Bent Bond
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Bent Bond
In organic chemistry, a bent bond, also known as a banana bond, is a type of covalent chemical bond with a geometry somewhat reminiscent of a banana. The term itself is a general representation of electron density or configuration resembling a similar "bent" structure within small ring molecules, such as cyclopropane (C3H6) or as a representation of double or triple bonds within a compound that is an alternative to the sigma and pi bond model. Small cyclic molecules Bent bonds are a special type of chemical bonding in which the ordinary hybridization state of two atoms making up a chemical bond are modified with increased or decreased s-orbital character in order to accommodate a particular molecular geometry. Bent bonds are found in strained organic compounds such as cyclopropane, oxirane and aziridine. In these compounds, it is not possible for the carbon atoms to assume the 109.5° bond angles with standard sp3 hybridization. Increasing the p-character to sp5 (i.e. ...
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Coulson Moffit Model
Coulson is both a surname and a given name. Notable people with the name include: Surname: *Andy Coulson (born 1968), English journalist and political strategist *Bernie Coulson (born 1965), Canadian actor *Bob Coulson (1887–1953), American baseball player *Catherine E. Coulson (1943–2015), American actress *Charles Coulson (1910–1974), British applied mathematician, theoretical chemist and religious author *Charlie Coulson (born 1996), English footballer *Christian Coulson (born 1978), English actor *Danny Coulson, American law enforcement official, Deputy Assistant Director of the FBI *D'Arcy Coulson (1908–1996), Canadian ice hockey player and hotelier *Elizabeth Coulson (born 1954), Illinois politician *Elizabeth Kerr Coulson (1819–1876), English novelist *Frederick Coulson, rugby footballer *Gustavus Hamilton Blenkinsopp Coulson VC (1879–1901), British Army officer *Ivar "Pop" Coulson, American inventor of the malted milkshake *John Coulson (1910–1990), British prof ...
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Kenneth B
Kenneth is an English given name and surname. The name is an Anglicised form of two entirely different Gaelic personal names: ''Cainnech'' and '' Cináed''. The modern Gaelic form of ''Cainnech'' is ''Coinneach''; the name was derived from a byname meaning "handsome", "comely". A short form of ''Kenneth'' is '' Ken''. Etymology The second part of the name ''Cinaed'' is derived either from the Celtic ''*aidhu'', meaning "fire", or else Brittonic ''jʉ:ð'' meaning "lord". People :''(see also Ken (name) and Kenny)'' Places In the United States: * Kenneth, Indiana * Kenneth, Minnesota * Kenneth City, Florida In Scotland: * Inch Kenneth, an island off the west coast of the Isle of Mull Other * "What's the Frequency, Kenneth?", a song by R.E.M. * Hurricane Kenneth * Cyclone Kenneth Intense Tropical Cyclone Kenneth was the strongest tropical cyclone to make landfall in Mozambique since modern records began. The cyclone also caused significant damage in the Comoro Islands a ...
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Unitary Transformation
In mathematics, a unitary transformation is a transformation that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation. Formal definition More precisely, a unitary transformation is an isomorphism between two inner product spaces (such as Hilbert spaces). In other words, a ''unitary transformation'' is a bijective function U : H \to H_2\, between two inner product spaces, H and H_2, such that \langle Ux, Uy \rangle_ = \langle x, y \rangle_ \quad \text x, y \in H. Properties A unitary transformation is an isometry, as one can see by setting x=y in this formula. Unitary operator In the case when H_1 and H_2 are the same space, a unitary transformation is an automorphism of that Hilbert space, and then it is also called a unitary operator. Antiunitary transformation A closely related notion is that of antiunitary transformation, which is a bijective function :U:H_1\to H_2\, between two co ...
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Erich Hückel
Erich Armand Arthur Joseph Hückel (August 9, 1896, Berlin – February 16, 1980, Marburg) was a German physicist and physical chemist. He is known for two major contributions: *The Debye–Hückel theory of electrolytic solutions *The Hückel method of approximate molecular orbital (MO) calculations on π electron systems. Hückel was born in the Charlottenburg suburb of Berlin. He studied physics and mathematics from 1914 to 1921 at the University of Göttingen. On receiving his doctorate, he became an assistant at Göttingen, but soon became an assistant to Peter Debye at Zürich. It was there that he and Debye developed their theory (the Debye–Hückel theory, in 1923) of electrolytic solutions, elucidating the behavior of strong electrolytes by considering interionic forces, in order to account for their electrical conductivity and their thermodynamic activity coefficients. After spending 1928 and 1929 in England and Denmark, working briefly with Niels Bohr, Hückel joi ...
