Hydrogen bonding relating to molecular orbital theory

In [1, p. 232] here is an explanation of how alcohols hydrogen bond to each other and I do understand how the alcohols form hydrogen bonds to each other:

FIGURE 6.15 Water and alcohols are both Brønsted acids and Brønsted bases. This figure shows hydrogen bonding between molecules of water $$(\ce{R=H})$$ and alcohols.

Is it possible to think of hydrogen bonding as a Lewis Acid-Base reaction rather than just a Brønsted Acid-Base reaction, and, by extension, think of this whole scheme as a HOMO-LUMO interaction?

Like, can I think of hydrogen bonding as a HOMO-LUMO interaction in general, arising from the idea that it can be classified as a Lewis Acid-Base reaction?

References

1. Jones, M.; Gingrich, H. L.; Fleming, S. A. Organic Chemistry, 4th ed.; W.W. Norton: New York, 2010. ISBN 978-0-393-93149-5.

Yes you can think of hydrogen bonding in terms of MO theory. Consider a hydrogen bond between two water molecules as a simple example.

The donor hydrogen donates electron density into the $$\pi^*$$ orbital of oxygen which is the LUMO of the acceptor oxygen. This thus weakens the donor $$\ce{O-H}$$ bond, but shortens the distance between the donor hydrogen and acceptor oxygen.

Thus, there are two components to be considered: the pure electrostatic attraction and the stabilization due to covalent interactions.

Because all you're asking about is the MO side of things, as explained above, hydrogen bonding can be viewed as donation of electrons into the $$\pi*$$ orbital of some acceptor atom. This could indeed be called a Lewis acid-base interaction, but I don't hear this very often.

I'm not sure what your textbook is talking about with hydrogen bonding being a Brønsted-Lowry reaction. Hydrogen bonding is not a reaction (in the traditional sense) so I would disagree with your textbook. The acceptor oxygens are accepting electrons much more than they are accepting the whole proton which would make them Lewis acids. It's certainly possible for water/alcohols to behave as either Lewis acids or bases and Brønsted-Lowry acids or bases, but the former is much more common based on the fact that auto-ionization is quite a small effect but hydrogen-bonding is a very large (and common) one.

Regarding the MO view of things, the exact same logic can be applied in inorganic chemistry when considering carbonyl compounds or dihydrogen/dihydride compounds. In that case the donation of electrons into a $$\pi*$$ orbital (or $$\sigma*$$ orbital in the case of dihydrogen compounds) is internal to the molecule however and we call it backbonding.

Here's an MO and orbital diagram showing that interaction.

• Oh but my textbook isn't exactly saying that it's a reaction. I think it's just saying that hydrogen bonding can be thought of as a Bronsted Lowry interaction, though that might be misleading to a certain extent.
– Abhi
Aug 12 '16 at 12:20
• That sounds rather unlikely. The hydrogen atom is the electron deficient atom. How could it be the electron donor? I would think that it is more likely that the oxygen lone pair orbital is the HOMO which interacts with the O-H sigma* LUMO Aug 30 '18 at 2:27

If you want to think of the hydrogen bond in valence bond terms then it is possible to write down five terms that contribute to the structure$^*$.
$\ce{A-H..A}$ , covalent A-H bond
$\ce{A^- -H^+ ..A}$ and $\ce{A^+ -H^- ..A}$ ionic A-H bond
$\ce{A^- -H ..A^+}$ and $\ce{A^+ -H ..A^-}$ charge transfer A..A bond.

The ionic (electrostatic) contribution accounts for approx 65% of the bonding, with charge transfer more important for shorter bonds (<0.28nm) and ionic contribution for longer bonds.

$^*$ Jeffrey, 'An introduction to hydrogen bonding'

• How does that answer my question? I'm asking for how i could think of it in terms of MO theory and whether the thinking above is legitimate i.e. Whether thinking of hydrogen bonding as a HOMO-LUMO interaction is correct
– Abhi
Aug 10 '16 at 11:15
• Rather than consider the dots in your picture, (which actually don't mean much) using the terms above means that you can say what electronic structures you can expect to contribute to a hydrogen bond. The alternative is to use a molecular orbital approach then there are terms such as electron repulsion, charge transfer, dispersion & polarisation contributing. Take you pick :) Aug 10 '16 at 11:26
• I should add that using mo theory, as used to build up, say, $\ce{O2}$, or benzene is difficult to apply when there is a 3 centre bond such as O..H-O. Aug 10 '16 at 13:04

In fact, yes. It can be explained by a HOMO-LUMO interaction. I am currently running NBO (natural bond orbital) computations for a theoretical study of hydrogen bonds in some models. And NBO interprets hydrogen bond as the donation of electrons from the lone pair (non-bonding electrons) of the hydrogen acceptor to the (LUMO) antibonding orbital of the hydrogen donor.

For example LP1 O--- BD* (O--H) This means that there is a donation of electrons from one lone pair (LP) of oxygen (which is in a non-bonding orbital) to the antibonding (LUMO) orbital of the O-H bond. Interestingly, I just found out that there can be a type of hydrogen bonding between a lone pair of oxygen and C-H as the hydrogen donor. In some old papers in the literature, it is referred to as weak CH/O hydrogen bonds. (10.1021/ma0485585)

I hope that this is enlightening.