Runge–Kutta methodsIn numerical analysis, the Runge–Kutta methods (ˈrʊŋəˈkʊtɑː ) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discretization for the approximate solutions of simultaneous nonlinear equations. These methods were developed around 1900 by the German mathematicians Carl Runge and Wilhelm Kutta. The most widely known member of the Runge–Kutta family is generally referred to as "RK4", the "classic Runge–Kutta method" or simply as "the Runge–Kutta method".
Azide-alkyne Huisgen cycloadditionThe azide-alkyne Huisgen cycloaddition is a 1,3-dipolar cycloaddition between an azide and a terminal or internal alkyne to give a 1,2,3-triazole. Rolf Huisgen was the first to understand the scope of this organic reaction. American chemist Karl Barry Sharpless has referred to this cycloaddition as "the cream of the crop" of click chemistry and "the premier example of a click reaction". In the reaction above azide 2 reacts neatly with alkyne 1 to afford the product triazole as a mixture of 1,4-adduct (3a) and 1,5-adduct (3b) at 98 °C in 18 hours.
AldolIn organic chemistry, an aldol describes a structural motif consisting of a 3-hydroxy ketone or 3-hydroxyaldehyde. An aldol consisting of a 3-hydroxy ketone is called a β-hydroxy ketone, and an aldol consisting of a 3-hydroxy aldehyde is called a β-hydroxy aldehyde. The term "aldol" may refer to 3-hydroxybutanal. Aldols are usually the product of aldol addition, i.e. the condensation of two aldehydes. Stereoselective syntheses of aldols is an active area of asymmetric synthesis.
Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
CatalysisCatalysis (kəˈtæləsɪs) is the process of change in rate of a chemical reaction by adding a substance known as a catalyst (ˈkætəlɪst). Catalysts are not consumed by the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recycles quickly, very small amounts of catalyst often suffice; mixing, surface area, and temperature are important factors in reaction rate. Catalysts generally react with one or more reactants to form intermediates that subsequently give the final reaction product, in the process of regenerating the catalyst.
Carbonyl reductionIn organic chemistry, carbonyl reduction is the organic reduction of any carbonyl group by a reducing agent. Typical carbonyl compounds are ketones, aldehydes, carboxylic acids, esters, and acid halides. Carboxylic acids, esters, and acid halides can be reduced to either aldehydes or a step further to primary alcohols, depending on the strength of the reducing agent; aldehydes and ketones can be reduced respectively to primary and secondary alcohols. In deoxygenation, the alcohol can be further reduced and removed altogether.
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.
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.
