# Delocalized electron

In chemistry, delocalized electrons are electrons in a molecule, ion or solid metal that are not associated with a single atom or a covalent bond.[1] The term is general and can have slightly different meanings in different fields. In organic chemistry, this refers to resonance in conjugated systems and aromatic compounds. In solid-state physics, this refers to free electrons that facilitate electrical conduction. In quantum chemistry, this refers to molecular orbital electrons that extend over several adjacent atoms.

Benzene, with the delocalization of the electrons indicated by the circle.

## Resonance

In the simple aromatic ring of benzene the delocalization of six π electrons over the C6 ring is often graphically indicated by a circle. The fact that the six C-C bonds are equidistant is one indication that the π electrons are delocalized; if the structure were to have isolated double bonds alternating with discrete single bonds, the bond would likewise have alternating longer and shorter lengths. In valence bond theory, delocalization in benzene is represented by resonance structures.

## Electrical conduction

Delocalized electrons also exist in the structure of solid metals. Metallic structure consists of aligned positive ions (cations) in a "sea" of delocalized electrons. This means that the electrons are free to move throughout the structure, and gives rise to properties such as conductivity.

In diamond all four outer electrons of each carbon atom are 'localized' between the atoms in covalent bonding. The movement of electrons is restricted and diamond does not conduct an electric current. In graphite, each carbon atom uses only 3 of its 4 outer energy level electrons in covalently bonding to three other carbon atoms in a plane. Each carbon atom contributes one electron to a delocalized system of electrons that is also a part of the chemical bonding. The delocalized electrons are free to move throughout the plane. For this reason, graphite conducts electricity along the planes of carbon atoms, but does not conduct in a direction at right angles to the plane.

## Molecular orbitals

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 methane molecule for example, ab initio calculations show bonding character in four molecular orbitals, sharing the electrons uniformly among all five atoms. There are two orbital levels, a bonding molecular orbital formed from the 2s orbital on carbon and triply degenerate bonding molecular orbitals from each of the 2p orbitals on carbon. The localized sp3 orbitals corresponding to each individual bond in valence bond theory can be obtained from a linear combination of the four molecular orbitals.

## References

1. ^ IUPAC Gold Book delocalization
1-aminocyclopropane-1-carboxylate synthase

Aminocyclopropane-1-carboxylic acid synthase (ACC synthase, ACS) (EC 4.4.1.14) is an enzyme that catalyzes the synthesis of 1-Aminocyclopropane-1-carboxylic acid (ACC), a precursor for ethylene, from S-Adenosyl methionine (AdoMet, SAM), an intermediate in the Yang cycle and activated methyl cycle and a useful molecule for methyl transfer. ACC synthase, like other PLP dependent enzymes, catalyzes the reaction through a quinonoid zwitterion intermediate and uses cofactor pyridoxal phosphate (PLP, the active form of vitamin B6) for stabilization.

In enzymology, a 1-aminocyclopropane-1-carboxylate synthase is an enzyme that catalyzes the chemical reaction

S-adenosyl-L-methionine ${\displaystyle \rightleftharpoons }$ 1-aminocyclopropane-1-carboxylate + methylthioadenosine

Hence, this enzyme has one substrate, S-adenosyl-L-methionine, and two products, 1-aminocyclopropane-1-carboxylate and methylthioadenosine.

This enzyme belongs to the family of lyases, specifically carbon-sulfur lyases. The systematic name of this enzyme class is S-adenosyl-L-methionine methylthioadenosine-lyase(1-aminocyclopropane-1-carboxylate-forming). Other names in common use include 1-aminocyclopropanecarboxylate synthase, 1-aminocyclopropane-1-carboxylic acid synthase, 1-aminocyclopropane-1-carboxylate synthetase, aminocyclopropanecarboxylic acid synthase, aminocyclopropanecarboxylate synthase, ACC synthase, and S-adenosyl-L-methionine methylthioadenosine-lyase. This enzyme participates in propanoate metabolism. It employs one cofactor, pyridoxal phosphate.

Energy level splitting

In quantum physics, energy level splitting of a quantum system occurs when a degenerate energy level of two or more states is split because corresponding Hamiltonian's eigenvalues become different. The outcome is several distinct energy levels in place of the former degenerate (multi-state) level. This may occur because of external fields, quantum tunnelling between states, or other effects. The term is most commonly used in reference to the electron configuration in atoms or molecules.

The simplest case of level splitting is a quantum system with two states whose unperturbed Hamiltonian is a diagonal operator: Ĥ0 = E0I, where I is the 2 × 2 identity matrix. Eigenstates and eigenvalues (energy levels) of a perturbed Hamiltonian

${\displaystyle {\hat {H}}_{\varepsilon }={\hat {H}}_{0}+\varepsilon \sigma _{3}={\begin{pmatrix}E_{0}+\varepsilon &0\\0&E_{0}-\varepsilon \end{pmatrix}}}$

will be:

|0⟩: the E0 + ε level, and
|1⟩: the E0ε level,

so this degenerate E0 eigenvalue splits in two whenever ε ≠ 0. Though, if a perturbed Hamiltonian is not diagonal for this quantum states basis {|0⟩, |1⟩} , then Hamiltonian's eigenstates are linear combinations of these two states.

For a physical implementation such as a charged spin-½ particle in an external magnetic field, the z-axis of the coordinate system is required to be collinear with the magnetic field to obtain a Hamiltonian in the form above (the σ3 Pauli matrix corresponds to z-axis). These basis states, referred to as spin-up and spin-down, are hence eigenvectors of the perturbed Hamiltonian, so this level splitting is both easy to demonstrate mathematically and intuitively evident.

But in cases where the choice of state basis is not determined by a coordinate system, and the perturbed Hamiltonian is not diagonal, a level splitting may appear counter-intuitive, as in examples from chemistry below.

