A Group Electronegativity Method with Pauling Units Steven G. Bratsch The University of Texas. Austin, TX 78712
In a previous paper (I)a simple method of partial charge estimation was developed through the application of Sanderson's Principle of Electronegativity Equalization (2a) to Pauling units. T h e net charge on any group of atoms in a molecule orpolyatomic ion may he calculated as the weighted sum of the atomic partial charges 6c = X(u6)
Two examples serve to illustrate this method. Example 1. Boric acid, B(0H)a (Paulingvalues from (411,
(1)
Here, 6c is the net group charge, u represents the number of atoms of a particular element in the group and 8 represents the partial charges on the atoms. On the basis of eqn. (1)it might be argued that a discussion of group electronegativity is technically unnecessary. Nevertheless, the idea of n.. r o u. ~electronenativitv is historically important heoiusi. the electronegativity concept evolved I;irgrly from the desire of organic chemists to understand reaction mechanisms in termsif the inductive effeds of various functional groups (3). Also, as discussed below, groups are fundamentally different from atoms in their ability to donate or withdraw charge.
Example 2. Methanol, CH30H.
A Group Electronegativity Method
In the previous paper ( I ) it was demonstrated that partial charges on combined atoms can be derived from Pauling electronegativities by making two assumptions: 1) All atoms in a molecule or polyatomic ion achieve the same electronegativity (20). 2) The electronegativity of an atom varies linearly with charge,
doubling when the charge is +I and becoming zero when the charge is -1.
T h e equalized electronegativity X,, is defined according to
where N = x ( u ) = the number of atoms in the species formula and a is the charge of the soecies. The oartial charge on any parti'cular atom is given by
A
Some Other Group Electronegativity Methods (see Table) Group electronegativities have been derived by both "experimental" and "computational" methods. The first approach involves the establishment of a relationship between pre-bonded atomic electronegativities and some experimentally measurable quantity. The relationship is then assumed to remain valid for groups, although such an assumption may occasionally be unjustified (see Discussion below). Experimental quantities that have been employed include: 1) bond energies for evaluation by the Pauling thennochemical
method (3,5),
Adaptation of this method to groups yields the following rules: 1) The group electronegativityis calculated hy
2) ionization potentials and electron affinities for evaluation by
the Mulliken method (3,6), 3) solubility products of predominantly covalent compounds
(71,
4) basicities and oxidative coupling potentials (a), and 5) bond-stretching frequencies (9). These methods (and others) have been reviewed hy Wells 19) ,"I.
where Nc is the number of atoms in the group formula. 2) X , is calrulat~,lw a etp. (?Ibut X,: muvt he weighted in acrord with both h'c and t h p nurnbrrof groups per twtnula. 3 The net group charge is given hy 6c = ~c
X,, - Xc (y)
The second approach involves the calculation of group electronegativity from atomic properties. For example, 11 Cordy's rlrctroctatic potential scale of rlertnmrgativity (101 has bren extended by Wilmshurbt 1111toaccommvdate yruups, Inamutoand Maiuda 112, hare r~centlycorrected an ermr in \Vdmshurst's method of electron counting. ?I In drwluping n group elecfrcmegnt~vitymethod bawl on wlublllty pruducts. Cliffmi ,71 ha* noted that reasmahle crimp values
Volume 62
Number 2 February 1965
101
can often he obtained simply hy averaging the atomic electronegativities. 3) Sanderson has recently revised his electronegativityscale and adjusted the values to the range of the Pauling scale (2b). Group electronegativities can be derived by application of Sanderson's postulate of the geometric mean (2a) to the atomic values. These group values deviate systematically from the others in the table hecause the Sanderson atomic electronegativities,even in their revised form, are not linearly related to the Pauling scale. Combination of Sanderson's conversion equations (2c,13) gives X = (0.33s
+ 0.66)2
(6)
Group electronegativityvalues converted via eqn. (6) are given in the tahle for comparison; in general they are very close to the values calculated from Pauling units via eqn. (4). 4) Huheev has develo~eda .. erOUD. method for Mulliken . (14.15) . elrctroneyativit~es (17) which is mathenlatically ~imilart u the mrthod ~rrsrntedabove. .lardinr et nl. (161have mdified Huheey's method somewhat and extended it to additional valence states. I n compliance with Sanderson's Principle of Electronegativity Equalization (2a), the values in the tahle are "prehonded" moun - . electronegativities that can he expected to vary in response to the chemical environment. The variation among the values in the table reflects both the methods used a n d the atomic electronegativity values assumed. Larae inconsistencies often occur with groups containing multiply bonded atom? multiple honding corresponds to an increase ins-orbital chararter which isclaimed to raise the electronegativity (3, 15). Sanderson (2d) views electronegativity as a fundamental atomic property and does not consider orbital variations important. Another inconsistency in the "computational" group electronegativity values may result from the usage of a single atomic electrunegativity value for different oxidation states, rhrrp heins" evidence that this is incorrect ( 3 . 4 , 7). For ex.--.-ample, it may he necessary to use a pre-bonded atomic electronegativity for phosphorus in -PF2 which is different from that in -PF4. However, as in the preceding paper (I), the purpose of this paper is merely to establish a method of calculation. More accurate atomic electronegativity values will probably eliminate most of the problems. ~
~
~
~~~
Discussion An important difference between atoms and groups is the ability of the latter to dissipate charge over several atoms, increasingly so with increasing Nc (14.17). Polyatomic groups may he viewed as reservoirs of enhanced charge capacity, potentially able to donate or withdraw considerable amounts of charge with only small variations in electronegativity (18) (see figure). Therefore, a group cannot really he treated as a "pseudo-atom" in electronegativity discussions (7,9), and it
follows that some of the "experimental" methods of group electronegativity determination mentioned above may be unreliable. The importance of charge capacity is illustrated by the behavior of the alkyl groups. Despite the fact that pre-bonded alkyl groups are slightly more electronegative than hydrogen (see table), an alkyl group is usually considered to be electron-releasing relative to hydrogen (14,17,19). This is because comnarisons are tv~icallvmade when the alkyl group (or hydroien, is bunded;"an initially electronegati~~~suhst~atesuch as N,0 , halogm, or phenyl (171. Undersurh cunditions .Y, is high and 6,; exceeds d~ (see figure; similar plots have been given by Huheey (14) using Mullikenelectronrgativities). In kwoinr with this. basicities uiamines follow the order R R N >I{?NH > R N H ~ >NH.9 when rorwcted for solvationeffects (171. and the Drotun affinities (basirities) of methanol and &a& are in th'e order CH30H > Hz0 (20). When X .. is low the alkvl arouu is predicted to better absorb negatiye charge than hyi~rogin(i4.17).As evidence for this effcrt. the e a s - ~ h a shaiicities r of alkoxide ions iolloa the order OC~H;
