DicarbonylIn organic chemistry, a dicarbonyl is a molecule containing two carbonyl () groups. Although this term could refer to any organic compound containing two carbonyl groups, it is used more specifically to describe molecules in which both carbonyls are in close enough proximity that their reactivity is changed, such as 1,2-, 1,3-, and 1,4-dicarbonyls. Their properties often differ from those of monocarbonyls, and so they are usually considered functional groups of their own.
AromaticityIn chemistry, aromaticity means the molecule has cyclic (ring-shaped) structures with pi bonds in resonance (those containing delocalized electrons). Aromatic rings give increased stability compared to saturated compounds having single bonds, and other geometric or connective non-cyclic arrangements with the same set of atoms. Aromatic rings are very stable and do not break apart easily. Organic compounds that are not aromatic are classified as aliphatic compounds—they might be cyclic, but only aromatic rings have enhanced stability.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
Möbius aromaticityIn organic chemistry, Möbius aromaticity is a special type of aromaticity believed to exist in a number of organic molecules. In terms of molecular orbital theory these compounds have in common a monocyclic array of molecular orbitals in which there is an odd number of out-of-phase overlaps, the opposite pattern compared to the aromatic character to Hückel systems. The nodal plane of the orbitals, viewed as a ribbon, is a Möbius strip, rather than a cylinder, hence the name.
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
Heun's methodIn mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.
Aromatic ring currentAn aromatic ring current is an effect observed in aromatic molecules such as benzene and naphthalene. If a magnetic field is directed perpendicular to the plane of the aromatic system, a ring current is induced in the delocalized π electrons of the aromatic ring. This is a direct consequence of Ampère's law; since the electrons involved are free to circulate, rather than being localized in bonds as they would be in most non-aromatic molecules, they respond much more strongly to the magnetic field.
Jacobi methodIn numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.
FuranFuran is a heterocyclic organic compound, consisting of a five-membered aromatic ring with four carbon atoms and one oxygen atom. Chemical compounds containing such rings are also referred to as furans. Furan is a colorless, flammable, highly volatile liquid with a boiling point close to room temperature. It is soluble in common organic solvents, including alcohol, ether, and acetone, and is slightly soluble in water. Its odor is "strong, ethereal; chloroform-like". It is toxic and may be carcinogenic in humans.
Polycyclic aromatic hydrocarbonA polycyclic aromatic hydrocarbon (PAH) is a class of organic compounds that is composed of multiple aromatic rings. The simplest representative is naphthalene, having two aromatic rings and the three-ring compounds anthracene and phenanthrene. PAHs are uncharged, non-polar and planar. Many are colorless. Many of them are found in coal and in oil deposits, and are also produced by the incomplete combustion of organic matter—for example, in engines and incinerators or when biomass burns in forest fires.
