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.

Now, at this point you may be thinking, who cares? Lone pair orbitals aren’t all that important anyway, and VSEPR works for me. Understandable, but the shapes of lone pair orbitals do have important conformational consequences. The Landis + Weinhold paper lists a number of important applications, but the one I’ll mention here is the conformational dynamics of disulfide bonds. “Rabbit-ear” lone pairs on sulfur suggest that anti (180º R–S–S–R dihedral) and gauche (60º R–S–S–R dihedral) conformations ought to be most important. The gauche structure benefits from the anomeric effect, so we might expect this to be even the global minimum. However, the global minimum actually has an R–S–S–R dihedral of ninety degrees. Wha…?

The favored dihedral angle of R–S–S–R is 90º. Proper depiction of lone pair orbitals helps us see this.

The favored dihedral angle of R–S–S–R is 90º. Proper depiction of lone pair orbitals helps us see this.

Once we admit that one of the lone pairs on each sulfur is in a pure 2p orbital, perpendicular to the S–S–R plane, the beauty of the 90º dihedral becomes apparent. This angle aligns the high-energy 2p lone pair orbital with the σ* orbital of the adjacent S–R bond, which results in very nice p-σ* hyperconjugation. This orbital overlap explains the favored dihedral beautifully. As an aside, the importance of hyperconjugation is supported by studies on R–S–S–R where R is of varying electronegativity. As the electronegativity of R increases, the S–S bond length decreases, as predicted by the hyperconjugation model. Thus, the 90º dihedral is not just the lone pairs wanting to get as far away from one another as possible due to electrostatic repulsion. (Caveat: I can’t find a reference for these studies, aside from the paper linked above.)

The latest paper from the Wisconsin NBO guys is a great one. Worth a read!

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2 Comments

  1. Excellent and enjoyable writing, but I think there are a few common misconceptions here. 1)The VSEPR theory has a strong theoretical foundation, and it is not the electrostatic repulsion of pairs of electrons (if it was, why would they form pairs!); it is based on the Pauli Exclusion Principle, the result of which requires that electrons with the same spin avoid each other. 2) The attempt to equate MOs to localized electrons pairs is not correct. The electron density is an observable (unlike MOs!) and if you examine the electron density of water using the Laplacian or ELF (electron localization function), both of which tease out where there is a local excess of electron density, the lone pairs appear exactly where expected.

    Reply

    1. Very true—thanks for the clarifications. The difference between electrostatic repulsion and the PEP effect is subtle but important.

      Localized lone pairs cannot often be equated with canonical MOs, sure, but I think part of Landis & Weinhold’s argument is that lone pairs can be thought of as “occupying” natural bond orbitals (although NBO theory allows fractional occupancies, which makes things weird). You’re right that the electron density map shows density right where we’d expect it to be based on the VSEPR model.

      Thanks for reading!

      Reply

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