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Spherical Aromaticity
In organic chemistry, spherical aromaticity is formally used to describe an unusually stable nature of some spherical compounds such as fullerenes and polyhedral boranes. In 2000, Andreas Hirsch and coworkers in Erlangen, Germany, formulated a rule to determine when a spherical compound would be aromatic. They found that those with 2(''n''+1)2 π-electrons could display aromatic properties, as spherical molecular orbitals are filled when there are 2(''n''+1)2 π-electrons for some positive integer ''n''. For example, in buckminsterfullerene (C60) this happens for the species C6010+, which has 50 π-electrons: 50/2 = 25, which is a perfect square. In 2011, Jordi Poater and Miquel Solà expanded Hirsch's rule to open-shell spherical compounds, which have unfilled outer shells but are still aromatic. They found that spherical compounds with 2''n''2+2''n''+1 π-electrons with spin S = (n + 1/2) would also display aromatic properties, sometimes more aromatic than comparable closed- ...
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Organic Chemistry
Organic chemistry is a subdiscipline within chemistry involving the science, scientific study of the structure, properties, and reactions of organic compounds and organic matter, organic materials, i.e., matter in its various forms that contain carbon atoms.Clayden, J.; Greeves, N. and Warren, S. (2012) ''Organic Chemistry''. Oxford University Press. pp. 1–15. . Study of structure determines their structural formula. Study of properties includes Physical property, physical and Chemical property, chemical properties, and evaluation of Reactivity (chemistry), chemical reactivity to understand their behavior. The study of organic reactions includes the organic synthesis, chemical synthesis of natural products, drugs, and polymers, and study of individual organic molecules in the laboratory and via theoretical (in silico) study. The range of chemicals studied chemistry includes hydrocarbons (compounds containing only carbon and hydrogen) as well as compounds based on carbon, but a ...
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Spin (physics)
Spin is an Intrinsic and extrinsic properties, intrinsic form of angular momentum carried by elementary particles, and thus by List of particles#Composite particles, composite particles such as hadrons, atomic nucleus, atomic nuclei, and atoms. Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory. The existence of electron spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. The relativistic spin–statistics theorem connects electron spin quantization to the Pauli exclusion principle: observations of exclusion imply half-integer spin, and observations of half-integer spin imply exclusion. Spin is described mathematically as a vector for some particles such as photons, and as a spinor or bispinor for other particles such as electrons. Sp ...
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Aromatic Compounds
Aromatic compounds or arenes are organic compounds "with a chemistry typified by benzene" and "cyclically conjugated." The word "aromatic" originates from the past grouping of molecules based on odor, before their general chemical properties were understood. The current definition of aromatic compounds does not have any relation to their odor. Aromatic compounds are now defined as cyclic compounds satisfying Hückel's rule. Aromatic compounds have the following general properties: * Typically unreactive * Often non polar and hydrophobic * High carbon-hydrogen ratio * Burn with a strong sooty yellow flame, due to high C:H ratio * Undergo electrophilic substitution reactions and nucleophilic aromatic substitutions Arenes are typically split into two categories - benzoids, that contain a benzene derivative and follow the benzene ring model, and non-benzoids that contain other aromatic cyclic derivatives. Aromatic compounds are commonly used in organic synthesis and are involved in m ...
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Boranes
A borane is a compound with the formula although examples include multi-boron derivatives. A large family of boron hydride clusters is also known. In addition to some applications in organic chemistry, the boranes have attracted much attention as they exhibit structures and bonding that differs strongly from the patterns seen in hydrocarbons. Hybrids of boranes and hydrocarbons, the carboranes, are also a well developed class of compounds. pp 151-195 History The development of the chemistry of boranes led to innovations in synthetic methods as well as structure and bonding. First, new synthetic techniques were required to handle diborane and many of its derivatives, which are both pyrophoric and volatile. Alfred Stock invented the glass vacuum line for this purpose. The structure of diborane was correctly predicted in 1943 many years after its discovery. Interest in boranes increased during World War II due to the potential of uranium borohydride for enrichment of the uranium ...
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Carborane
Carboranes (or carbaboranes) are electron-delocalized (non-classically bonded) clusters composed of boron, carbon and hydrogen atoms.Grimes, R. N., ''Carboranes 3rd Ed.'', Elsevier, Amsterdam and New York (2016), . Like many of the related boron hydrides, these clusters are Polyhedron, polyhedra or fragments of polyhedra. Carboranes are one class of heteroboranes. In terms of scope, carboranes can have as few as 5 and as many as 14 atoms in the cage framework. The majority have two cage carbon atoms. The corresponding carbon, C-alkyl and boron, B-alkyl analogues are also known in a few cases. Structure and bonding Carboranes and boranes adopt 3-dimensional cage (Cluster chemistry, cluster) geometries in sharp contrast to typical organic compounds. Cages are compatible with sigma—delocalized bonding, whereas hydrocarbons are typically chains or rings. Like for other electron-delocalized polyhedral clusters, the electronic structure of these cluster compounds can be described by ...
