Pauling was able to calculate the electronegativity for the main elements from the periodic table (see Table 4.1). 

This method deficiency consists in the fact that the association of a single electronegativity value for each atom do not cover all the cases of coordination, in this case, the effects due to the hybridizations and also the charges distributed to atoms in molecule, are not counted. 

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Electronegativities of Atoms According to the Scales of Pauling and Mulliken ... 

Distinguish between the Pauling and Mulliken electronegativity scales. 

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.

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,... 

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. 

Actually, if we define the absolute EN, x, as (/+ it is not quite the same as Mulliken s EN. He was interested in a scale which could be used to estimate the polarity of chemical bonds, just as Pauling was. Mulliken s 1 and A are for supposed valence states of an atom or radical, such as it might have in a molecule. The DFT values of I and A are for the ground state of any system, atom, ion, radical or molecule. Also, since v is to be constant, they refer to vertical values and not adiabatic ones. 

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. 

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. 

When electronegativity values obtained by the Allred-Rochow and Mulliken formula are converted to the Pauling scale, they produce values comparable to those from the Pauling scale (Figure 3.2). 

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. 

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. 

The superscript M stands for Mulliken. When the ionization energy and electron affinity are expressed in MJ/mol, the Mulliken electronegativities can be expressed on the Pauling scale using the following formula ... 

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... 

Mulliken has arrived at an electronegativity scale by another and better way, obtaining good agreement with that of Pauling (Table 15). 

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