Correlation between the electronegativity ansatz of Mulliken and Gordy

Journal of Molecular Structure: THEOCHEM 947 (2010) 123

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Correlation between the electronegativity ansatz of Mulliken and Gordy Nazmul Islam Department of Chemistry, Global Environment Research Foundation (Centre for Post Graduate Programme), University of Mysore, Kalyani 741235, India

a r t i c l e

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Article history: Received 19 December 2009 Received in revised form 21 January 2010 Accepted 21 January 2010 Available online 6 February 2010

a b s t r a c t This study shows that the Gordy and Mulliken definitions of electronegativity are nicely converged to a single point. Ó 2010 Elsevier B.V. All rights reserved.

Keywords: Gordy electronegativity ansatz Mulliken electronegativity ansatz Electrostatic definitions of ionization energy Electron affinity and electronegativity Correlation between Gordy Mulliken and DFT scale of electronegativity

The concept of electronegativity has been extensively used in chemistry to correlate chemical binding, reactivity and other physico-chemical properties of atoms and molecules. In this note, a relationship between the electronegativity scales of Mulliken [1] and Gordy [2] is shown. Mulliken proposed an empirical definition of electronegativity (vM) as:

vM ¼ 1/2 ðI þ AÞ

ð1Þ

Putz [3] showed that the density function electronegativity (vDFT) [4] approximates the former Mulliken electronegativity formula.

vDFT ¼ ð@E=@NÞv ¼ ðENþ1  EN1 Þ=2 ¼ 1/2 ðI þ AÞ ¼ vM

ð2Þ

Gordy [2] suggested that the electronegativity of an atom is equal to the electrostatic potential of the effective nuclear charge, Zeff, of the nucleus felt by one of its valence electrons at a radial distance equal to the atom’s single bond covalent radius (rcov).

vG ¼ Z eff =rcov ðIn atomic unitÞ

ð4Þ

Now, for an atom, the change in energy associated with the increase of q, on removal of an electron of charge e, would be the ionization energy, I. Similarly, the energy evolved on addition of an electron with q would be the electron affinity, A. Hence, putting I = E(N + 1)  E(N) = {(q + e)2/ E-mail address: [email protected] 0166-1280/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2010.01.039

vDFT ¼ vM ¼ 1/2 ½ðq þ eÞ2 =ð2rÞ  ðq2 =2rÞ þ ðq2 =2rÞ  ðq  eÞ2 =2r ¼ ðZ eff e2 Þ=r

ð5Þ

where Zeff = q/e In atomic units Eq. (5) is

vDFT ¼ vM ¼ Z eff =r ¼ vG

ð6Þ

Hence, we may conclude that the Gordy’s scale of atomic electronegativity can be derived relying upon the charge sphere model for I and A. This study further reveals that the three definitions of electronegativity are nicely converged to a single point.

Acknowledgement

ð3Þ

Classically, the energy E (N) of charging a conducting sphere of radius r with charge q is given by [5]

EðNÞ ¼ q2 =2r ðIn C:G:S UnitÞ

2r}  (q2/2r) and A = E(N)  E(N  1) = [(q2/2r)  {(q  e)2/2r}] in Eq. (2), we get

I am thankful to Prof. D.C. Ghosh (University of Kalyani). References [1] [2] [3] [4] [5]

R.S. Mulliken, J. Chem. Phys. 2 (1934) 782. W. Gordy, Phys. Rev. 69 (1946) 604. M.V. Putz, Int. J. Quantum Chem. 106 (2006) 361. R.G. Parr, R.A. Donnelly, M. Levy, W.E. Palke, J. Chem. Phys. 68 (1978) 3801. R.P. Feynman, R.B. Leighton, M. Sands, The Feynman Lecture on Physics, vol. 2, Addison-Wesley, Massachusetts, 1964.