In
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 wo ...
, 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 de ...
directly, but not so in three dimensions. The key step was taken by
Hauptman and
Karle, who developed a practical method to employ the
Sayre equation
In crystallography, the Sayre equation, named after David Sayre who introduced it in 1952, is a mathematical relationship that allows one to calculate probable values for the phases of some diffracted beams. It is used when employing direct met ...
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, respon ...
s.
Several
software
Software is a set of computer programs and associated software documentation, documentation and data (computing), data. This is in contrast to Computer hardware, hardware, from which the system is built and which actually performs the work.
...
packages implement direct methods.
See also
*
Direct methods (electron microscopy)
In crystallography, direct methods is a set of techniques used for structure determination using diffraction data and ''a priori'' information. It is a solution to the crystallographic phase problem, where phase information is lost during a diffra ...
*
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 de ...
*
X-ray crystallography
X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angle ...
References
Crystallography
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