crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wor ...

, direct methods are a family of methods for estimating the phases of the

Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...

of the scattering density from the corresponding magnitudes. The methods generally exploit constraints or statistical correlations between the phases of different Fourier components that result from the fact that the scattering density must be a positive real number. In two dimensions, it is relatively easy to solve the

phase problem In physics, the phase problem is the problem of loss of information concerning the phase that can occur when making a physical measurement. The name comes from the field of X-ray crystallography, where the phase problem has to be solved for the det ...

directly, but not so in three dimensions. The key step was taken by

Hauptman Hauptman is a surname. Notable people with the surname include: * Bruno Hauptmann (1899–1936), perpetrator of the Lindbergh kidnapping * Herbert A. Hauptman (1917–2011), mathematician and winner of the 1985 Nobel Prize in Chemistry *Judith Haup ...

and Karle, who developed a practical method to employ the Sayre equation for which they were awarded the 1985

Nobel prize in Chemistry ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then "M ...

. The Nobel Prize citation was "for their outstanding achievements in the development of direct methods for the determination of crystal structures." At present, direct methods are the preferred method for phasing crystals of small molecules having up to 1000 atoms in the asymmetric unit. However, they are generally not feasible by themselves for larger molecules such as

protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, respo ...

s. Several

software Software is a set of computer programs and associated documentation and data. This is in contrast to hardware, from which the system is built and which actually performs the work. At the lowest programming level, executable code consists ...

packages implement direct methods.

References

Crystallography {{crystallography-stub

See also

References