Bicapped Square Antiprismatic Molecular Geometry
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Bicapped Square Antiprismatic Molecular Geometry
In chemistry, the capped square antiprismatic molecular geometry describes the shape of compounds where nine atoms, groups of atoms, or ligands are arranged around a central atom, defining the vertices of a gyroelongated square pyramid. The symmetry group of the resulting object is C4v. The gyroelongated square pyramid is a square pyramid with a square antiprism connected to the square base. In this respect, it can be seen as a "capped" square antiprism (a square antiprism with a pyramid erected on one of the square faces). It is very similar to the tricapped trigonal prismatic molecular geometry, and there is some dispute over the specific geometry exhibited by certain molecules. Examples: * iCo9(CO)21sup>2-, defined by the Co9 framework, which encapsulates the Si atom * b(phen)4(OClO3)sup>+, defined by the N8O framework, which encapsulates the Pb2+ ion * e9sup>4−, a zintl ion *Th( troopolonate)4(H2O), defined by the O9 framework, which encapsulates the Th4+ ion * is sometime ...
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Chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during chemical reaction, reactions with other chemical substance, substances. Chemistry also addresses the nature of chemical bonds in chemical compounds. In the scope of its subject, chemistry occupies an intermediate position between physics and biology. It is sometimes called the central science because it provides a foundation for understanding both Basic research, basic and Applied science, applied scientific disciplines at a fundamental level. For example, chemistry explains aspects of plant growth (botany), the formation of igneous rocks (geology), how atmospheric ozone is formed and how environmental pollutants are degraded (ecology), the prop ...
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Ligand
In coordination chemistry, a ligand is an ion or molecule with a functional group that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's electron pairs, often through Lewis acids and bases, Lewis bases. The nature of metal–ligand bonding can range from covalent bond, covalent to ionic bond, ionic. Furthermore, the metal–ligand bond order can range from one to three. Ligands are viewed as Lewis bases, although rare cases are known to involve Lewis acids and bases, Lewis acidic "ligands". Metals and metalloids are bound to ligands in almost all circumstances, although gaseous "naked" metal ions can be generated in a high vacuum. Ligands in a complex dictate the reactivity (chemistry), reactivity of the central atom, including ligand substitution rates, the reactivity of the ligands themselves, and redox. Ligand selection requires critical consideration in many practical are ...
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Gyroelongated Square Pyramid
In geometry, the gyroelongated square pyramid is the Johnson solid that can be constructed by attaching an equilateral square pyramid to a square antiprism. It occurs in chemistry; for example, the capped square antiprismatic molecular geometry. Construction The gyroelongated square pyramid is composite, since it can constructed by attaching one equilateral square pyramid to the square antiprism, a process known as the gyroelongation. This construction involves the covering of one of two square faces and replacing them with the four equilateral triangles, so that the resulting polyhedron has twelve equilateral triangles and one square. The convex polyhedron in which all of the faces are regular is the Johnson solid, and the gyroelongated square pyramid is one of them, enumerated as J_ , the tenth Johnson solid. Properties The surface area of a gyroelongated square pyramid with edge length a is: \left(1 + 3\sqrt\right)a^2 \approx 6.196a^2, the area of twelve equilateral ...
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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, ...
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Square Pyramid
In geometry, a square pyramid is a Pyramid (geometry), pyramid with a square base and four triangles, having a total of five faces. If the Apex (geometry), apex of the pyramid is directly above the center of the square, it is a ''right square pyramid'' with four isosceles triangles; otherwise, it is an ''oblique square pyramid''. When all of the pyramid's edges are equal in length, its triangles are all equilateral triangle, equilateral. It is called an ''equilateral square pyramid'', an example of a Johnson solid. Square pyramids have appeared throughout the history of architecture, with examples being Egyptian pyramids and many other similar buildings. They also occur in chemistry in Square pyramidal molecular geometry, square pyramidal molecular structures. Square pyramids are often used in the construction of other polyhedra. Many mathematicians in ancient times discovered the formula for the volume of a square pyramid with different approaches. Special cases Right squar ...
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Square Antiprism
In geometry, the square antiprism is the second in an infinite family of antiprisms formed by an even number, even-numbered sequence of triangle sides closed by two polygon caps. It is also known as an ''anticube''. If all its faces are regular polygon, regular, it is a semiregular polyhedron or uniform polyhedron. A nonuniform ''D''4-symmetric variant is the cell of the Noble polyhedron, noble square antiprismatic 72-cell. Points on a sphere When eight points are distributed on the surface of a sphere with the aim of maximising the distance between them in some sense, the resulting shape corresponds to a square antiprism rather than a cube (geometry), cube. Specific methods of distributing the points include, for example, the Thomson problem (minimizing the sum of all the reciprocal (mathematics), reciprocals of distances between points), maximising the distance of each point to the nearest point, or minimising the sum of all reciprocals of squares of distances between points ...
