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In chemistry, electron counting is a formalism for assigning a number of valence electrons to individual atoms in a molecule. It is used for classifying compounds and for explaining or predicting their electronic structure and bonding. Many rules in chemistry rely on electron-counting:
A fullerene is an allotrope of carbon whose molecules consist of carbon atoms connected by single and double bonds so as to form a closed or partially closed mesh, with fused rings of five to six atoms. The molecules may have hollow sphere- and ellipsoid-like forms, tubes, or other shapes.
Buckminsterfullerene is a type of fullerene with the formula C60. It has a cage-like fused-ring structure (truncated icosahedron) made of twenty hexagons and twelve pentagons, and resembles a soccer ball. Each of its 60 carbon atoms is bonded to its three neighbors.
Boron hydride clusters are compounds with the formula BxHy or related anions, where x ≥ 3. Many such cluster compounds are known. Common examples are those with 5, 10, and 12 boron atoms. Although they have few practical applications, the borane hydride clusters exhibit structures and bonding that differs strongly from the patterns seen in hydrocarbons. Hybrids of boranes and hydrocarbons, the carboranes are also well developed.
In theoretical chemistry, a conjugated system is a system of connected p-orbitals with delocalized electrons in a molecule, which in general lowers the overall energy of the molecule and increases stability. It is conventionally represented as having alternating single and multiple bonds. Lone pairs, radicals or carbenium ions may be part of the system, which may be cyclic, acyclic, linear or mixed. The term "conjugated" was coined in 1899 by the German chemist Johannes Thiele.
In organic chemistry, aromaticity is a chemical property describing the way in which a conjugated ring of unsaturated bonds, lone pairs, or empty orbitals exhibits a stabilization stronger than would be expected by the stabilization of conjugation alone. The earliest use of the term was in an article by August Wilhelm Hofmann in 1855. There is no general relationship between aromaticity as a chemical property and the olfactory properties of such compounds.
In quantum mechanics, the case of a particle in a one-dimensional ring is similar to the particle in a box. The Schrödinger equation for a free particle which is restricted to a ring is
In organic chemistry, Hückel's rule predicts that a planar ring molecule will have aromatic properties if it has 4n + 2 π-electrons, where n is a non-negative integer. The quantum mechanical basis for its formulation was first worked out by physical chemist Erich Hückel in 1931. The succinct expression as the 4n + 2 rule has been attributed to W. v. E. Doering (1951), although several authors were using this form at around the same time.
Antiaromaticity is a chemical property of a cyclic molecule with a π electron system that has higher energy, i.e., it is less stable due to the presence of 4n delocalised electrons in it, as opposed to aromaticity. Unlike aromatic compounds, which follow Hückel's rule and are highly stable, antiaromatic compounds are highly unstable and highly reactive. To avoid the instability of antiaromaticity, molecules may change shape, becoming non-planar and therefore breaking some of the π interactions. In contrast to the diamagnetic ring current present in aromatic compounds, antiaromatic compounds have a paramagnetic ring current, which can be observed by NMR spectroscopy.
Borazine, also known as borazole, inorganic benzene, is an inorganic compound with the chemical formula B3H6N3. In this cyclic compound, the three BH units and three NH units alternate. The compound is isoelectronic and isostructural with benzene. For this reason borazine is sometimes referred to as “inorganic benzene”. Like benzene, borazine is a colourless liquid with an aromatic odor.
In chemistry the polyhedral skeletal electron pair theory (PSEPT) provides electron counting rules useful for predicting the structures of clusters such as borane and carborane clusters. The electron counting rules were originally formulated by Kenneth Wade, and were further developed by others including Michael Mingos; they are sometimes known as Wade's rules or the Wade–Mingos rules. The rules are based on a molecular orbital treatment of the bonding. These rules have been extended and unified in the form of the Jemmis mno rules.
Metal aromaticity or metalloaromaticity is the concept of aromaticity, found in many organic compounds, extended to metals and metal-containing compounds. The first experimental evidence for the existence of aromaticity in metals was found in aluminium cluster compounds of the type MAl−
4 where M stands for lithium, sodium or copper. These anions can be generated in a helium gas by laser vaporization of an aluminium / lithium carbonate composite or a copper or sodium / aluminium alloy, separated and selected by mass spectrometry and analyzed by photoelectron spectroscopy. The evidence for aromaticity in these compounds is based on several considerations. Computational chemistry shows that these aluminium clusters consist of a tetranuclear Al2−
4 plane and a counterion at the apex of a square pyramid. The Al2−
4 unit is perfectly planar and is not perturbed by the presence of the counterion or even the presence of two counterions in the neutral compound M
2Al
4. In addition its HOMO is calculated to be a doubly occupied delocalized pi system making it obey Hückel's rule. Finally a match exists between the calculated values and the experimental photoelectron values for the energy required to remove the first 4 valence electrons. The first fully metal aromatic compound was a cyclogallane with a Ga32- core discovered by Gregory Robinson in 1995.
