Heck reactionThe Heck reaction (also called the Mizoroki–Heck reaction) is the chemical reaction of an unsaturated halide (or triflate) with an alkene in the presence of a base and a palladium catalyst to form a substituted alkene. It is named after Tsutomu Mizoroki and Richard F. Heck. Heck was awarded the 2010 Nobel Prize in Chemistry, which he shared with Ei-ichi Negishi and Akira Suzuki, for the discovery and development of this reaction.
Organopalladium chemistryOrganopalladium chemistry is a branch of organometallic chemistry that deals with organic palladium compounds and their reactions. Palladium is often used as a catalyst in the reduction of alkenes and alkynes with hydrogen. This process involves the formation of a palladium-carbon covalent bond. Palladium is also prominent in carbon-carbon coupling reactions, as demonstrated in tandem reactions. 1873 - A. N. Zaitsev reports reduction of benzophenone over palladium with hydrogen.
Sonogashira couplingThe Sonogashira reaction is a cross-coupling reaction used in organic synthesis to form carbon–carbon bonds. It employs a palladium catalyst as well as copper co-catalyst to form a carbon–carbon bond between a terminal alkyne and an aryl or vinyl halide. R1: aryl or vinyl R2: arbitrary X: I, Br, Cl or OTf The Sonogashira cross-coupling reaction has been employed in a wide variety of areas, due to its usefulness in the formation of carbon–carbon bonds.
DiazoIn organic chemistry, the diazo group is an organic moiety consisting of two linked nitrogen atoms (azo, ) at the terminal position. Overall charge-neutral organic compounds containing the diazo group bound to a carbon atom are called diazo compounds or diazoalkanes and are described by the general structural formula . The simplest example of a diazo compound is diazomethane, . Diazo compounds () should not be confused with azo compounds () or with diazonium compounds ().
Cross productIn mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here ), and is denoted by the symbol . Given two linearly independent vectors a and b, the cross product, a × b (read "a cross b"), is a vector that is perpendicular to both a and b, and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming.
Infinite productIn mathematics, for a sequence of complex numbers a1, a2, a3, ... the infinite product is defined to be the limit of the partial products a1a2...an as n increases without bound. The product is said to converge when the limit exists and is not zero. Otherwise the product is said to diverge. A limit of zero is treated specially in order to obtain results analogous to those for infinite sums. Some sources allow convergence to 0 if there are only a finite number of zero factors and the product of the non-zero factors is non-zero, but for simplicity we will not allow that here.
Wallis productIn mathematics, the Wallis product for pi, published in 1656 by John Wallis, states that Wallis derived this infinite product using interpolation, though his method is not regarded as rigorous. A modern derivation can be found by examining for even and odd values of , and noting that for large , increasing by 1 results in a change that becomes ever smaller as increases. Let (This is a form of Wallis' integrals.) Integrate by parts: Now, we make two variable substitutions for convenience to obtain: We obtain values for and for later use.
YlideAn ylide or ylid (ˈɪlɪd) is a neutral dipolar molecule containing a formally negatively charged atom (usually a carbanion) directly attached to a heteroatom with a formal positive charge (usually nitrogen, phosphorus or sulfur), and in which both atoms have full octets of electrons. The result can be viewed as a structure in which two adjacent atoms are connected by both a covalent and an ionic bond; normally written X+–Y−. Ylides are thus 1,2-dipolar compounds, and a subclass of zwitterions.
Triple productIn geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors. The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product. The scalar triple product (also called the mixed product, box product, or triple scalar product) is defined as the dot product of one of the vectors with the cross product of the other two.
