An interesting controversy has emerged in the Journal of Chemical Education this month, following a paper by Grushow calling for the retirement of the hybrid orbital concept from the chemistry curriculum. The flurry of rebuttals that followed Grushow’s letter are an excellent summary of current thought about the relationship between canonical, delocalized molecular orbitals and localized MOs. The latter, although derived qualitatively from hybrid atomic orbitals, are just as legitimate as the canonical MOs that result from traditional quantum chemical calculations. A wonderful description of the idea with just the right amount of math has been provided by Hilberty, Volatron, and Shaik.
An important point of almost all of the rebuttals is that the traditional photoelectron spectroscopy argument in support of canonical MOs (and arguing against localized MOs) is totally bogus. I mention this particular aspect of the debate because I learned something myself! The traditional argument goes that because methane possesses two different ionization energies, its filled MOs must sit at two different energy levels. The two different ionization energies observed are the result of pulling an electron from MOs of two different energies. Hilberty et al. and DeKock + Strickwerda both point out that localized MO theory may be used with success to explain the two different ionization energies—and that the premises of those who claim otherwise are false. From Hilberty:
The reasoning of those people eager to retire the LMO model, is as follows: since the [Hybrid Atomic Orbital] model puts four electron pairs into four equivalent localized orbitals…then extracting an electron from anyone of these four orbitals should always cost the same energy, leading to a single unique ionization potential (IP). The error in this reasoning is simple: it completely ignores the quantum mechanical requirement that any wave function must match the symmetry of the molecule.
Hilberty goes on to illustrate that when the localized MO approach is applied to this problem, although the filled MOs of CH4 all reside at the same energy, the MOs of ionized CH4+ must bear two different symmetries and sit at two different energies. Hence, two ionization energies should be expected on the localized MO model as well.A second important point of the rebuttals is that the canonical and localized MOs are related by a unitary transformation, and both are solutions to the Schrödinger equation. The canonical MOs are direct solutions to the Schrödinger equation involving the monoelectronic Fock operator, but transforming these MOs such that the distance between electrons is maximized produces the localized MOs! Furthermore, the values of observables associated with the molecule (electron density, energy, etc.) do not change upon the transformation. It makes a lot of intuitive sense that maximizing the distances between electrons should yield the localized MOs.
Ironically, I think Grushow’s letter has had the unintended consequence of strengthening the argument for retaining hybrid atomic orbitals. Their equivalence to canonical MOs is amply demonstrated by the flurry of papers that followed. I should mention that he replied to the rebuttals, offering a weak “that’s not what I meant” argument. Still, the whole series of papers is required reading for those interested in teaching localized MO theory to general or organic chemistry students. Both Grushow and the rebuttals point out that misconceptions among general and organic chemists about the relationship between the two models (e.g., one is more “real” than the other) are far too common.