Bürgi-Dunitz Angle

35 years ago anyone who thought of a nucleophile attacking a C=O group, imagined its approaching along path "A" from straight above the carbon.

Thinking in a more sophisticated way about achieving maximum overlap, one might have thought that approach from direction "B" would make more sense, because it avoids unfavorable overlap with the top of the 2p AO of the oxygen atom.

But no one I know thought in this way at that time.
They didn't think about HOMOs, LUMOs, and overlap.

In the 1970s Hans-Beat Bürgi and Jack Dunitz in Zurich devised a way to get a sort of "movie" of nitrogen "attacking" a carbonyl group. Their method was to find x-ray crystal structures of many different compounds that had both C=O groups and nitrogen atoms, and to plot positions of the relevant atoms (N, C, O, and the two other atoms attached to C) on the same graph.


The graph at the right superimposes 14 of these structures with N-C distances less than 3Ċ (A through O) such that:

All central carbons lie exactly on top of one another

All oxygens fall on the same C-O line (only A and L are shown)

All nitrogens lie in the plane of the page (as do C and O) and are labeled A-O

The two R groups of each compound lie in and out of the plane of the figure on top of one another to the left of C and are labeled A-O.

Bürgi and Dunitz noticed what you notice from the graph:

The nitrogen atoms do not group randomly about the C=O. They tend to be found along a line that makes an angle of 110° with the C-O bond (as in "B" above).

Furthermore, the closer N gets to C (note particularly structures H, I, K, L), the longer the C-O bond gets, and the more the R groups bend back, in all cases approaching the geometry expected in the product from addition of the nitrogen to the C=O.

You might wonder what keeps the nitrogen from adding fully to C=O in these structures that represent early and intermediate stages of "reaction". Of course the plot above does not show the other atoms in the 14 molecules pictured. The other atoms are involved in various bonds and non-bonded repulsions that keep the nitrogen from approaching the C=O more closely. Although attraction of the HOMO of nitrogen for the LUMO of C=O may not be enough to bring them all the way to bonding distance, it seems sufficient to favor alignment at the appropriate bonding angle, especially once the atoms come within about 2.4 Ċ.

Figure modified from Bürgi and Dunitz, Accounts of Chemical Research, 16, 153-161 (1983)

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copyright 2000 J.M.McBride