Dear Mal,

Calculating the electronegativity by semi-empirical methods:

Mulliken electronegativity:

 The correlation between Mulliken electronegativities (x-axis, in kJ/mol) and Pauling electronegativities (y-axis).

Robert S. Mulliken proposed that the arithmetic mean of the first ionization energy (Ei) and the electron affinity (Eea) 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, with the units of kilojoules per mole or electronvolts.

X = (Ei + Eea)/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,

X = 0.187(Ei + Eea) + 0.17

and for energies in kilojoules per mole,

uMulliken = -XMulliken = - (Ei + Eea)/2

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.,

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. Bibcode:1934JChPh...2..782M. doi:10.1063/1.1749394.

 Mulliken, R. S. (1935). "Electronic Structures of Molecules XI. Electroaffinity, Molecular Orbitals and Dipole Moments". J. Chem. Phys. 3 (9): 573–585. Bibcode:1935JChPh...3..573M. doi:10.1063/1.1749731.

Pearson, R. G. (1985). "Absolute electronegativity and absolute hardness of Lewis acids and bases". J. Am. Chem. Soc. 107 (24): 6801–6806. doi:10.1021/ja00310a009.

 Huheey, J. E. (1978). Inorganic Chemistry (2nd Edn.). New York: Harper & Row. p. 167.

This second relation has been recalculated using the best values of the first ionization energies and electron affinities available in 2006.

Allred–Rochow electronegativity

 The correlation between Allred–Rochow electronegativities (x-axis, in Å−2) and Pauling electronegativities (y-axis).

A. Louis Allred and Eugene G. Rochow considered that electronegativity should be related to the charge experienced by an electron on the "surface" of an atom: The higher the charge per unit area of atomic surface the greater the tendency of that atom to attract electrons. The effective nuclear charge, Zeff, experienced by valence electrons can be estimated usingSlater's rules, while the surface area of an atom in a molecule can be taken to be proportional to the square of the covalent radius, rcov. When rcov is expressed in picometres,

X = 3590 Zeff/r2cov + 0.744

Allred, A. L.; Rochow, E. G. (1958). "A scale of electronegativity based on electrostatic force". Journal of Inorganic and Nuclear Chemistry 5 (4): 264–268. doi:10.1016/0022-1902(58)80003-2.

Jump up ^ Housecroft C.E. and Sharpe A.G. Inorganic Chemistry (2nd ed., Pearson Prentice-Hall 2005) p.38

Specific Papers Using Semi-emperical Methods For Calculating The Electronegativity:

1-Parameterization of the electronegativity equalization method based

on the charge model 1

G. Menegon,*a K. Shimizu,b J. P. S. Farah,b L. G. Dias*a and H. Chaimovicha

a Department of Biochemistry, Institute of Chemistry, University of Sa˜ o Paulo, Sa˜ o Paulo,

Fast calculation of charge distributions in molecules is feasible in thelectronegativity equalization method, EEM. Atomic electronegativities and hardnesses, fundamental parameters in EEM, were obtained here by using CM1 atomic charges at semiempirical PM3 level as targets. A new optimization approach composed of Genetic and Simplex algorithms is also described. The correlation between EEM and CM1 charges improved considerably (correlation coefficient improved from 0.931 to 0.977, standard deviation from 0.079 to 0.032 and Fisher’s F from 31 627 to 102 977, for 4093 data points) in comparison to previous EEM parameters (L. G. Dias et al., Chem. Phys., 2002, 282, 237, ref. 23). Atomic parameters obtained here are discussed and compared to other EEM schemes and to parameters derived from empirical approaches.

For more details, see attached file.

2-Molecular Physics: An International Journal at the Interface Between Chemistry and Physics

Volume 2, Issue 4, 1959

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Original Articles: A determination of the electronegativity parameter in molecular orbital calculations on heteronuclear molecules containing nitrogen

DOI: 10.1080/00268975900100351

Abstract

Using the semi-empirical LCAO molecular orbital method, the electronegativity parameter δ for nitrogen has been chosen to give reasonable fit between computed and ‘correct’ bond orders for a series of heterocyclic molecules. A δ-value of about 0·9–1·0 has been found for nitrogen in six-membered rings, and about 1·8–2·0 for pyrrole.

En employant la méthode des orbitales moléculaires LCAO semi-empirique, on a choisi le paramètre d'electronegativité δ de l'azote afin d'obtenir un accord raisonnable entre les indices de liaison calculés et les indices ‘corrects’ pour une série de molécules hétérocycliques. On trouve une valeur δ d'environ 0,9–1,0 pour l'azote dans les cycles à six atomes, et d'environ 1,8–2,0 pour le pyrrole.

Mit Hilfe der halbempirischen LCAO Methode zur Berechnung von Molecular Orbitals wird der Elektronegativitätsparameter δ für Stickstoff so angepasst, dass die abgeschätzten Bindungsordnungen für eine Reihe heterozyklischer Molekeln gut mit den ‘richtigen’ Bindungsordnungen übereinstimmen. Für Stickstoff in sechsgliedrigen Ringen wird ein δ-Wert von etwa 0,9–1,0 gefunden, für Pyrrol 1,8–2,0.

http://www.tandfonline.com/doi/abs/10.1080/00268975900100351?journalCode=tmph20

Hoping this will be helpful,

Rafik