An aromatic ring current is an effect observed in aromatic molecules such as benzene and naphthalene. If a magnetic field is directed perpendicular to the plane of the aromatic system, a ring current is induced in the delocalized π electrons of the aromatic ring. This is a direct consequence of Ampère's law; since the electrons involved are free to circulate, rather than being localized in bonds as they would be in most non-aromatic molecules, they respond much more strongly to the magnetic field.
Fullerene chemistry is a field of organic chemistry devoted to the chemical properties of fullerenes. Research in this field is driven by the need to functionalize fullerenes and tune their properties. For example, fullerene is notoriously insoluble and adding a suitable group can enhance solubility. By adding a polymerizable group, a fullerene polymer can be obtained. Functionalized fullerenes are divided into two classes: exohedral fullerenes with substituents outside the cage and endohedral fullerenes with trapped molecules inside the cage.
In chemistry, a Zintl phase is a product of a reaction between a group 1 or group 2 and main group metal or metalloid. 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.
In organic and physical organic chemistry, Clar's rule is an empirical rule that relates the chemical stability of a molecule to its aromaticity. It was introduced in 1972 by the Austrian organic chemist Erich Clar in his book The Aromatic Sextet. The rule states that given a polycyclic aromatic hydrocarbon, the resonance structure most important to characterize its properties is that with the largest number of aromatic π-sextets i.e. benzene-like moieties.
Eluvathingal Devassy Jemmis is a professor of theoretical chemistry at the Indian Institute of Science, Bangalore, India. He was the founding director of Indian Institute of Science Education and Research, Thiruvananthapuram (IISER-TVM). His primary area of research is applied theoretical chemistry with emphasis on structure, bonding and reactivity, across the periodic table of the elements. Apart from many of his contributions to applied theoretical chemistry, an equivalent of the structural chemistry of carbon, as exemplified by the Huckel 4n+2 Rule, benzenoid aromatics and graphite, and tetrahedral carbon and diamond, is brought in the structural chemistry of boron by the Jemmis mno rules which relates polyhedral and macropolyhedral boranes to allotropes of boron and boron-rich solids. He has been awarded Padma Shri in Science and Engineering category by the Government of India.
In chemistry, the Jemmis mno rules represent a unified rule for predicting and systematizing structures of compounds, usually clusters. The rules involve electron counting. They were formulated by E. D. Jemmis to explain the structures of condensed polyhedral boranes such as B20H16, which are obtained by condensing polyhedral boranes by sharing a triangular face, an edge, a single vertex, or four vertices. These rules are additions and extensions to Wade's rules and polyhedral skeletal electron pair theory. The Jemmis mno rule provides the relationship between polyhedral boranes, condensed polyhedral boranes, and β-rhombohedral boron. This is similar to the relationship between benzene, condensed benzenoid aromatics, and graphite, shown by Hückel's 4n + 2 rule, as well as the relationship between tetracoordinate tetrahedral carbon compounds and diamond. The Jemmis mno rules reduce to Hückel's rule when restricted to two dimensions and reduce to Wade's rules when restricted to one polyhedron.
Azafullerenes are a class of heterofullerenes in which the element substituting for carbon is nitrogen. They can be in the form of a hollow sphere, ellipsoid, tube, and many other shapes. Spherical azafullerenes resemble the balls used in football (soccer). They are also a member of the carbon nitride class of materials that include beta carbon nitride (β-C3N4), predicted to be harder than diamond. Besides the pioneering work of a couple of academic groups, this class of compounds has so far garnered little attention from the broader fullerene research community. Many properties and structures are yet to be discovered for the highly-nitrogen substituted subset of molecules.
The Goldberg–Coxeter construction or Goldberg–Coxeter operation is a graph operation defined on regular polyhedral graphs with degree 3 or 4. It also applies to the dual graph of these graphs, i.e. graphs with triangular or quadrilateral "faces". The GC construction can be thought of as subdividing the faces of a polyhedron with a lattice of triangular, square, or hexagonal polygons, possibly skewed with regards to the original face: it is an extension of concepts introduced by the Goldberg polyhedra and geodesic polyhedra. The GC construction is primarily studied in organic chemistry for its application to fullerenes, but it has been applied to nanoparticles, computer-aided design, basket weaving, and the general study of graph theory and polyhedra.
References
- ↑ Hirsch, Andreas; Chen, Zhongfang; Jiao, Haijun (2000), "Spherical Aromaticity in Ih Symmetrical Fullerenes: The 2(N+1)2 Rule", Angew. Chem. Int. Ed. Engl., 39 (21): 3915–17, Bibcode:2000AngCh..39.3915H, doi:10.1002/1521-3773(20001103)39:21<3915::AID-ANIE3915>3.0.CO;2-O .
- ↑ Poater, Jordi; Solà, Miquel (2011), "Open-shell spherical aromaticity: the 2N2 + 2N + 1 (with S = N + ½) rule", Chemical Communications, 47 (42): 11647–11649, doi:10.1039/C1CC14958J, PMID 21952479 .
