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Ab Initio Multiple Spawning
The ab initio multiple spawning, or AIMS, method is a time-dependent formulation of quantum chemistry. In AIMS, nuclear dynamics and electronic structure problems are solved wikt:simultaneously, simultaneously. Quantum mechanics, Quantum mechanical effects in the nuclear dynamics are included, especially the vibronic coupling, nonadiabatic effects which are crucial in modeling dynamics on multiple electronic states. The AIMS method makes it possible to describe photochemistry from first principles molecular dynamics, with no empirical parameters. The method has been applied to two molecules of interest in organic photochemistry - ethylene and cyclobutene. The photodynamics of ethylene involves both covalent and ionic electronic excited states and the return to the ground state proceeds through a pyramidalized geometry. For the photoinduced ring opening of cyclobutene, is it shown that the disrotatory motion predicted by the Woodward–Hoffmann rules is established within the first ...
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Formulation
Formulation is a term used in various senses in various applications, both the material and the abstract or formal. Its fundamental meaning is the putting together of components in appropriate relationships or structures, according to a formula. Etymologically ''formula'' is the diminutive of the Latin ''forma'', meaning shape. In that sense a ''formulation'' is created according to the standard for the product. Abstract applications Disciplines in which one might use the word ''formulation'' in the abstract sense include logic, mathematics, linguistics, legal theory, and computer science. For details, see the related articles. Material applications In more material senses the concept of ''formulation'' appears in the physical sciences, such as physics, chemistry, and biology. It also is ubiquitous in industry, engineering and medicine, especially pharmaceutics. Pharmacy In pharmacy, a formulation is a mixture or a structure such as a capsule, tablet, or an emulsion ...
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Quantum Chemistry
Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions to physical and chemical properties of molecules, materials, and solutions at the atomic level. These calculations include systematically applied approximations intended to make calculations computationally feasible while still capturing as much information about important contributions to the computed wave functions as well as to observable properties such as structures, spectra, and thermodynamic properties. Quantum chemistry is also concerned with the computation of quantum effects on molecular dynamics and chemical kinetics. Chemists rely heavily on spectroscopy through which information regarding the quantization of energy on a molecular scale can be obtained. Common methods are infra-red (IR) spectroscopy, nuclear magnetic r ...
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Simultaneously
Simultaneity may refer to: * Relativity of simultaneity, a concept in special relativity. * Simultaneity (music), more than one complete musical texture occurring at the same time, rather than in succession * Simultaneity, a concept in Endogeneity See also * Non-simultaneity * Diversity factor, or simultaneity factor *Time Structured Mapping Time Structured Mapping (TSM) is a score based system created and used by the composer Pete M Wyer. It uses the bar-lines found in conventional musical scores to indicate durational periods during which performers, who may include actors, sing ...
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Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves ( wave–particle duality); and there ar ...
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Vibronic Coupling
Vibronic coupling (also called nonadiabatic coupling or derivative coupling) in a molecule involves the interaction between electronic and nuclear vibrational motion. The term "vibronic" originates from the combination of the terms "vibrational" and "electronic", denoting the idea that in a molecule, vibrational and electronic interactions are interrelated and influence each other. The magnitude of vibronic coupling reflects the degree of such interrelation. In theoretical chemistry, the vibronic coupling is neglected within the Born–Oppenheimer approximation. Vibronic couplings are crucial to the understanding of nonadiabatic processes, especially near points of conical intersections. The direct calculation of vibronic couplings is not common due to difficulties associated with its evaluation. Definition Vibronic coupling describes the mixing of different electronic states as a result of small vibrations. : \mathbf_\equiv\langle\,\chi_(\mathbf;\mathbf)\,, \, \hat_\m ...
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Photochemistry
Photochemistry is the branch of chemistry concerned with the chemical effects of light. Generally, this term is used to describe a chemical reaction caused by absorption of ultraviolet (wavelength from 100 to 400  nm), visible light (400–750 nm) or infrared radiation (750–2500 nm). In nature, photochemistry is of immense importance as it is the basis of photosynthesis, vision, and the formation of vitamin D with sunlight. Photochemical reactions proceed differently than temperature-driven reactions. Photochemical paths access high energy intermediates that cannot be generated thermally, thereby overcoming large activation barriers in a short period of time, and allowing reactions otherwise inaccessible by thermal processes. Photochemistry can also be destructive, as illustrated by the photodegradation of plastics. Concept Grotthuss–Draper law and Stark-Einstein law Photoexcitation is the first step in a photochemical process where the reactant is elevated ...
