|
Direct Methods (crystallography)
In crystallography, direct methods are a family of methods for estimating the phases of the Fourier transform 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 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 for which they were awarded the 1985 Nobel prize in Chemistry. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystallography
Crystallography is the branch of science devoted to the study of molecular and crystalline structure and properties. The word ''crystallography'' is derived from the Ancient Greek word (; "clear ice, rock-crystal"), and (; "to write"). In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming 2014 the International Year of Crystallography.UN announcement "International Year of Crystallography" iycr2014.org. 12 July 2012 Crystallography is a broad topic, and many of its subareas, such as X-ray crystallography, are themselves important scientific topics. Crystallography ranges from the fundamentals of crystal structure to the mathematics of Crystal system, crystal geometry, including those that are Aperiodic crystal, not periodic or quasi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex-valued function of frequency. The term ''Fourier transform'' refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 determination of a structure from diffraction data. The phase problem is also met in the fields of imaging and signal processing. Various approaches of phase retrieval have been developed over the years. Overview Light detectors, such as photographic plates or CCDs, measure only the intensity of the light that hits them. This measurement is incomplete (even when neglecting other degrees of freedom such as polarization and angle of incidence) because a light wave has not only an amplitude (related to the intensity), but also a phase (related to the direction), and polarization which are systematically lost in a measurement. In diffraction or microscopy experiments, the phase part of the wave often contains valuable information on the stu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herbert A
Herbert may refer to: People * Herbert (musician), a pseudonym of Matthew Herbert * Herbert (given name) * Herbert (surname) Places Antarctica * Herbert Mountains, Coats Land * Herbert Sound, Graham Land Australia * Herbert, Northern Territory, a rural locality * Herbert, South Australia. former government town * Division of Herbert, an electoral district in Queensland * Herbert River, a river in Queensland * County of Herbert, a cadastral unit in South Australia Canada * Herbert, Saskatchewan, Canada, a town * Herbert Road, St. Albert, Canada New Zealand * Herbert, New Zealand, a town * Mount Herbert (New Zealand) United States * Herbert, Illinois, an unincorporated community * Herbert, Michigan, a former settlement * Herbert Creek, a stream in South Dakota * Herbert Island, Alaska Arts, entertainment, and media Fictional entities * Herbert (Disney character) * Herbert Pocket, a character in the Charles Dickens novel ''Great Expectations'' * Herbert West ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jerome Karle
Jerome Karle (born Jerome Karfunkle; June 18, 1918 – June 6, 2013) was an American physical chemist. Jointly with Herbert A. Hauptman, he was awarded the Nobel Prize in Chemistry in 1985, for the direct analysis of crystal structures using X-ray scattering techniques.NRL Scientists Receive 1985 Nobel Prize in Chemistry , . Accessed September 22, 2009.W.A. Hendrickson (2013) ''Jerome Karle (1918–2013)'', 499(7459), pp 410. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 methods to solve a structure. Its formulation is the following: F_ = \sum_ F_F_ which states how the structure factor for a beam can be calculated as the sum of the products of pairs of structure factors whose indices sum to the desired values of h,k,l. Since weak diffracted beams will contribute a little to the sum, this method can be a powerful way of finding the phase of related beams, if some of the initial phases are already known by other methods. In particular, for three such related beams in a centrosymmetric structure, the phases can only be 0 or \pi and the Sayre equation reduces to the triplet relationship: S_ \approx S_ S_ where the S indicates the sign of the structure factor (positive if the phase is 0 and negative if it is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nobel Prize In Chemistry
The Nobel Prize in Chemistry () is awarded annually by the Royal Swedish Academy of Sciences to scientists in the various fields of chemistry. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895, awarded for outstanding contributions in chemistry, physics, literature, peace, and physiology or medicine. This award is administered by the Nobel Foundation and awarded by the Royal Swedish Academy of Sciences on proposal of the Nobel Committee for Chemistry, which consists of five members elected by the Academy. The award is presented in Stockholm at an annual ceremony on December 10th, the anniversary of Nobel's death. The first Nobel Prize in Chemistry was awarded in 1901 to Jacobus Henricus van 't Hoff, of the Netherlands, "for his discovery of the laws of chemical dynamics and osmotic pressure in solutions". From 1901 to 2024, the award has been bestowed on a total of 195 individuals. The 2024 Nobel Prize in Chemistry was awarded to Demis Hassabis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Protein
Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residue (biochemistry), residues. Proteins perform a vast array of functions within organisms, including Enzyme catalysis, catalysing metabolic reactions, DNA replication, Cell signaling, responding to stimuli, providing Cytoskeleton, structure to cells and Fibrous protein, organisms, and Intracellular transport, transporting molecules from one location to another. Proteins differ from one another primarily in their sequence of amino acids, which is dictated by the Nucleic acid sequence, nucleotide sequence of their genes, and which usually results in protein folding into a specific Protein structure, 3D structure that determines its activity. A linear chain of amino acid residues is called a polypeptide. A protein contains at least one long polypeptide. Short polypeptides, containing less than 20–30 residues, are rarely considered to be proteins and are commonly called pep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 (waves), phase information is lost during a diffraction measurement. Direct methods provides a method of estimating the phase information by establishing statistical relationships between the recorded amplitude information and phases of strong reflection (physics), reflections. Background Phase Problem In electron diffraction, a diffraction pattern is produced by the interaction of the electron beam and the crystal potential. The real coordinate space, real space and reciprocal space information about a crystal structure can be related through the Fourier transform relationships shown below, where f(\textbf) is in real space and corresponds to the crystal potential, and F(\textbf) is its Fourier transform in reciprocal space. The Euclidean vector, vectors \textbf and \text ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 determination of a structure from diffraction data. The phase problem is also met in the fields of imaging and signal processing. Various approaches of phase retrieval have been developed over the years. Overview Light detectors, such as photographic plates or CCDs, measure only the intensity of the light that hits them. This measurement is incomplete (even when neglecting other degrees of freedom such as polarization and angle of incidence) because a light wave has not only an amplitude (related to the intensity), but also a phase (related to the direction), and polarization which are systematically lost in a measurement. In diffraction or microscopy experiments, the phase part of the wave often contains valuable information on the stu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
X-ray Crystallography
X-ray crystallography is the experimental science of determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to Diffraction, diffract in specific directions. By measuring the angles and intensities of the X-ray diffraction, a crystallography, crystallographer can produce a three-dimensional picture of the density of electrons within the crystal and the positions of the atoms, as well as their chemical bonds, crystallographic disorder, and other information. X-ray crystallography has been fundamental in the development of many scientific fields. In its first decades of use, this method determined the size of atoms, the lengths and types of chemical bonds, and the atomic-scale differences between various materials, especially minerals and alloys. The method has also revealed the structure and function of many biological molecules, including vitamins, drugs, proteins and nucleic acids such as DNA. X-ray crystall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