Glossary of chemistry terms

Most of the terms listed in Wikipedia glossaries are already defined and explained within Wikipedia itself. However, glossaries like this one are useful for looking up, comparing and reviewing large numbers of terms together. You can help enhance this page by adding new terms or writing definitions for existing ones.

This glossary of chemistry terms is a list of terms and definitions relevant to chemistry, including chemical laws, diagrams and formulae, laboratory tools, glassware, and equipment. Chemistry is a physical science concerned with the composition, structure, and properties of matter, as well as the changes it undergoes during chemical reactions; it has an extensive vocabulary and a significant amount of jargon.

Note: All periodic table references refer to the IUPAC Style of the Periodic Table.

Index of physics articles (D)

The index of physics articles is split into multiple pages due to its size.

Organolithium reagent

Organolithium reagents are organometallic compounds that contain carbon – lithium bonds. They are important reagents in organic synthesis, and are frequently used to transfer the organic group or the lithium atom to the substrates in synthetic steps, through nucleophilic addition or simple deprotonation. Organolithium reagents are used in industry as an initiator for anionic polymerization, which leads to the production of various elastomers. They have also been applied in asymmetric synthesis in the pharmaceutical industry. Due to the large difference in electronegativity between the carbon atom and the lithium atom, the C-Li bond is highly ionic. Owing to the polar nature of the C-Li bond, organolithium reagents are good nucleophiles and strong bases. For laboratory organic synthesis, many organolithium reagents are commercially available in solution form. These reagents are highly reactive, and are sometimes pyrophoric.

P–n junction

A p–n junction is a boundary or interface between two types of semiconductor materials, p-type and n-type, inside a single crystal of semiconductor. The "p" (positive) side contains an excess of holes, while the "n" (negative) side contains an excess of electrons in the outer shells of the electrically neutral atoms there. This allows electrical current to pass through the junction only in one direction. The p-n junction is created by doping, for example by ion implantation, diffusion of dopants, or by epitaxy (growing a layer of crystal doped with one type of dopant on top of a layer of crystal doped with another type of dopant). If two separate pieces of material were used, this would introduce a grain boundary between the semiconductors that would severely inhibit its utility by scattering the electrons and holes.p–n junctions are elementary "building blocks" of semiconductor electronic devices such as diodes, transistors, solar cells, LEDs, and integrated circuits; they are the active sites where the electronic action of the device takes place. For example, a common type of transistor, the bipolar junction transistor, consists of two p–n junctions in series, in the form n–p–n or p–n–p; while a diode can be made from a single p-n junction. A Schottky junction is a special case of a p–n junction, where metal serves the role of the p-type semiconductor.

Surface plasmon

Surface plasmons (SPs) are coherent delocalized electron oscillations that exist at the interface between any two materials where the real part of the dielectric function changes sign across the interface (e.g. a metal-dielectric interface, such as a metal sheet in air). SPs have lower energy than bulk (or volume) plasmons which quantise the longitudinal electron oscillations about positive ion cores within the bulk of an electron gas (or plasma).

The charge motion in a surface plasmon always creates electromagnetic fields outside (as well as inside) the metal. The total excitation, including both the charge motion and associated electromagnetic field, is called either a surface plasmon polariton at a planar interface, or a localized surface plasmon for the closed surface of a small particle.

The existence of surface plasmons was first predicted in 1957 by Rufus Ritchie. In the following two decades, surface plasmons were extensively studied by many scientists, the foremost of whom were T. Turbadar in the 1950s and 1960s, and Heinz Raether, E. Kretschmann, and A. Otto in the 1960s and 1970s. Information transfer in nanoscale structures, similar to photonics, by means of surface plasmons, is referred to as plasmonics.

Thermodynamic temperature

Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics.

Thermodynamic temperature is defined by the third law of thermodynamics in which the theoretically lowest temperature is the null or zero point. At this point, absolute zero, the particle constituents of matter have minimal motion and can become no colder. In the quantum-mechanical description, matter at absolute zero is in its ground state, which is its state of lowest energy. Thermodynamic temperature is often also called absolute temperature, for two reasons: one, proposed by Kelvin, that it does not depend on the properties of a particular material; two that it refers to an absolute zero according to the properties of the ideal gas.

The International System of Units specifies a particular scale for thermodynamic temperature. It uses the kelvin scale for measurement and selects the triple point of water at 273.16 K as the fundamental fixing point. Other scales have been in use historically. The Rankine scale, using the degree Fahrenheit as its unit interval, is still in use as part of the English Engineering Units in the United States in some engineering fields. ITS-90 gives a practical means of estimating the thermodynamic temperature to a very high degree of accuracy.

Roughly, the temperature of a body at rest is a measure of the mean of the energy of the translational, vibrational and rotational motions of matter's particle constituents, such as molecules, atoms, and subatomic particles. The full variety of these kinetic motions, along with potential energies of particles, and also occasionally certain other types of particle energy in equilibrium with these, make up the total internal energy of a substance. Internal energy is loosely called the heat energy or thermal energy in conditions when no work is done upon the substance by its surroundings, or by the substance upon the surroundings. Internal energy may be stored in a number of ways within a substance, each way constituting a "degree of freedom". At equilibrium, each degree of freedom will have on average the same energy: ${\displaystyle k_{B}T/2}$ where ${\displaystyle k_{B}}$ is the Boltzmann constant, unless that degree of freedom is in the quantum regime. The internal degrees of freedom (rotation, vibration, etc.) may be in the quantum regime at room temperature, but the translational degrees of freedom will be in the classical regime except at extremely low temperatures (fractions of kelvins) and it may be said that, for most situations, the thermodynamic temperature is specified by the average translational kinetic energy of the particles.

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