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Crystal-Cloudy, Crystal-Clear

Roald Hoffmann

Snapshots Along the Way

The very same crystal-packing forces, which in a given crystal structure make for more chemical uncertainty than the standard deviations lull you into believing, also teach us so much more than what we imagined we could learn from a static structure. For a group of structures, judiciously chosen, can reveal the geometric changes that a flexible molecule undergoes and even the course of atomic motions in reaction.

Figure 2. Nucleophilic additionClick to Enlarge Image

There is a time to praise. I recall so vividly the impact made in this context by two 1973 papers, and I celebrate here their untarnished silver anniversary. In the first Hans-Beat Bürgi, Jack Dunitz and Eli Shefter of the Federal Institute of Technology in Zurich took six structures of reasonably complex organic molecules (perhaps only one of them, notorious methadone, widely known) containing within one and the same molecule an amine (R3N) and a carbonyl group (RR'C=O). These are relatively placid organic functionalities, but they also interact; indeed a ubiquitous organic reaction, a so-called nucleophilic addition of an amine to a carbonyl group, is shown in Figure 2. In solution further steps follow, but the reaction is (and was in 1973) thought to begin as indicated.

Figure 3. Structure of methadone.Click to Enlarge Image

Bürgi, Dunitz and Shefter's six molecules all had the requisite amine and carbonyl in the same molecule. I show only one of the six, the aforementioned methadone (Figure 3). The six molecules are very different, and the packing forces acting on them differ too. Intramolecular flexibility (influenced by strain and conformational restrictions in a given molecule) and variable intermolecular pressures (those packing differences) conspire—no, by beautiful chance, just happen—to "freeze in" the molecules in different points along a reaction pathway. By design, labor and with much luck, the static molecular structures may trace out the way a chemical reaction proceeds, dynamically.

Figure 4. Plot (atom positions on the CO plane)Click to Enlarge Image

Many more points have been added to this curve, but I choose to show the six molecules that Bürgi, Dunitz and Shefter plotted on one graph, the fixed carbonyl group pointing to 4 o'clock (Figure 4). See the amine approaching at top? Oh say, can you see the RR' groups on the C of the carbonyl swing down as the amine approaches? We did see, by the x-ray's strong light! The Bürgi, Dunitz and Shefter paper was a true revelation.

Figure 5. Trigonal bipyramidClick to Enlarge Image

A few months later in 1973, Earl L. Muetterties and Lloyd J. Guggenberger, then at du Pont de Nemours's Central Research Department, looked at a seemingly very different problem. Inorganic molecules in which five ligands are bonded to a central atom can assume a variety of geometries. Most common is a trigonal bipyramid (Figure 5, left). At the time one also had a few square pyramids (Figure 5, right) and a straggling of weird structures not one, not the other.

Figure 6. Crystal structuresClick to Enlarge Image

As drawn the two extreme geometries look very different. They're actually pretty close to each other, as R. Stephen Berry at the University of Chicago recognized some time before. A special slight motion of the ligands, named the Berry pseudorotation, takes one into the other. Now look at the crystal structures of seven molecules plotted by Muetterties and Guggenberger (Figure 6).

Cut them out, mount them on cards, flip the cards—you have a movie of the Berry pseudorotation. All that certainty a crystal-clear consequence, as was the beautiful path for nucleophilic addition discovered by Bürgi, Dunitz and Shefter, of the same totality of small forces that make us feel that measured distances might be substantially less certain than indicated.

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