StereoselectivityIn chemistry, stereoselectivity is the property of a chemical reaction in which a single reactant forms an unequal mixture of stereoisomers during a non-stereospecific creation of a new stereocenter or during a non-stereospecific transformation of a pre-existing one. The selectivity arises from differences in steric and electronic effects in the mechanistic pathways leading to the different products. Stereoselectivity can vary in degree but it can never be total since the activation energy difference between the two pathways is finite: both products are at least possible and merely differ in amount.
Silyl enol etherSilyl enol ethers in organic chemistry are a class of organic compounds that share a common functional group composed of an enolate bonded through its oxygen end to an organosilicon group. They are important intermediates in organic synthesis. Silyl enol ethers are generally prepared by reacting an enolizable carbonyl compound with a silyl electrophile and a base, or just reacting an enolate with a silyl electrophile. Since silyl electrophiles are hard and silicon-oxygen bonds are very strong, the oxygen (of the carbonyl compound or enolate) acts as the nucleophile to form a Si-O single bond.
Α,β-Unsaturated carbonyl compoundα,β-Unsaturated carbonyl compounds are organic compounds with the general structure (O=CR)−Cα=Cβ-R. Such compounds include enones and enals. In these compounds the carbonyl group is conjugated with an alkene (hence the adjective unsaturated). Unlike the case for carbonyls without a flanking alkene group, α,β-unsaturated carbonyl compounds are susceptible to attack by nucleophiles at the β-carbon. This pattern of reactivity is called vinylogous. Examples of unsaturated carbonyls are acrolein (propenal), mesityl oxide, acrylic acid, and maleic acid.
Trigonometric substitutionIn mathematics, trigonometric substitution is the replacement of trigonometric functions for other expressions. In calculus, trigonometric substitution is a technique for evaluating integrals. Moreover, one may use the trigonometric identities to simplify certain integrals containing radical expressions. Like other methods of integration by substitution, when evaluating a definite integral, it may be simpler to completely deduce the antiderivative before applying the boundaries of integration.
Tangent half-angle substitutionIn integral calculus, the tangent half-angle substitution is a change of variables used for evaluating integrals, which converts a rational function of trigonometric functions of into an ordinary rational function of by setting . This is the one-dimensional stereographic projection of the unit circle parametrized by angle measure onto the real line. The general transformation formula is: The tangent of half an angle is important in spherical trigonometry and was sometimes known in the 17th century as the half tangent or semi-tangent.
N-Butyllithiumn-Butyllithium C4H9Li (abbreviated n-BuLi) is an organolithium reagent. It is widely used as a polymerization initiator in the production of elastomers such as polybutadiene or styrene-butadiene-styrene (SBS). Also, it is broadly employed as a strong base (superbase) in the synthesis of organic compounds as in the pharmaceutical industry. Butyllithium is commercially available as solutions (15%, 25%, 1.5 M, 2 M, 2.5 M, 10 M, etc.) in alkanes such as pentane, hexanes, and heptanes.
Arene substitution patternArene substitution patterns are part of organic chemistry IUPAC nomenclature and pinpoint the position of substituents other than hydrogen in relation to each other on an aromatic hydrocarbon. Electrophilic aromatic substitution In ortho-substitution, two substituents occupy positions next to each other, which may be numbered 1 and 2. In the diagram, these positions are marked R and ortho. In meta-substitution the substituents occupy positions 1 and 3 (corresponding to R and meta in the diagram).
Nucleophilic additionIn organic chemistry, a nucleophilic addition reaction is an addition reaction where a chemical compound with an electrophilic double or triple bond reacts with a nucleophile, such that the double or triple bond is broken. Nucleophilic additions differ from electrophilic additions in that the former reactions involve the group to which atoms are added accepting electron pairs, whereas the latter reactions involve the group donating electron pairs.
Chiral auxiliaryIn stereochemistry, a chiral auxiliary is a stereogenic group or unit that is temporarily incorporated into an organic compound in order to control the stereochemical outcome of the synthesis. The chirality present in the auxiliary can bias the stereoselectivity of one or more subsequent reactions. The auxiliary can then be typically recovered for future use. Most biological molecules and pharmaceutical targets exist as one of two possible enantiomers; consequently, chemical syntheses of natural products and pharmaceutical agents are frequently designed to obtain the target in enantiomerically pure form.
Direct sumThe direct sum is an operation between structures in abstract algebra, a branch of mathematics. It is defined differently, but analogously, for different kinds of structures. To see how the direct sum is used in abstract algebra, consider a more elementary kind of structure, the abelian group. The direct sum of two abelian groups and is another abelian group consisting of the ordered pairs where and . To add ordered pairs, we define the sum to be ; in other words addition is defined coordinate-wise.
