lonic Character, Polarity,
J. K. Wilmshurst
Union Carbide Corporation Parmo, Ohio
and Electronegativity
The concepts of ionic character and polarity differ between the valence bond (VB) or molecular orbital (MO) treatments of chemical bonding, a t least to the degree of approximation that is normally considered in all empirical correlations and many theoretical calculations. This distinction is, unfortunately, often overlooked and the concepts of one theory erroneously used in conjunction wit,hthose of the other. Especially is this true of the electronegativity concept which is itself obtained only very loosely from the concept,^ of ionic character and polarity. I n the present article an attempt is made to define clearly ionic character and polarity in both the VB and MO approximations; in addition, the electronegativity concept is discussed. Two basically different, though relatively fundamental, definitions of electronegativity can be made in both the VB and MO approximations but, because of the necessity in any electronegativity definition of defining the electronegativity of an atom with respect to that of a second atom, no single electmnegativity value for an atom in all environments appears possible.
difficulty, can, however, be made. First, the overlap contribution can be arbitrarily equally divided between the covalent and ionic contributors and the ionic character written as (@Si, P2)/(1 ZPSi, p2); or, secondly, the overlap integral can be ignored and the ionic character written as b2/(1 p2). The first approximation is analogous to that used by Mulliken ( I ) in his population analysis method, while the second is that normally accepted and widely used in all empirical correlations ( 2 ) . The difference between ionic character calculated from either of these approximate definitions is not serious and we, therefore, prefer to define ionic character in the VB approximation as simply P2/(l +P2). Writing the one-electron MO wavefunction as
+
+ +
+
~
the MO for a two-electron bond can be written as a product of these oneelectron functions in terms of Equations (1)and (2), giving
lonic Character
The VB wavefunction for a two-electron bond can he written in terms of the Heitler-London function
*.."
= (2
+ 2SP)-'/4**(1)*e(Z) + **(2)*s(l)l
(1)
where #a, #B are the normalized wave functions descrihing the electron in the vicinity of A or B, respectively, 1 and 2 refer to the pair of electrons, and S = . f # ~ $ ~ d . ris the overlap integral, together with an ionic function +ion
= (1
+ 2 0 9 + a2)-'/g [$~(1)+*(2)+ a h ( 1 ) + ~ ( 2 ) 1 (2)
For the one-electron MO, as given by Equation (4), the concept of ionic character does not arise, but for the two-electron MO of Equation (5), the ionic character can be approximately defined, similarly to the VB case above, by ignoring S, as (1 +or2)/(1
+
Polarity
The ionic function of Equation (2) leads to the concept of an intrinsic polarity, which can be defined rigorously as I1
- a'[/(l
+ 2aS' + a4)
and if this is combined with the concept of ionic character as defined above, the bond polaxity can be written as Now the contributions of the ionic and covalent functions to the hybrid, represented by Equation (3), are simply P2/(1 ZPSi, P2)and 1/(1 26St0 P2), respectively, and clearly these two contributions do not total unity, the difference depending on the magnitude of the overlap integral S,,. Thus, a rigorous definition of ionic character is impossible. Two approximate definitions of ionic character, which overcome this
+
+
+
+
Presented a8 part of the Symposium on the Nature of Chemical Banding before the Division of Inorganic Chemistry at the 139th Meeting of the ACS, St. Louis, March, 1961.
132
/
Journol of Chemical Education
Pl(1
+ P') X
I1
- a a l / ( l + 2aSx + aB)
in the VB approximation, or (1
+ az)/(l + a)l X
I1
- a a l / ( l + 2aS2 + a x )
in the MO approximation. It is of interest to point out here the dependence of both ionic character and polarity in the MO approach on the same parameter a, in contrast to the VB approximation where the ionic character depends explicitly only on @whilethe polarity depends upon both a and 8. If we ignore the overlap integral S in the expressions for bond polarity above, the polarity in the MO case may be written simply as
+
11 - al/(l a) which is just that obtained directly from the one-electron MO of Equation (4). Electronegotivity
The concept of polarity has inherent in it an idea of relative electron attracting power or electronegativity and can, therefore, he used as a definition of electronegativity. Thus, we can define two electronegativity concepts; intrinsic electronegativities, XA,XB, in terms of the intrinsic. polarity as
electron affinity of an atom is a measure of its electronegativity, and while this has long been accepted and appears from experience to he leasonably valid, it should be made clear that it is not a fundamental definition of electronegativity as is often assumed. However, the inequality that if IA EA
