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Diradicaloid
Biradicaloids or diradicaloids are molecules with two Radical (chemistry), radical electrons that have significant interaction with each other. The two unpaired electrons are coupled and can either form a Singlet state, singlet ground state (Antiferromagnetism, antiferromagnetic coupling) or a Triplet state, triplet ground state (Ferromagnetism, ferromagnetic coupling) (Figure 1). This is in contrast to "disbiradicals," where the two radical electrons have no significant interaction and act independently as isolated radical species. Diradical, Diradicals are characterized by their diradical character, commonly quantified using an indicator \gamma. In the limit of fully Degenerate energy levels, degenerate frontier Molecular orbital, molecular orbitals, \gamma approaches a value of 1, representing 100% diradical character. However, diradicaloids have a small gap between the HOMO and LUMO, highest occupied molecular orbital (HOMO) and the lowest occupied molecular orbital (LUMO) and ...
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Radical (chemistry)
In chemistry, a radical, also known as a free radical, is an atom, molecule, or ion that has at least one unpaired valence electron. With some exceptions, these unpaired electrons make radicals highly chemically reactive. Many radicals spontaneously dimerize. Most organic radicals have short lifetimes. A notable example of a radical is the hydroxyl radical (HO·), a molecule that has one unpaired electron on the oxygen atom. Two other examples are triplet oxygen and triplet carbene (꞉) which have two unpaired electrons. Radicals may be generated in a number of ways, but typical methods involve redox reactions. Ionizing radiation, heat, electrical discharges, and electrolysis are known to produce radicals. Radicals are intermediates in many chemical reactions, more so than is apparent from the balanced equations. Radicals are important in combustion, atmospheric chemistry, polymerization, plasma chemistry, biochemistry, and many other chemical processes. A majority ...
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Electron Configuration
In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. For example, the electron configuration of the neon atom is , meaning that the 1s, 2s, and 2p subshells are occupied by two, two, and six electrons, respectively. Electronic configurations describe each electron as moving independently in an orbital, in an average field created by the nuclei and all the other electrons. Mathematically, configurations are described by Slater determinants or configuration state functions. According to the laws of quantum mechanics, a level of energy is associated with each electron configuration. In certain conditions, electrons are able to move from one configuration to another by the emission or absorption of a quantum of energy, in the form of a photon. Knowledge of the electron configuration of different atoms is useful in understanding the structu ...
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Van Der Waals Radius
The van der Waals radius, ''r'', of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. It is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics, as he was the first to recognise that atoms were not simply points and to demonstrate the physical consequences of their size through the van der Waals equation of state. van der Waals volume The van der Waals volume, ''V'', also called the atomic volume or molecular volume, is the atomic property most directly related to the van der Waals radius. It is the volume "occupied" by an individual atom (or molecule). The van der Waals volume may be calculated if the van der Waals radii (and, for molecules, the inter-atomic distances, and angles) are known. For a single atom, it is the volume of a sphere whose radius is the van der Waals radius of the atom:V_ = \pi r_^3. For a molecule, it is the volume enclosed by the van der Waals surf ...
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Covalent Radius
The covalent radius, ''r''cov, is a measure of the size of an atom that forms part of one covalent bond. It is usually measured either in picometres (pm) or angstroms (Å), with 1 Å = 100 pm. In principle, the sum of the two covalent radii should equal the covalent bond length between two atoms, ''R''(AB) = ''r''(A) + ''r''(B). Moreover, different radii can be introduced for single, double and triple bonds (r1, r2 and r3 below), in a purely operational sense. These relationships are certainly not exact because the size of an atom is not constant but depends on its chemical environment. For heteroatomic A–B bonds, ionic terms may enter. Often the polar covalent bonds are shorter than would be expected based on the sum of covalent radii. Tabulated values of covalent radii are either average or idealized values, which nevertheless show a certain transferability (chemistry), transferability between different situations, which makes them useful. The bond lengths ''R' ...
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Natural Bond Orbital
In quantum chemistry, a natural bond orbital or NBO is a calculated ''bonding orbital'' with maximum electron density. The NBOs are one of a sequence of natural localized orbital sets that include "natural atomic orbitals" (NAO), "natural hybrid orbitals" (NHO), "natural bonding orbitals" (NBO) and "natural (semi-)localized molecular orbitals" (NLMO). These natural localized sets are intermediate between basis atomic orbitals (AO) and molecular orbitals (MO): :Atomic orbital → NAO → NHO → NBO → NLMO → Molecular orbital Natural (localized) orbitals are used in computational chemistry to calculate the distribution of electron density in atoms and in bonds between atoms. They have the "maximum-occupancy character" in localized 1-center and 2-center regions of the molecule. Natural bond orbitals (NBOs) include the highest possible percentage of the electron density, ideally close to 2.000, providing the most accurate possible “natural Lewis structure” of ψ. A high perc ...