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Linus Pauling
Linus Carl Pauling (; February 28, 1901August 19, 1994) was an American chemist, biochemist, chemical engineer, peace activist, author, and educator. He published more than 1,200 papers and books, of which about 850 dealt with scientific topics. ''New Scientist'' called him one of the 20 greatest scientists of all time, and as of 2000, he was rated the 16th most important scientist in history. For his scientific work, Pauling was awarded the Nobel Prize in Chemistry in 1954. For his peace activism, he was awarded the Nobel Peace Prize in 1962. He is one of five people to have won more than one Nobel Prize (the others being Marie Curie, John Bardeen, Frederick Sanger and Karl Barry Sharpless). Of these, he is the only person to have been awarded two unshared Nobel Prizes, and one of two people to be awarded Nobel Prizes in different fields, the other being Marie Curie. Pauling was one of the founders of the fields of quantum chemistry and molecular biology. His contributions t ...
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Ground State
The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. In quantum field theory, the ground state is usually called the vacuum state or the vacuum. If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator that acts non-trivially on a ground state and commutes with the Hamiltonian of the system. According to the third law of thermodynamics, a system at absolute zero temperature exists in its ground state; thus, its entropy is determined by the degeneracy of the ground state. Many systems, such as a perfect crystal lattice, have a unique ground state and therefore have zero entropy at absolute zero. It is also possible for the highest excited state to have absolute zero temper ...
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Walsh Diagram
Walsh diagrams, often called angular coordinate diagrams or correlation diagrams, are representations of calculated orbital binding energies of a molecule versus a distortion coordinate (bond angles), used for making quick predictions about the geometries of small molecules. By plotting the change in molecular orbital levels of a molecule as a function of geometrical change, Walsh diagrams explain why molecules are more stable in certain spatial configurations (e.g. why water adopts a bent conformation). A major application of Walsh diagrams is to explain the regularity in structure observed for related molecules having identical numbers of valence electrons (e.g. why H2O and H2S look similar), and to account for how molecules alter their geometries as their number of electrons or spin state changes. Additionally, Walsh diagrams can be used to predict distortions of molecular geometry from knowledge of how the LUMO (Lowest Unoccupied Molecular Orbital) affects the HOMO (Highest Oc ...
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Alkane
In organic chemistry, an alkane, or paraffin (a historical trivial name that also has other meanings), is an acyclic saturated hydrocarbon. In other words, an alkane consists of hydrogen and carbon atoms arranged in a tree structure in which all the carbon–carbon bonds are single. Alkanes have the general chemical formula . The alkanes range in complexity from the simplest case of methane (), where ''n'' = 1 (sometimes called the parent molecule), to arbitrarily large and complex molecules, like pentacontane () or 6-ethyl-2-methyl-5-(1-methylethyl) octane, an isomer of tetradecane (). The International Union of Pure and Applied Chemistry (IUPAC) defines alkanes as "acyclic branched or unbranched hydrocarbons having the general formula , and therefore consisting entirely of hydrogen atoms and saturated carbon atoms". However, some sources use the term to denote ''any'' saturated hydrocarbon, including those that are either monocyclic (i.e. the cycloalkanes) or ...
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Steric Repulsion
Steric effects arise from the spatial arrangement of atoms. When atoms come close together there is a rise in the energy of the molecule. Steric effects are nonbonding interactions that influence the shape ( conformation) and reactivity of ions and molecules. Steric effects complement electronic effects, which dictate the shape and reactivity of molecules. Steric repulsive forces between overlapping electron clouds result in structured groupings of molecules stabilized by the way that opposites attract and like charges repel. Steric hindrance Steric hindrance is a consequence of steric effects. Steric hindrance is the slowing of chemical reactions due to steric bulk. It is usually manifested in ''intermolecular reactions'', whereas discussion of steric effects often focus on ''intramolecular interactions''. Steric hindrance is often exploited to control selectivity, such as slowing unwanted side-reactions. Steric hindrance between adjacent groups can also affect torsional ...
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Cyclobutane
Cyclobutane is a cycloalkane and organic compound with the formula (CH2)4. Cyclobutane is a colourless gas and commercially available as a liquefied gas. Derivatives of cyclobutane are called cyclobutanes. Cyclobutane itself is of no commercial or biological significance, but more complex derivatives are important in biology and biotechnology. Structure The bond angles between carbon atoms are significantly strained and as such have lower bond energies than related linear or unstrained hydrocarbons, e.g. butane or cyclohexane. As such, cyclobutane is unstable above about 500 °C. The four carbon atoms in cyclobutane are not coplanar; instead the ring typically adopts a folded or "puckered" conformation. This implies that the C-C-C angle is less than 90°. One of the carbon atoms makes a 25° angle with the plane formed by the other three carbons. In this way some of the eclipsing interactions are reduced. The conformation is also known as a "butterfly". Equivalent p ...
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Picometer
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 are t ...
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