Russell 5. Drago University of Illinois at Urbona-Champaign Urbano, IIinois 61801
A Criticism of the Valence Shell Electron Pair Repulsion Model
Recent articles in the literature have championed the use of the valence shell electron pair repulsion, VSEPR, approach to predicting molecular structure.' Recently, the authors of general chemistry textbooks have grasped this idea and incorporated it into the curriculum. This approach leads to the impression that electron-electron repulsions determine the geometries of molecules, because the model is presented in the form of an explanation and structures are used to confirm the model. The factors that influence the geometry of molecules are much more complicated than the VSEPR model lead one to believe. Furthermore, the evaluation of the electron-electron interactions are not simple and; in the VSEPR model, they are not fundamentally based, e.g., all of the e2/r,, integrals are never evaluated for the different structures. One is told that bond pair-bond pair repulsions are less important than lone pair-bond pair. This is quite acceptable. However, when one goes from NH3 to PHs, one would expect both lone pair-bond pair and hond pair-bond pair repulsions to decrease. With an increased radial projection of the lone pair, i t is difficult to determine a priori for a tetrahedral geometry whether hond pair-bond pair or hond pair-lone pair repulsions would be changed more. We know what must he assumed to make the answer come out right. But, this is an additional assumption to be memorized. Next, we are' told that hond pairs have a pear-shaped charge distribution, and there is less bond pair-bond pair repulsion when an electronegative atom is attached to the central atom. This accounts for the fact that NF3 hond angles are 102.1" and those for NH3 are 107.3". It does not account for the fact that the angles in PH3 are 93.3, in PF3, 97.8", and in PC13, 100.3". Some new effect is needed. There are many other failures of this rule which have not been presented. The F-C-F angle in H-CF3, where hond repulsions between C-F and C-H should he larger than C-F with C-F, is 108.8", while the C1-C-CI angle in HCCb is 110.4" and the I-C-I angle in H-CIS is 113". In HzCC12, the angle is 111.8", i.e., greater than in CHC13. In CHzFz, the F-C-F angle is 108.3', hardly changed from HCF3. There are many more examples. We really do not understand all of the factors giving rise to molecular geometries. The approach I recommend does not overcome this difficulty but it does not mislead students into thinking they understand a problem whose answer is not known. Quantum mechanists have had trouble in understanding where the 3 kcal mole-' harrier to rotation in ethane arises. Thus, we should teach our students that many factors influence the geometrical arrangement of the atoms in a molecule and, in nearly all cases, the relative importance of the various effects is not understood. If there were no other way of predicting structures, some people might justify using the VSEPR approach even though i t is modelbased by presenting it as a qualitative explanation that has not been confirmed by quantum mechanics or any rigorouslv accentable auantitative evaluation of the electronelectron rep;lsions but which often gives the right answer. However, there is an alternative apvroach which involves -. memorizing a few empirical facts and is intellectually more satisfying. 244
/ Journal of Chemical Education
US
a Teaching Device Table 1. Number of Attached Groups, Geometries and Hybridization
HYbrid. izagroups tion No. of
4
Geometry
2
sp
Linear
3
spZ
Planar, 120' angle
spJ
Tetrahedral, 109" angle
Example H-Be-H CkTI/CI CI,B/cI I I
a
a
H
0
I H-C-H
I
H
I CI-~b-CI
I
Ci
F
I I
F-B-F F
This alternative approach2 is capable of predicting the moss structural features of the molecule and does not atiempt to pi6dict when 5" distortions from this gross structure occur. This is certainlv adequate for any considerations one is likely to encounter in general chemistry. Prediction of Geometry The following empirical rules enable one to predict the approximate geometry and, if one desires, to guess at the hybridization of many molecules. These rules apply to structures that the molecules have in the gaseous state. 1) When there are no lone pairs on a central main grouv. atom, the geometry depends'on the number of groups attached to the central atom in the manner described in Tahle 1. 2) Here we shall consider central atoms with eight or less electrons about it. When there are lone pairs on the central atom, each lone pair counts as a group in the above scheme if the central atom is a second row element. If the central element is a third, fourth, etc., row atom and if the groups attached to the central atom are oxygen or a halogen, the lone pair also counts as a group. If the g . rou . ~ sattached are less electronegative than bromine (that is, if almost anything other than a halogen or oxygen is attached), rhe lone pair orcupies nn unhyhridired irk& tal and does not count as a When the s orbital is used to accommodate a lone pair, only p orbitals remain for bonding, and the geometry involves an arrangement of Gillespie, R. J. and Nyholm, R. S., Quart. Reus., 11, 339 (1957).Gillespie, R. J., J. CHEM. EDUC., 40, 295 (1963). Gillespie, R. J., Angew. Chemie (int. ed.). 6, 819 (1967). Gillespie, R. J., J. CHEM. EDUC., 47.18 (1970). ZIn the course of writing a textbook for general chemistry, I thdught of how I went about predicting structures; 1 usually got them right long before VSEPR was heard of. The empirical rules in the followingsection resulted and are integrated into the chapter on bonding in: Drago, R. S., "Chemistry and its Impact on Modern Man." The Maemillan Co., New York, to be published.
