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Equatorial Bond
Cyclohexane conformations are any of several three-dimensional shapes adopted by cyclohexane. Because many compounds feature structurally similar six-membered rings, the structure and dynamics of cyclohexane are important prototypes of a wide range of compounds. The internal angles of a regular, flat hexagon are 120°, while the preferred angle between successive bonds in a carbon chain is about 109.5°, the tetrahedral angle (the arc cosine of −). Therefore, the cyclohexane ring tends to assume non-planar (warped) conformations, which have all angles closer to 109.5° and therefore a lower strain energy than the flat hexagonal shape. Consider the carbon atoms numbered from 1 to 6 around the ring. If we hold carbon atoms 1, 2, and 3 stationary, with the correct bond lengths and the tetrahedral angle between the two bonds, and then continue by adding carbon atoms 4, 5, and 6 with the correct bond length and the tetrahedral angle, we can vary the three dihedral angles for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Groups In Three Dimensions
In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O(3), the group (mathematics), group of all isometry, isometries that leave the origin fixed, or correspondingly, the group of orthogonal matrix, orthogonal matrices. O(3) itself is a subgroup of the Euclidean group E(3) of all isometries. Symmetry groups of geometric objects are isometry groups. Accordingly, analysis of isometry groups is analysis of possible symmetry, symmetries. All isometries of a Bounded set, bounded (finite) 3D object have one or more common fixed points. We follow the usual convention by choosing the Origin (mathematics), origin as one of them. The symmetry group of an object is sometimes also called its full symmetry group, as opposed to its proper symmetry group, the intersection of its full symmetry group with Euclidean group#Direct and indirect is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steric Strain
Van der Waals strain is strain resulting from Van der Waals repulsion when two substituents in a molecule approach each other with a distance less than the sum of their Van der Waals radii. Van der Waals strain is also called Van der Waals repulsion and is related to steric hindrance. One of the most common forms of this strain is eclipsing hydrogen, in alkanes. In rotational and pseudorotational mechanisms In molecules whose vibrational mode involves a rotational or pseudorotational mechanism (such as the Berry mechanism or the Bartell mechanism), Van der Waals strain can cause significant differences in potential energy, even between molecules with identical geometry. PF5, for example, has significantly lower potential energy than PCl5. Despite their identical trigonal bipyramidal molecular geometry, the higher electron count of chlorine as compared to fluorine causes a potential energy spike as the molecule enters its intermediate in the mechanism and the substitue ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Group
In organic chemistry, a functional group is any substituent or moiety (chemistry), moiety in a molecule that causes the molecule's characteristic chemical reactions. The same functional group will undergo the same or similar chemical reactions regardless of the rest of the molecule's composition. This enables systematic prediction of chemical reactions and behavior of chemical compounds and the design of chemical synthesis. The Reactivity (chemistry), reactivity of a functional group can be modified by other functional groups nearby. Functional group interconversion can be used in retrosynthetic analysis to plan organic synthesis. A functional group is a group of atoms in a molecule with distinctive Chemical property, chemical properties, regardless of the other atoms in the molecule. The atoms in a functional group are linked to each other and to the rest of the molecule by covalent bonds. For repeating units of polymers, functional groups attach to their Chemical polarity, nonp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Halogen
The halogens () are a group in the periodic table consisting of six chemically related elements: fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and the radioactive elements astatine (At) and tennessine (Ts), though some authors would exclude tennessine as its chemistry is unknown and is theoretically expected to be more like that of gallium. In the modern IUPAC nomenclature, this group is known as group 17. The word "halogen" means "salt former" or "salt maker". When halogens react with metals, they produce a wide range of salts, including calcium fluoride, sodium chloride (common table salt), silver bromide and potassium iodide. The group of halogens is the only periodic table group that contains elements in three of the main states of matter at standard temperature and pressure, though not far above room temperature the same becomes true of groups 1 and 15, assuming white phosphorus is taken as the standard state.This could also be the case for group 12, al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strain (chemistry)
In chemistry, a molecule experiences strain when its chemical structure undergoes some Stress (mechanics), stress which raises its internal energy in comparison to a strain-free reference Chemical compound, compound. The internal energy of a molecule consists of all the energy stored within it. A strained molecule has an additional amount of internal energy which an unstrained molecule does not. This extra internal energy, or strain energy, can be likened to a compression (physics), compressed spring (device), spring.Anslyn and Dougherty, ''Modern Physical Organic Chemistry'', University Science Books, 2006, Much like a compressed spring must be held in place to prevent release of its potential energy, a molecule can be held in an energetically unfavorable conformation by the Chemical bond, bonds within that molecule. Without the bonds holding the conformation in place, the strain energy would be released. Summary Thermodynamics The Chemical equilibrium, equilibrium of two c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Staggered Conformation