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Tricapped Trigonal Prismatic Molecular Geometry
In chemistry, the tricapped trigonal prismatic molecular geometry describes the shape of compounds where nine atoms, groups of atoms, or ligands are arranged around a central atom, defining the vertices of a triaugmented triangular prism (a trigonal prism In chemistry, octahedral molecular geometry, also called square bipyramidal, describes the shape of compounds with six atoms or groups of atoms or ligands symmetrically arranged around a central atom, defining the vertices of an octahedron. The oc ... with an extra atom attached to each of its three rectangular faces). It is very similar to the capped square antiprismatic molecular geometry, and there is some dispute over the specific geometry exhibited by certain molecules. Examples * * (Ln = La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy) * References Stereochemistry Molecular geometry {{Stereochemistry-stub ...
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Zintl Ion
In chemistry, a Zintl phase is a product of a reaction between a group 1 (alkali metal) or group 2 (alkaline earth metal) and main group metal or metalloid (from groups 13, 14, 15, or 16). It is characterized by intermediate metallic/ ionic bonding. Zintl phases are a subgroup of brittle, high-melting intermetallic compounds that are diamagnetic or exhibit temperature-independent paramagnetism and are poor conductors or semiconductors.Sevov, S.C., Zintl Phases in Intermetallic Compounds, Principles and Practice: Progress, Westbrook, J.H.; *Freisher, R.L.: Eds.; John Wiley & Sons. Ltd., Chichester, England, 2002, pp. 113-13Slavi Chapter/ref> This type of solid is named after German chemist Eduard Zintl who investigated them in the 1930s. The term "Zintl Phases" was first used by Laves in 1941. In his early studies, Zintl noted that there was an atomic volume contraction upon the formation of these products and realized that this could indicate cation formation. He suggested that t ...
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Tropolone
Tropolone is an organic compound with the chemical formula . It is a pale yellow solid that is soluble in organic solvents. The compound has been of interest to research chemists because of its unusual electronic structure and its role as a ligand precursor. Although not usually prepared from tropone, it can be viewed as its derivative with a hydroxyl group in the 2-position. Synthesis and reactions Many methods have been described for the synthesis of tropolone. One involves bromination of 1,2-cycloheptanedione with ''N''-bromosuccinimide followed by dehydrohalogenation at elevated temperatures, while another uses acyloin condensation of the ethyl ester of pimelic acid the acyloin again followed by oxidation by bromine. : An alternate route is a +2 cycloaddition of cyclopentadiene with a ketene to give a bicyclo .2.0eptyl structure, followed by hydrolysis and breakage of the fusion bond to give the single ring: : Thy hydroxyl group of tropolone is acidic, having a ...
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Potassium Nonahydridorhenate
Potassium nonahydridorhenate(VII) is an inorganic compound having the formula . This colourless salt is soluble in water but only poorly soluble in most alcohols. This salt contains the nonahydridorhenate(VII) anion, , which is a rare example of a coordination complex bearing only hydride ligands. History The study of rhenium hydrides can be traced to the 1950s and included reports of the "rhenide" anion, supposedly . These reports led to a series of investigations by A. P. Ginsberg and coworkers on the products from the reduction of perrhenate. The ''rhenide'' anion, , was based on the product of the reduction of perrhenate salts, such as the reduction of potassium perrhenate () by potassium metal. "Potassium rhenide" was shown to exist as a tetrahydrated complex, with the postulated chemical formula (potassium rhenide tetrahydrate). This compound exhibits strongly reducing properties, and slowly yields hydrogen gas when dissolved in water. The lithium and thallous salts were a ...
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Lanthanum
Lanthanum is a chemical element; it has symbol La and atomic number 57. It is a soft, ductile, silvery-white metal that tarnishes slowly when exposed to air. It is the eponym of the lanthanide series, a group of 15 similar elements between lanthanum and lutetium in the periodic table, of which lanthanum is the first and the prototype. Lanthanum is traditionally counted among the rare earth elements. Like most other rare earth elements, its usual oxidation state is +3, although some compounds are known with an oxidation state of +2. Lanthanum has no biological role in humans but is used by some bacteria. It is not particularly toxic to humans but does show some antimicrobial activity. Lanthanum usually occurs together with cerium and the other rare earth elements. Lanthanum was first found by the Swedish chemist Carl Gustaf Mosander in 1839 as an impurity in cerium nitrate – hence the name ''lanthanum'', from the ancient Greek (), meaning 'to lie hidden'. Although ...
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Gyroelongated Square Bipyramid
In geometry, the gyroelongated square bipyramid is a polyhedron with 16 triangular faces. it can be constructed from a square antiprism by attaching two equilateral square pyramid, equilateral square pyramids to each of its square faces. The same shape is also called hexakaidecadeltahedron, heccaidecadeltahedron, or tetrakis square antiprism; these last names mean a polyhedron with 16 triangular faces. It is an example of deltahedron, and of a Johnson solid. The dual polyhedron of the gyroelongated square bipyramid is a square truncated trapezohedron with eight pentagons and two squares as its faces. The gyroelongated square pyramid appears in chemistry as the basis for the bicapped square antiprismatic molecular geometry, and in mathematical optimization as a solution to the Thomson problem. Construction Like other Gyroelongated bipyramid, gyroelongated bipyramids, the gyroelongated square bipyramid can be constructed by attaching two Equilateral square pyramid, equilateral sq ...
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