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Cyclohexane Conformation
In organic chemistry, cyclohexane conformations are any of several three-dimensional shapes adopted by molecules of 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle (topology)
In mathematics, an -sphere or a hypersphere is a topological space that is homeomorphic to a ''standard'' -''sphere'', which is the set of points in -dimensional Euclidean space that are situated at a constant distance from a fixed point, called the ''center''. It is the generalization of an ordinary sphere in the ordinary three-dimensional space. The "radius" of a sphere is the constant distance of its points to the center. When the sphere has unit radius, it is usual to call it the unit -sphere or simply the -sphere for brevity. In terms of the standard norm, the -sphere is defined as : S^n = \left\ , and an -sphere of radius can be defined as : S^n(r) = \left\ . The dimension of -sphere is , and must not be confused with the dimension of the Euclidean space in which it is naturally embedded. An -sphere is the surface or boundary of an -dimensional ball. In particular: *the pair of points at the ends of a (one-dimensional) line segment is a 0-sphere, *a circle, which 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 substituents ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flagpole Interaction
In organic chemistry, cyclohexane conformations are any of several three-dimensional shapes adopted by molecules of 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equilateral Triangle
In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. It is also a regular polygon, so it is also referred to as a regular triangle. Principal properties Denoting the common length of the sides of the equilateral triangle as a, we can determine using the Pythagorean theorem that: *The area is A=\frac a^2, *The perimeter is p=3a\,\! *The radius of the circumscribed circle is R = \frac *The radius of the inscribed circle is r=\frac a or r=\frac *The geometric center of the triangle is the center of the circumscribed and inscribed circles *The altitude (height) from any side is h=\frac a Denoting the radius of the circumscribed circle as ''R'', we can determine using trigonometry that: *The area of the triangle is \mathrm=\fracR^2 Many of these quantities have simple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces. The tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex, and may thus also be called a 3-simplex. The tetrahedron is one kind of 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 nets. For any tetrahedron there exists a sphere (called the circumsphere) on which all four vertices lie, and anot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Group
In organic chemistry, a functional group is a substituent or 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 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 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 nonpolar core of carbon atoms and thus add chemical character to carbon chains. F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Halogen
The halogens () are a group in the periodic table consisting of five or six chemically related elements: fluorine (F), chlorine (Cl), bromine (Br), iodine (I), astatine (At), and tennessine (Ts). 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. All of the halogens form acids when bonded to hydrogen. Most halogens are typically produced from minerals or salts. The middle halogens—chlorine, bromine, and iodine—are often used as disinfectants. Organobromides are the most important class of flame retardants, while elemental halogens are dangerous and can be toxic. His ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strain (chemistry)
In chemistry, a molecule experiences strain when its chemical structure undergoes some stress which raises its internal energy in comparison to a strain-free reference 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 compressed 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 bonds within that molecule. Without the bonds holding the conformation in place, the strain energy would be released. Summary Thermodynamics The equilibrium of two molecular conformations is determined by the difference in Gibbs free energy of the two conformations. From thi ... [...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. Crystal structures: The staggered/eclipsed configurations 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 c ... [...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 fiel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudorotation
In chemistry, a pseudorotation is a set of intramolecular movements of attached groups (i.e., ligands) on a highly symmetric molecule, leading to a molecule indistinguishable from the initial one. The International Union of Pure and Applied Chemistry (IUPAC) defines a pseudorotation as a " ereoisomerization resulting in a structure that ''appears'' to have been produced by rotation of the entire initial molecule", the result of which is a "product" that is "superposable on the initial one, unless different positions are distinguished by substitution, including isotopic substitution." Well-known examples are the intramolecular isomerization of trigonal bipyramidal compounds by the Berry pseudorotation mechanism, and the out-of-plane motions of carbon atoms exhibited by cyclopentane, leading to the interconversions it experiences between its many possible conformers (envelope, twist). Note, no angular momentum is generated by this motion. In these and related examples, a small ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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