Peterson olefinationThe Peterson olefination (also called the Peterson reaction) is the chemical reaction of α-silyl carbanions (1 in diagram below) with ketones (or aldehydes) to form a β-hydroxysilane (2) which eliminates to form alkenes (3). Several reviews have been published. One attractive feature of the Peterson olefination is that it can be used to prepare either cis- or trans-alkenes from the same β-hydroxysilane. Treatment of the β-hydroxysilane with acid will yield one alkene, while treatment of the same β-hydroxysilane with base will yield the alkene of opposite stereochemistry.
Wittig reactionThe Wittig reaction or Wittig olefination is a chemical reaction of an aldehyde or ketone with a triphenyl phosphonium ylide called a Wittig reagent. Wittig reactions are most commonly used to convert aldehydes and ketones to alkenes. Most often, the Wittig reaction is used to introduce a methylene group using methylenetriphenylphosphorane (Ph3P=CH2). Using this reagent, even a sterically hindered ketone such as camphor can be converted to its methylene derivative.
Tebbe's reagentTebbe's reagent is the organometallic compound with the formula (C5H5)2TiCH2ClAl(CH3)2. It is used in the methylidenation of carbonyl compounds, that is it converts organic compounds containing the R2C=O group into the related R2C=CH2 derivative. It is a red solid that is pyrophoric in the air, and thus is typically handled with air-free techniques. It was originally synthesized by Fred Tebbe at DuPont Central Research. Tebbe's reagent contains two tetrahedral metal centers linked by a pair of bridging ligands.
Substitution reactionA substitution reaction (also known as single displacement reaction or single substitution reaction) is a chemical reaction during which one functional group in a chemical compound is replaced by another functional group. Substitution reactions are of prime importance in organic chemistry. Substitution reactions in organic chemistry are classified either as electrophilic or nucleophilic depending upon the reagent involved, whether a reactive intermediate involved in the reaction is a carbocation, a carbanion or a free radical, and whether the substrate is aliphatic or aromatic.
Integration by substitutionIn calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables, is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation, and can loosely be thought of as using the chain rule "backwards". Before stating the result rigorously, consider a simple case using indefinite integrals. Compute Set This means or in differential form, Now where is an arbitrary constant 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.
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.
Nucleophilic substitutionIn chemistry, a nucleophilic substitution is a class of chemical reactions in which an electron-rich chemical species (known as a nucleophile) replaces a functional group within another electron-deficient molecule (known as the electrophile). The molecule that contains the electrophile and the leaving functional group is called the substrate.R. A. Rossi, R. H. de Rossi, Aromatic Substitution by the SRN1 Mechanism, ACS Monograph Series No. 178, American Chemical Society, 1983. .