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Change Of Basis From Delocalized To Localized
Change, Changed or Changing may refer to the below. Other forms are listed at Alteration * Impermanence, a difference in a state of affairs at different points in time * Menopause, also referred to as "the change", the permanent cessation of the menstrual period * Metamorphosis, or change, a biological process by which an animal physically develops after birth or hatching * Personal development, or personal change, activities that improve awareness and identity * Social change, an alteration in the social order of a society * Technological change, invention, innovation, and diffusion of technology Organizations and politics * Change (company), a brokerage company in the Netherlands * Change (manifesto), a 2024 political manifesto in the United Kingdom * Change 2011, a Finnish political party * Change We Need, a slogan for Barack Obama's 2008 presidential campaign * Change.gov, the transition website for the incoming Obama administration in 2008–2009 * Change.org, a petition w ...
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Zwitterion
In chemistry, a zwitterion ( ; ), also called an inner salt or dipolar ion, is a molecule that contains an equal number of positively and negatively charged functional groups. : (1,2- dipolar compounds, such as ylides, are sometimes excluded from the definition.) Some zwitterions, such as amino acid zwitterions, are in chemical equilibrium with an uncharged "parent" molecule. Betaines are zwitterions that cannot isomerize to an all-neutral form, such as when the positive charge is located on a quaternary ammonium group. Similarly, a molecule containing a phosphonium group and a carboxylate group cannot isomerize. Amino acids Tautomerism of amino acids follows this stoichiometry: : The ratio of the concentrations of the two species in solution is independent of pH. It has been suggested, on the basis of theoretical analysis, that the zwitterion is stabilized in aqueous solution by hydrogen bonding with solvent water molecules. Analysis of neutron diffraction data for g ...
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Ionic Bonding
Ionic bonding is a type of chemical bonding that involves the Coulomb's law, electrostatic attraction between oppositely charged ions, or between two atoms with sharply different electronegativities, and is the primary interaction occurring in ionic compounds. It is one of the main types of bonding, along with covalent bonding and metallic bonding. Ions are atoms (or groups of atoms) with an electrostatic charge. Atoms that gain electrons make negatively charged ions (called anions). Atoms that lose electrons make positively charged ions (called cations). This transfer of electrons is known as electrovalence in contrast to covalent bond, covalence. In the simplest case, the cation is a metal atom and the anion is a Nonmetal (chemistry), nonmetal atom, but these ions can be more complex, e.g. polyatomic ions, polyatomic ions like or . In simpler words, an ionic bond results from the transfer of electrons from a metal to a non-metal to obtain a full valence shell for both atoms. '' ...
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Covalent Bond
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 "covalence" was introduced by Irving Langmuir in 1919, with Nevil Sidgwick using "co-valent link" in the 1920s. Merriam-Webster dates the specific phrase ''covalent bond'' to 1939, recognizing its first known ...
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Orbital Overlap
In chemical bonds, an orbital overlap is the concentration of orbitals on adjacent atoms in the same regions of space. Orbital overlap can lead to bond formation. The general principle for orbital overlap is that, the greater the overlap between orbitals, the greater the bond strength. Linus Pauling explained the importance of orbital overlap in the molecular bond angles observed through experimentation; it is the basis for orbital hybridization. As ''s'' orbitals are spherical (and have no directionality) and ''p'' orbitals are oriented 90° to each other, a theory was needed to explain why molecules such as methane (CH4) had observed bond angles of 109.5°. Pauling proposed that s and p orbitals on the carbon atom can combine to form hybrids (sp3 in the case of methane) which are directed toward the hydrogen atoms. The carbon hybrid orbitals have greater overlap with the hydrogen orbitals, and can therefore form stronger C–H bonds.Pauling, Linus. (1960). ''The Nature ...
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Localized Molecular Orbitals
Localized molecular orbitals are molecular orbitals which are concentrated in a limited spatial region of a molecule, such as a specific bond or lone pair on a specific atom. They can be used to relate molecular orbital calculations to simple bonding theories, and also to speed up post-Hartree–Fock electronic structure calculations by taking advantage of the local nature of electron correlation. Localized orbitals in systems with periodic boundary conditions are known as Wannier functions. Standard ab initio quantum chemistry methods lead to delocalized orbitals that, in general, extend over an entire molecule and have the symmetry of the molecule. Localized orbitals may then be found as linear combinations of the delocalized orbitals, given by an appropriate unitary transformation. In the water molecule for example, ab initio calculations show bonding character primarily in two molecular orbitals, each with electron density equally distributed among the two O-H bonds. The local ...
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