Herbert Aaron Hauptman, the mathematician who won Nobel Prize in Chemistry for his outstanding contribution to X-ray Crystallography passed away. Hauptman was the first to apply rigours mathematical methods for crystal structure determination with X-ray Diffraction (XRD).
Hauptman along with co-inventor Jerome Karle took the guesswork out of the problem. They used probability theory to interpret the patterns on XRD and calculated the angles at which the X-ray beams were deflected as they passed near the electrons surrounding the nucleus of an atom. They then came up with equations that translated this information into maps that pinpointed the location of individual atoms.
Structure determination employs radiation of so short a wavelength that it becomes possible to “see” the atoms – X-rays are normally used for this. This means that the wavelength must be shorter than the distance between each atom. X-rays striking a crystal are deflected and concentrated in different directions, and the intensity of the deflected rays is measured. In order to determine the positions of the atom in a crystal, however, is it not enough to know the direction and intensity of the rays, it is also necessary to know the “phase” of each deflected ray, that is, how much the waves in the different rays are displaced in relation to each other.
The fact that electron density is positive (electrons either exist or they do not) limits the possibilities for phase displacement. Hauptman and Karle have constructed systems of equations that are based on the values of the intensities measured and that describe the limitations. The two scientists have also developed a procedure for solving the equations: the solutions give direct connections between the phases sought.
The Hauptman-Karle method, popularly known as The Direct Method in XRD, took the guess work out of the X-ray analysis and speed up the structure determination of complex proteins, hormones, antibiotics, vitamins and geological minerals.