In organic chemistry, a staggered conformation is a chemical conformation of an ethane-like moiety abcX–Ydef in which the substituents a, b, and c are at the maximum distance from d, e, and f; this requires the torsion angles to be 60°. It is the opposite of an eclipsed conformation, in which those substituents are as close to each other as possible. Such a conformation exists in any open chain single chemical bond connecting two sp3- hybridised atoms, and is normally a conformational energy minimum. For some molecules such as those of ''n''-butane, there can be special versions of staggered conformations called ''gauche'' and ''anti''; see first Newman projection diagram in conformational isomerism. Staggered/eclipsed configurations also distinguish different crystalline structures of e.g. cubic/hexagonal boron nitride, and diamond/lonsdaleite. See also * Alkane stereochemistry * Eclipsed conformation In chemistry an eclipsed conformation is a conformation in w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Symmetry
In chemistry, molecular symmetry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a fundamental concept in chemistry, as it can be used to predict or explain many of a molecule's chemical property, chemical properties, such as whether or not it has a molecular dipole moment, dipole moment, as well as its allowed spectroscopy, spectroscopic transitions. To do this it is necessary to use group theory. This involves classifying the states of the molecule using the irreducible representations from the character table of the symmetry group of the molecule. Symmetry is useful in the study of molecular orbitals, with applications to the Hückel method, to ligand field theory, and to the Woodward–Hoffmann rules. Many university level textbooks on physical chemistry, quantum chemistry, spectroscopy and inorganic chemistry discuss symmetry. Another framework on a larger scale is the use of crystal sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry Group
In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object. A frequent notation for the symmetry group of an object ''X'' is ''G'' = Sym(''X''). For an object in a metric space, its symmetries form a subgroup of the isometry group of the ambient space. This article mainly considers symmetry groups in Euclidean geometry, but the concept may also be studied for more general types of geometric structure. Introduction We consider the "objects" possessing symmetry to be geometric figures, images, and patterns, such as a wallpaper pattern. For symmetry of physical objects, one may also take their physical composition as part of the pattern. (A pattern may be specified formally as a scalar field, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equilateral Triangle
An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the special case of an isosceles triangle by modern definition, creating more special properties. The equilateral triangle can be found in various tilings, and in polyhedrons such as the deltahedron and antiprism. It appears in real life in popular culture, architecture, and the study of stereochemistry resembling the molecular known as the trigonal planar molecular geometry. Properties An equilateral triangle is a triangle that has three equal sides. It is a special case of an isosceles triangle in the modern definition, stating that an isosceles triangle is defined at least as having two equal sides. Based on the modern definition, this leads to an equilateral triangle in which one of the three sides may be considered its base. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrahedron
In geometry, a tetrahedron (: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular Face (geometry), faces, six straight Edge (geometry), edges, and four vertex (geometry), vertices. The tetrahedron is the simplest of all the ordinary convex polytope, convex polyhedra. The tetrahedron is the three-dimensional case of the more general concept of a Euclidean geometry, Euclidean simplex, and may thus also be called a 3-simplex. The tetrahedron is one kind of pyramid (geometry), pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron, the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid". Like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper. It has two such net (polyhedron), nets. For any tetrahedron there exists a sphere (called th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diamond Cubic
In crystallography, the diamond cubic crystal structure is a repeating pattern of 8 atoms that certain materials may adopt as they solidify. While the first known example was diamond, other elements in group 14 also adopt this structure, including α-tin, the semiconductors silicon and germanium, and silicon–germanium alloys in any proportion. There are also crystals, such as the high-temperature form of cristobalite, which have a similar structure, with one kind of atom (such as silicon in cristobalite) at the positions of carbon atoms in diamond but with another kind of atom (such as oxygen) halfway between those (see :Minerals in space group 227). Although often called the diamond lattice, this structure is not a lattice in the technical sense of this word used in mathematics. Crystallographic structure Diamond's cubic structure is in the Fdm space group (space group 227), which follows the face-centered cubic Bravais lattice. The lattice describes the repeat pat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