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Fullerene Chemistry
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. This article covers the chemistry of these so-called "buckyballs," while the chemistry of carbon nanotubes is covered in carbon nanotube chemistry. Chemical properties of fullerenes Fullerene or C60 is soccer-ball-shaped or ''Ih'' with 12 pentagons and 20 hexagons. According to Euler's theorem these 12 pentagons are required for closure of the carbon network consisting of ''n'' hexagons and C60 is the first stable fullerene because it ...
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Picometre
The picometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: pm) or picometer (American spelling) is a unit of length in the International System of Units (SI), equal to , or one trillionth of a metre, which is the SI base unit of length. The picometre is one thousand femtometres, one thousandth of a nanometre ( nm), one millionth of a micrometre (also known as a micron), one billionth of a millimetre, and one trillionth of a metre. The symbol μμ was once used for it. It is also one hundredth of an ångström, an internationally known (but non-SI) unit of length. Use The picometre's length is of an order so small that its application is almost entirely confined to particle physics, quantum physics, chemistry, and acoustics. Atoms are between 62 and 520 pm in diameter, and the typical length of a carbon–carbon single bond is 154 pm. Smaller units still may be used to describe smaller particles (some of which ar ...
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Baird's Rule
In organic chemistry, Baird's rule estimates whether the lowest triplet state of planar, cyclic structures will have aromatic properties or not. The quantum mechanical basis for its formulation was first worked out by physical chemist N. Colin Baird at the University of Western Ontario in 1972. The lowest triplet state of an annulene is, according to Baird's rule, aromatic when it has 4''n'' π-electrons and antiaromatic when the π-electron count is 4''n'' + 2, where ''n'' is any positive integer. This trend is opposite to that predicted by Hückel's rule for the ground state, which is usually the lowest singlet state In quantum mechanics, a singlet state usually refers to a system in which all electrons are paired. The term 'singlet' originally meant a linked set of particles whose net angular momentum is zero, that is, whose overall spin quantum number s=0. A ... (S0). Baird's rule has thus become known as the photochemical analogue of Hückel's rule. Through various ...
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Square Number
In mathematics, a square number or perfect square is an integer that is the square (algebra), square of an integer; in other words, it is the multiplication, product of some integer with itself. For example, 9 is a square number, since it equals and can be written as . The usual notation for the square of a number is not the product , but the equivalent exponentiation , usually pronounced as " squared". The name ''square'' number comes from the name of the shape. The unit of area is defined as the area of a unit square (). Hence, a square with side length has area . If a square number is represented by ''n'' points, the points can be arranged in rows as a square each side of which has the same number of points as the square root of ''n''; thus, square numbers are a type of Figurate number, figurate numbers (other examples being Cube (algebra), cube numbers and triangular numbers). In the Real number, real number system, square numbers are non-negative. A non-negative integer ...
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Fullerene
A fullerene is an allotropes of carbon, 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, cylinder (geometry), tubes, or other shapes. Fullerenes with a closed mesh topology are informally denoted by their empirical formula C''n'', often written C''n'', where ''n'' is the number of carbon atoms. However, for some values of ''n'' there may be more than one isomer. The family is named after buckminsterfullerene (C60), the most famous member, which in turn is named after Buckminster Fuller. The closed fullerenes, especially C60, are also informally called buckyballs for their resemblance to the standard ball (association football), ball of association football. Nested closed fullerenes have been named bucky onions. Cylindrical fullerenes are also called carbon nanotubes or buckytubes ...
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Buckminsterfullerene
Buckminsterfullerene is a type of fullerene with the formula . It has a cage-like fused-ring structure ( truncated icosahedron) made of twenty hexagons and twelve pentagons, and resembles a football. Each of its 60 carbon atoms is bonded to its three neighbors. Buckminsterfullerene is a black solid that dissolves in hydrocarbon solvents to produce a violet solution. The substance was discovered in 1985 and has received intense study, although few real world applications have been found. Molecules of buckminsterfullerene (or of fullerenes in general) are commonly nicknamed buckyballs. Occurrence Buckminsterfullerene is the most common naturally occurring fullerene. Small quantities of it can be found in soot. It also exists in space. Neutral has been observed in planetary nebulae and several types of star. The ionised form, , has been identified in the interstellar medium, where it is the cause of several absorption features known as diffuse interstellar bands in the ...
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Electrons
The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up quark, up and down quark, down quarks. Electrons are extremely lightweight particles that orbit the positively charged atomic nucleus, nucleus of atoms. Their negative charge is balanced by the positive charge of protons in the nucleus, giving atoms their overall electric charge#Charge neutrality, neutral charge. Ordinary matter is composed of atoms, each consisting of a positively charged nucleus surrounded by a number of orbiting electrons equal to the number of protons. The configuration and energy levels of these orbiting electrons determine the chemical properties of an atom. Electrons are bound to the nucleus to different degrees. The outermost or valence electron, valence electrons are the least tightly bound and are responsible for th ...
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