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Flack Parameter
In X-ray crystallography, the Flack parameter is a factor used to estimate the absolute configuration of a structural model determined by single-crystal structure analysis. In this approach, one determines the absolute structure of a noncentrosymmetric crystal. The processes used to decide the absolute structure use the anomalous dispersion effect. If atomic scattering factors did not have imaginary parts, the Friedel pairs would have exactly the same amplitudes (i.e., the scattering intensity , F(h k l), ^ from crystal plane (h k l) is equal to , F(-h -k -l), ^). However, atomic scattering factors have imaginary parts due to the anomalous dispersion effect, and Friedel's law is broken by this effect. There are several ways to determine the absolute structure by X-ray crystallography. For example, a comparison of the intensities of Bijvoet pairs or of the R-factors for the two possible structures can suggest the correct absolute structure. One of the more powerful and sim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their crystallographic disorder, and various other information. Since many materials can form crystals—such as salts, metals, minerals, semiconductors, as well as various inorganic, organic, and biological molecules—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 among various mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absolute Configuration
Absolute configuration refers to the spatial arrangement of atoms within a chiral molecular entity (or group) and its resultant stereochemical description. Absolute configuration is typically relevant in organic molecules, where carbon is bonded to four different substituents. This type of construction creates two possible enantiomers. Absolute configuration uses a set of rules to describe the relative positions of each bond around the chiral center atom. The most common labeling method uses the descriptors ''R'' or ''S'' is based on the Cahn–Ingold–Prelog priority rules. R and S refer to Rectus and Sinister, which are Latin for right and left, respectively. Chiral molecules can differ in their chemical properties, but are identical in their physical properties, which can make distinguishing enantiomers challenging. Absolute configurations for a chiral molecule (in pure form) are most often obtained by X-ray crystallography, although with some important limitations. All enant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anomalous Dispersion Effect
Anomaly may refer to: Science Natural *Anomaly (natural sciences) **Atmospheric anomaly **Geophysical anomaly Medical *Congenital anomaly (birth defect), a disorder present at birth ** Physical anomaly, a deformation of an anatomical structure ***Congenital vertebral anomaly, any of several malformations of the spine **Collie eye anomaly, eye disease of dogs ***Coronary artery anomaly, a congenital abnormality in the heart ***Ebstein's anomaly, a congenital heart defect in which the opening of the tricuspid valve is displaced *** Uhl anomaly, a congenital heart disease affecting the myocardial muscle ***Vaginal anomalies Biology * Anomalous, a species of moth in the Noctuid family * Chromosome anomaly, a disorder caused by a structural error in a chromosome or an atypical number of chromosomes *Genetic anomaly, a disorder caused by mutation *Teratology, the study of developmental anomalies Physics *Anomalous diffusion is the movement of molecules from a region of lower concen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scattering
Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiation) in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections of radiation that undergo scattering are often called ''diffuse reflections'' and unscattered reflections are called ''specular'' (mirror-like) reflections. Originally, the term was confined to light scattering (going back at least as far as Isaac Newton in the 17th century). As more "ray"-like phenomena were discovered, the idea of scattering was extended to them, so that William Herschel could refer to the scattering of "heat rays" (not then recognized as electromagnetic in nature) in 1800. John Tyndall, a pioneer in light scattering researc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a + bi, where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number a+bi, is called the , and is called the . The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friedel Pair
Friedel's law, named after Georges Friedel, is a property of Fourier transforms of real functions. Given a real function f(x), its Fourier transform :F(k)=\int^_f(x)e^dx has the following properties. *F(k)=F^*(-k) \, where F^* is the complex conjugate of F. Centrosymmetric points (k,-k) are called Friedel's pairs. The squared amplitude (, F, ^2) is centrosymmetric: * , F(k), ^2=, F(-k), ^2 \, The phase \phi of F is antisymmetric: * \phi(k) = -\phi(-k) \,. Friedel's law is used in X-ray diffraction, crystallography and scattering from real potential within the Born approximation Generally in scattering theory and in particular in quantum mechanics, the Born approximation consists of taking the incident field in place of the total field as the driving field at each point in the scatterer. The Born approximation is named a .... Note that twin operation( ''Opération de maclage'') is equivalent to an inversion centre and the intensities from the individuals are equivalent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amplitude
The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplitude (see below), which are all functions of the magnitude of the differences between the variable's extreme values. In older texts, the phase of a periodic function is sometimes called the amplitude. Definitions Peak amplitude & semi-amplitude For symmetric periodic waves, like sine waves, square waves or triangle waves ''peak amplitude'' and ''semi amplitude'' are the same. Peak amplitude In audio system measurements, telecommunications and others where the measurand is a signal that swings above and below a reference value but is not sinusoidal, peak amplitude is often used. If the reference is zero, this is the maximum absolute value of the signal; if the reference is a mean value (DC component), the peak amplitude is the maximu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imaginary Part
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a + bi, where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number a+bi, is called the , and is called the . The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bijvoet Pairs
Johannes Martin Bijvoet (23 January 1892, Amsterdam – 4 March 1980, Winterswijk) was a Dutch chemist and crystallographer at the van 't Hoff Laboratory at Utrecht University. He is famous for devising a method of establishing the absolute configuration of molecules. In 1946, he became member of the Royal Netherlands Academy of Arts and Sciences. The concept of tetrahedrally bound carbon in organic compounds stems back to the work by van 't Hoff and Le Bel in 1874. At this time, it was impossible to assign the absolute configuration of a molecule by means other than referring to the projection formula established by Fischer, who had used glyceraldehyde as the prototype and assigned randomly its absolute configuration. In 1949 Bijvoet outlined his principle, which relies on the anomalous dispersion of X-ray radiation. Instead of the normally observed elastic scattering of X-rays when they hit an atom, which generates a scattered wave of the same energy but with a shift in pha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R-factor (crystallography)
In crystallography, the R-factor (sometimes called residual factor or reliability factor or the R-value or RWork) is a measure of the agreement between the crystallographic model and the experimental X-ray diffraction data. In other words, it is a measure of how well the refined structure predicts the observed data. The value is also sometimes called the discrepancy index, as it mathematically describes the difference between the experimental observations and the ideal calculated values. It is defined by the following equation: :R = \frac, where ''F'' is the so-called structure factor and the sum extends over all the reflections of X-rays measured and their calculated counterparts respectively. The structure factor is closely related to the intensity of the reflection it describes: :I_ \propto , F(hkl), ^2. The minimum possible value is zero, indicating perfect agreement between experimental observations and the structure factors predicted from the model. There is no theoretical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Uncertainty
Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or stochastic environments, as well as due to ignorance, indolence, or both. It arises in any number of fields, including insurance, philosophy, physics, statistics, economics, finance, medicine, psychology, sociology, engineering, metrology, meteorology, ecology and information science. Concepts Although the terms are used in various ways among the general public, many specialists in decision theory, statistics and other quantitative fields have defined uncertainty, risk, and their measurement as: Uncertainty The lack of certainty, a state of limited knowledge where it is impossible to exactly describe the existing state, a future outcome, or more than one possible outcome. ;Measurement of uncertainty: A set of possible states or outcom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