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Ethylene
Ethylene (IUPAC name: ethene) is a hydrocarbon which has the formula or . It is a colourless, flammable gas with a faint "sweet and musky" odour when pure. It is the simplest alkene (a hydrocarbon with carbon-carbon double bonds). Ethylene is widely used in the chemical industry, and its worldwide production (over 150 million tonnes in 2016) exceeds that of any other organic compound. Much of this production goes toward polyethylene, a widely used plastic containing polymer chains of ethylene units in various chain lengths. Ethylene is also an important natural plant hormone and is used in agriculture to force the ripening of fruits. The hydrate of ethylene is ethanol. Structure and properties This hydrocarbon has four hydrogen atoms bound to a pair of carbon atoms that are connected by a double bond. All six atoms that comprise ethylene are coplanar. The H-C-H angle is 117.4°, close to the 120° for ideal sp² hybridized carbon. The molecule is also relatively weak: ...
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Cyclobutene
Cyclobutene is a cycloalkene. It is of interest in research but currently has no practical applications. It is a colorless easily condensed gas. A modern synthesis involves the 2-step dehydration of cyclobutanol. The compound was first prepared by thermolysis of the ammonium salt 4H7NMe3H. Cyclobutene thermally isomerizes to 1,3-butadiene. This strongly exothermic reaction reflects the dominance of ring strain. In contrast, the corresponding equilibrium for hexafluorocyclobutene disfavors hexafluorobutadiene. See also * Cyclobutane * Cyclobutadiene * Cyclobutyne * Squaric acid Squaric acid, also called quadratic acid because its four carbon atoms approximately form a square, is a diprotic organic acid with the chemical formula C4O2(OH)2. The conjugate base of squaric acid is the hydrogensquarate anion ; and the conjug ... References Monomers {{hydrocarbon-stub ...
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Covalent
A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atoms, when they share electrons, is known as covalent bonding. For many molecules, the sharing of electrons allows each atom to attain the equivalent of a full valence shell, corresponding to a stable electronic configuration. In organic chemistry, covalent bonding is much more common than ionic bonding. Covalent bonding also includes many kinds of interactions, including σ-bonding, π-bonding, metal-to-metal bonding, agostic interactions, bent bonds, three-center two-electron bonds and three-center four-electron bonds. The term ''covalent bond'' dates from 1939. The prefix ''co-'' means ''jointly, associated in action, partnered to a lesser degree, '' etc.; thus a "co-valent bond", in essence, means that the atoms share " valence", such a ...
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Woodward–Hoffmann Rules
The Woodward–Hoffmann rules (or the pericyclic selection rules), devised by Robert Burns Woodward and Roald Hoffmann, are a set of rules used to rationalize or predict certain aspects of the stereochemistry and activation energy of pericyclic reactions, an important class of reactions in organic chemistry. The rules are best understood in terms of the concept of ''the conservation of orbital symmetry'' using ''orbital correlation diagrams'' (see Section 3 below). The Woodward–Hoffmann rules are a consequence of the changes in electronic structure that occur during a pericyclic reaction and are predicated on the phasing of the interacting molecular orbitals. They are applicable to all classes of pericyclic reactions (and their microscopic reverse 'retro' processes), including (1) electrocyclizations, (2) cycloadditions, (3) sigmatropic reactions, (4) group transfer reactions, (5) ene reactions, (6) cheletropic reactions, and (7) dyotropic reactions. Due to their elegance, simp ...
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Todd Martinez
Todd or Todds may refer to: Places ;Australia: * Todd River, an ephemeral river ;United States: * Todd Valley, California, also known as Todd, an unincorporated community * Todd, Missouri, a ghost town * Todd, North Carolina, an unincorporated community * Todd County, Kentucky * Todd County, Minnesota * Todd County, South Dakota * Todd Fork, a river in Ohio * Todd Township, Minnesota * Todd Township, Fulton County, Pennsylvania * Todd Township, Huntingdon County, Pennsylvania * Todds, Ohio, an unincorporated community People * Todd (given name) * Todd (surname) Arts and entertainment * ''Todd'' (album), a 1974 album by Todd Rundgren * Todd (''Cars''), a character in ''Cars'' * Todd (''Stargate''), a recurring character in the series ''Stargate Atlantis'' * The Todd (''Scrubs''), a character on ''Scrubs'' Other uses * Todd (elm cultivar) * Todd class, a characteristic class in algebraic topology * Todd-AO, a company in film post-production * Todd Corporation, a New Ze ...
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Quantum Chemistry
Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions to physical and chemical properties of molecules, materials, and solutions at the atomic level. These calculations include systematically applied approximations intended to make calculations computationally feasible while still capturing as much information about important contributions to the computed wave functions as well as to observable properties such as structures, spectra, and thermodynamic properties. Quantum chemistry is also concerned with the computation of quantum effects on molecular dynamics and chemical kinetics. Chemists rely heavily on spectroscopy through which information regarding the quantization of energy on a molecular scale can be obtained. Common methods are infra-red (IR) spectroscopy, nuclear magnetic r ...
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