Table 2. Geometries of Molecules with Lone Pairs Molecules NHJ. H.+
Hybrids (aeometrv) spS ttrtrahrdral~
PHs. Hz>
p o r b ~ t a l (90'ongles) s
PC13
sp3
(tetrahedral)
Pertinent aspect of above rule
Although we have not yet treated any examples, these rules also apply to molecules with double bonds. The * electrons are not counted as groups or lone pairs. For example, in ethylene, whose Lewis structure is
Secand.rw central aturn
Third mw arum, low
elecrroneeatlvrtvoi attached$oups Third-row atom halogens
-
attacherl -... ....
the groups a t about 90" angles toeach other. Some examples are listed in Table 2. We can find molecules with almost a complete range of angles between 90 and 108". These rules should enable you usually to come within 4" of the correct angle. If we have .two different groups attached to the central atom, one very electronegative and one not, and two lone pairs, the bond angles are often someplace in between 90 and 108", for example, the S-S-CI angle in SzClz is 104"
3) In the Lewis structure of many molecules, there are more than eight electrons about the central atom. A very common number is ten and a common geometry for ten electrons is the trigonal bipyramid. Two groups occupy apical positions and three equatorial. When the groups are different, the most electronegative groups occupy apical positions. The equatmial groups are bonded by three sp2 hybrids. This leaves phosphorus with one p orbital to bond three groups. It could use a 3d orbital to form two p-d hybrids to bond the apical chlorines. An alternative description of the bonding to the apical groups involves a three-center molecular orbital. The three a.o.'s, phosphorus p,, chlorine pr, and the p, orbital of the other chlorine, combine to form three MO's: ai, oz, and a3. TWOelectrons are added to a1 and two to an. If molecules with central atoms that contain ten or more electrons have lone pairs on the central atom, the lone pairs invariably count as groups. From this you see that the s and p orbitals can form only four conventional electron pair bonds and accommodate eight electrons. T o account for more than eight electrons around the central atom, either d orbitals must be used or delocalized threecenter bonds employed. The descriptions are not equivalent and the correct answer is somewhere in between these two alternatives. When twelve electrons are involved, the groups are arranged in an octahedral fashion about the central atom and the bonding can be described as sp3d2, for example SFs.
there are three groups around carbon which are joined by spz hybrids. (Taking the plane of this page as xz, p, and p,, AO's are involved. The p, orbitals left over on each carbon overlap in a * manner to form the * bond. Here, which ever atom we wish to describe becomes the "central" atom. There is no one central atom in the molecule. Actuallv. anv atom with more than one .Doup. attached to it can b i seleked as the .'central atom." As another example of a molecule with n bonds consider
The 0-N-CI angle is 116' (that is, the lone pair counts as a group: sp2 hybrids); the p, orbital on nitrogen CV perpendicular to page) and the p, orbital on oxygen overlap to form the r bond. In applying these rules, always draw the Lewis structure first. fieure out the a-bond hvbrids next. then describe t h i s conds. It should be emnhasized that the eeometrical nredictions in the above discussion are a m i d a t from empirical facts which are based on the results from many structural determinations. I believe if you confront most chemists with a completely new molecule and ask him to predict its structure (1) he will write the Lewis structure (2) he will think of an analogous compound whose structure is known (3) be will predict the new structure by analogy with the known one. It is deceptive to lead a freshman into believing anything else. The rules presented above summarize these analogies and enable you to predict the geometries of many molecules. If the need arises, one can then guess a t which hybrid orbitals would be used to point toward the atoms surrounding the central atom and bond these atoms to the central atom. I t is a simple matter to memorize the exceptions to these facts as they are encountered in your further study of chemistry and use them for future analogies. It is not very much more work to memorize the essential statements in the above discussion than i t would be to memorize all the VSEPR rules that would have to be used to "explain" all the structures treated here. The approach described here does have the advantage of telling it like it is. It is more desirable to memorize facts instead of unconfirmed and quite possibly incomplete theories when the effort involved is the same.
Volume 50. Number 4, April 1973 / 245
