Rethinking Hybridization

For more than 60 years, one of the most used concepts to come out of the valence bond model developed by Pauling was that of hybrid orbitals. The ideas of hybridization seemed to be consistent with many experimental observations. Hybrid orbitals were simple to envision, they predicted geometries most of the time for simple p-block compounds and they made the distinction between sigma and pi bonding easy to understand. However, it has always been true that when molecular structures and properties are probed more deeply, the hybrid orbital model – particularly the extreme limits of the model presented in introductory and organic chemistry texts – presents many difficulties. Some of these difficulties include:

Hybridization schemes as typically discussed represent extremes of orbital mixing

An sp3 orbital set on a carbon atom for example implies that all four hybrid orbitals are constituted identically, and that each has 25% s character and 75% p character. In addition, the directional properties of those orbitals – one of the features that make them attractive to chemists – imply that all bond angles around the sp3 hybridized atom will be the same. While this particular argument works fine for methane, it does not work for monochloromethane, where the bond angles are not all the same. The HCH angle is less than the tetrahedral angle and the only way to rationalize this in hybridization terms is to have more p character and less s character in the carbon orbitals interacting with the hydrogen atoms. These fractional hybridization schemes have been used, but have never gained wide acceptance.

More dramatic deviations from idealized hybridization are found in the hydrides of the group VI (16) elements. The bond angle in water is 105.4o, implying that the oxygen orbitals used to bond with the hydrogens have more than 75% p character. By the time you reach H2Se, the bond angle is essentially 90o, implying that only p orbitals are being used by the Se atom to form bonds. A detailed picture of the bonding in water shows that the OH bonds have predominately O p orbital and H s orbital parentage, with some O s character mixed in, while the lone pairs, typically represented as being equivalent (and in equivalent orbitals in a hybridization scheme) are quite different, one being purely O p in character and the other predominately O s in character with a little bit of p character mixed in.

The strict hybrid orbital model is inconsistent with the results of photoelectron spectroscopy

This is observed for many molecules. One of the most dramatic examples is that of methane. Hybrid orbital theory predicts four equivalent bonds in methane. Consequently, the photoelectron spectrum of methane in the bonding region should show a single peak (with associated vibrational structure). This is not the case – two peaks are clearly present, and the integrated intensities of those peaks are very close to 3:1. Likewise for water, where hybrid orbital theory would predict two ionizations – one from the two equivalent bonding orbitals and one from the equivalent lone pairs – four ionizations are observed, consistent with detailed molecular orbital calculations.

Hybrid orbital models are inconsistent with group theoretical predictions

The previous examples of methane and water are useful here. In the Td point group of methane the maximum degeneracy is three (a T representation). Rather than four equivalent bonds, molecular orbital theory and group theory predict that the bonding molecular orbitals fall into two sets – a triply degenerate T2 set and a singly degenerate A1 orbital. This is certainly consistent with the photoelectron spectral results for methane. The four bonds, which arise from the A1 and T2 molecular orbital are equivalent, but they arise from molecular orbitals that differ in symmetry and energy.

A similar situation is found in water. There are no degenerate irreducible representations in the C2v point group of the water molecule. Rather the four molecular orbitals in the bonding region have four distinct energies. One of these orbitals, of B1 symmetry, is a pure p orbital on oxygen, and is therefore one of the lone pairs of electrons. Another orbital, of A1 symmetry, is composed predominately of oxygen s character, and is best described as the second lone pair. The two orbitals that produce the O-H bonds are of A1 and B2 symmetry. As is the case in methane these two orbitals, when taken together, produce two equivalent bonds, but the orbitals themselves are of different symmetry and energy.

In the molecular orbital model there is orbital mixing, but that orbital mixing must be based on symmetry. In some molecules that orbital mixing can produce results that appear very similar to a hybrid orbital picture. For example, in carbon monoxide, a hybrid orbital model would invoke sp hybridization on both C and O with the unhybridized p orbitals forming the pi bonds. An examination of the wavefunctions for the molecular orbitals in this molecule shows that the degenerate pi molecular orbitals are indeed formed from C and O p orbitals only, and the singly-degenerate highest occupied molecular orbital (the sigma bond) is formed from s and p orbitals. However, this agreement is purely a consequence of symmetry. An examination of the coefficients in the wavefunctions shows the pi orbitals to be more than 70% oxygen in character and the sigma orbital to be more than 80% carbon in character, and to have essentially no oxygen s character. This latter orbital is best described as being predominately a lone pair located on the carbon atom (and it the electronic rationale for the fact that CO bonds to metal atoms almost exclusively through the C atom as is the case in binding to hemoglobin and in metal carbonyls).

So what are we to do? One option is to abandon the hybrid orbital model completely and to make descriptions based solely on the molecular orbital coefficients. Another, and perhaps one that is more palatable to many chemists, is to rethink what we mean by hybridization, and realize that all it really means is that orbitals of the same symmetry have been involved in forming a molecular wavefunction. This approach requires discussing fractional orbital mixing from the outset, and makes use of the results of detailed molecular calculations that though once prohibitive for all but the simplest molecules can down be done in minutes for fairly complicated systems. The importance of symmetry concepts in these arguments cannot be underestimated.

Contributors

• William F. Coleman, Professor Emeritus of Chemistry (Wellesley College)