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Crystal-Cloudy, Crystal-Clear

Roald Hoffmann

We are remembered by our exaggerations. So at a recent reunion of my former research-group members, several recalled my saying "When you see a standard deviation in an x-ray crystal structure, multiply it by pi [π, 3.141...], or if the structure is done by friends, by e [2.718...]."

I was talking about structures of molecules—details of their geometry, also of a particularly fruitful way to gain knowledge of these structures. And of the error estimates in such studies.

There is no more basic enterprise in chemistry than the determination of the geometrical structure of a molecule. Such a determination, when it is well done, ends speculation and provides us with the starting point for understanding every physical, chemical and biological property of the molecule. Indeed, the chemical sciences (only modestly imperialistic, I take them to range from materials science through molecular biology) are what they are today largely as the result of careful structure determination. We'd be still waiting in ignorance if we believed the hype of various microscopies. A few very accurate structures have come to us through ingenious use of electron diffraction and various spectroscopies. But the vast majority of what we know about shapes and metric detail of molecules and extended materials derives from studies of the diffraction of x rays by single crystals of molecules, a technique popularly called "x-ray crystallography."

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