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# Mulliken Electronegativity

Robert S. Mulliken proposed that the arithmetic mean of the first ionization energy (Ei) and the electron affinity ($$E_{ea}$$) should be a measure of the tendency of an atom to attract electrons. As this definition is not dependent on an arbitrary relative scale, it has also been termed absolute electronegativity:

$\chi_{Mulliken} = \dfrac{E_i + E_{ea}}{2}$

However, it is more usual to use a linear transformation to transform these absolute values into values that resemble the more familiar Pauling values. For ionization energies and electron affinities in electronvolts:

$\chi_{Mulliken} = 0.187 (E_i+E_{ea})+0.17.$

and for energies in kilojoules per mole,

$\chi_{Mulliken} = (1.97 \times 10^{-3})(E_i+E_{ea})+0.19.$

The Mulliken electronegativity can only be calculated for an element for which the electron affinity is known, fifty-seven elements as of 2006. The Mulliken electronegativity of an atom is sometimes said to be the negative of the chemical potential. By inserting the energetic definitions of the ionization potential and electron affinity into the Mulliken electronegativity, it is possible to show that the Mulliken chemical potential is a finite difference approximation of the electronic energy with respect to the number of electrons., i.e.,

$\mu_{Mulliken}= -\chi_{Mulliken} = -\dfrac{E_i + E_{ea}}{2}$

### Significance

Despite being developed from a very different set of principles than Pauling Electronegativity, which is based on bond dissociation energies, there is a good correlation between Muillikin and Pauling Electronegativities for the atoms, as shown in the plot below.

Although Pauling electronegativities are usually what are found in textbooks, the Mullikin electronegativity more intuitively corresponds to the "ability of an atom to draw electrons toward itself in bonding," and is probably a better indicator of that property.  However, because of the good correlation between the two scales, using the Pauling scale is sufficient for most purposes.

### References

1. Mulliken, R. S. (1934). "A New Electroaffinity Scale; Together with Data on Valence States and on Valence Ionization Potentials and Electron Affinities". Journal of Chemical Physics 2 (11): 782–793.
2. Mulliken, R. S. (1935). "Electronic Structures of Molecules XI. Electroaffinity, Molecular Orbitals and Dipole Moments". J. Chem. Phys.3 (9): 573–585.
3. Pearson, R. G. (1985). "Absolute electronegativity and absolute hardness of Lewis acids and bases". J. Am. Chem. Soc. 107 (24): 6801.
4. Huheey, J. E. (1978). Inorganic Chemistry (2nd Edn.). New York: Harper & Row. p. 167.
5. This second relation has been recalculated using the best values of the first ionization energies and electron affinities available in 2006.
19:57, 10 Jul 2014

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