Lone Electron Pairs: Beyond the Rabbit Ears

In chemistry, quantum mechanics and orbital theory often rub up uncomfortably against more naïve bonding theories, such as VSEPR and Lewis structures. For example, VSEPR tends to give the impression that the positions of lone pairs (or better yet, the orientations of filled non-bonding orbitals) are dictated by the number of electronic domains around the atom. Water, then, which has four electronic domains around oxygen—two single bonds and two lone pairs—apparently has lone pairs at 109.5º angles in a plane perpendicular to the H–O–H plane. The carbonyl oxygen, which VSEPR suggests is “really” trigonal, has two “rabbit-ear” lone pairs at 120º angles. These pictures make the lone pairs look equivalent, and helps us slot these structures in mentally with analogous structures, like imines (for the carbonyl) and ammonia (for water).

MO theory suggests that the lone pairs shown are not equivalent.

MO theory suggests that the lone pairs shown are not equivalent.

Yet, MO theory suggests that the lone pairs shown are not in equivalent orbitals! The simplest explanation for water is that the atomic 2p orbital on oxygen perpendicular to the H–O–H plane cannot interact with the 1s orbitals on hydrogen (there’s zero net overlap), so one of the 2p orbitals on oxygen must show up as a non-bonding molecular orbital. But this orbital can only hold two electrons, so the other lone-pair-bearing orbital on oxygen must be a hybrid. In a nutshell, one lone pair is best characterized as a π MO (the pure 2p orbital) while the other is a σ MO. The two lone pairs are not equivalent. As it turns out, this situation holds up even for lone-pair-bearing atoms in larger molecules. The inequivalency holds for both canonical and natural bond orbitals (NBOs), but the paper that inspired this post focuses on the usefulness of NBOs in the correct description. Continue reading →


Chemical Education Roundup, 7-22-12

Has it really been almost a year since I last published a roundup? Wow. I confess that I’ve been putting much more effort recently into another project, The Organometallic Reader. With BCCE 2012 coming on soon, it seems an appropriate time to start the roundup train going again. I can’t make it to BCCE this year, unfortunately, but the e-program looks fascinating. Follow my man Jeff Raker on Twitter for nods to talks he finds interesting.

So what’s new in the world of chemical education research? What are the cool jams? What is everybody up to? Here are some of my favorite papers over the past year, in no particular order.

On the theoretical side, all organic chemists should check out the hybrid orbital controversy that erupted in the pages of J. Chem. Educ. earlier this year. At issue is whether hybrid orbitals are “real” and whether they should be taught to general and organic chemistry undergraduates. Rebuttals to the original paper brilliantly come to the defense of hybrid orbitals. As an educator, I feel more confident teaching and discussing hybrid orbitals with students after reading this series.

I’ve been waiting on this one for a while: in April, Grove & Cooper’s article on representational competence while drawing organic reaction mechanisms was finally published. Although the papers’ results left me wanting more, the authors’ conclusions will resonate with any organic chemistry teacher. They found that many students avoid using mechanistic approaches to solving organic chemistry problems when mechanisms are not the direct goal, as in “predict-the-product” questions. However, among students who did draw mechanisms, a disturbing trend emerged: the proportion of students who drew nonsensical mechanisms containing cyclic electron flow actually increased with time! On the positive side, the most notable trend over time is a decrease in “nucleophile-attacks-nucleophile” and “electrophile-attacks-electrophile” mechanisms. Still, the (understandable) disrespect that students develop for physically correct mechanisms over time is staggering. Organic chemical educators must be relentless! Continue reading →

Should Hybrid Orbitals Sell the Farm and Move to Florida?

Should hybrid atomic orbitals be placed alongside ancient scientific misconceptions like phlogiston?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. Continue reading →