Enantiomeric excessIn stereochemistry, enantiomeric excess (ee) is a measurement of purity used for chiral substances. It reflects the degree to which a sample contains one enantiomer in greater amounts than the other. A racemic mixture has an ee of 0%, while a single completely pure enantiomer has an ee of 100%. A sample with 70% of one enantiomer and 30% of the other has an ee of 40% (70% − 30%). Enantiomeric excess is defined as the absolute difference between the mole fraction of each enantiomer: where In practice, it is most often expressed as a percent enantiomeric excess.
EnantiomerIn chemistry, an enantiomer (/ɪˈnænti.əmər, ɛ-, -oʊ-/ ih-NAN-tee-ə-mər; from Ancient Greek ἐνάντιος (enántios) 'opposite', and μέρος (méros) 'part') – also called optical isomer, antipode, or optical antipode – is one of two stereoisomers that are non-superposable onto their own . Enantiomers are much like one's right and left hands, when looking at the same face, they cannot be superposed onto each other. No amount of reorientation in three spatial dimensions will allow the four unique groups on the chiral carbon (see chirality) to line up exactly.
Chiral resolutionChiral resolution, or enantiomeric resolution, is a process in stereochemistry for the separation of racemic compounds into their enantiomers. It is an important tool in the production of optically active compounds, including drugs. Another term with the same meaning is optical resolution. The use of chiral resolution to obtain enantiomerically pure compounds has the disadvantage of necessarily discarding at least half of the starting racemic mixture. Asymmetric synthesis of one of the enantiomers is one means of avoiding this waste.
Total orderIn mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation on some set , which satisfies the following for all and in : (reflexive). If and then (transitive). If and then (antisymmetric). or (strongly connected, formerly called total). Reflexivity (1.) already follows from connectedness (4.), but is required explicitly by many authors nevertheless, to indicate the kinship to partial orders.
Lexicographic orderIn mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences of different lengths by comparing the lengths of the sequences before considering their elements.
Order isomorphismIn the mathematical field of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets (posets). Whenever two posets are order isomorphic, they can be considered to be "essentially the same" in the sense that either of the orders can be obtained from the other just by renaming of elements. Two strictly weaker notions that relate to order isomorphisms are order embeddings and Galois connections.
Racemic mixtureIn chemistry, a racemic mixture or racemate (reɪˈsiːmeɪt,_rə-,_ˈræsɪmeɪt), is one that has equal amounts of left- and right-handed enantiomers of a chiral molecule or salt. Racemic mixtures are rare in nature, but many compounds are produced industrially as racemates. The first known racemic mixture was racemic acid, which Louis Pasteur found to be a mixture of the two enantiomeric isomers of tartaric acid. He manually separated the crystals of a mixture by hand, starting from an aqueous solution of the sodium ammonium salt of racemate tartaric acid.
Order topologyIn mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets. If X is a totally ordered set, the order topology on X is generated by the subbase of "open rays" for all a, b in X. Provided X has at least two elements, this is equivalent to saying that the open intervals together with the above rays form a base for the order topology.
1,3-Dipolar cycloadditionThe 1,3-dipolar cycloaddition is a chemical reaction between a 1,3-dipole and a dipolarophile to form a five-membered ring. The earliest 1,3-dipolar cycloadditions were described in the late 19th century to the early 20th century, following the discovery of 1,3-dipoles. Mechanistic investigation and synthetic application were established in the 1960s, primarily through the work of Rolf Huisgen. Hence, the reaction is sometimes referred to as the Huisgen cycloaddition (this term is often used to specifically describe the 1,3-dipolar cycloaddition between an organic azide and an alkyne to generate 1,2,3-triazole).
Order theoryOrder theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article introduces the field and provides basic definitions. A list of order-theoretic terms can be found in the order theory glossary. Orders are everywhere in mathematics and related fields like computer science. The first order often discussed in primary school is the standard order on the natural numbers e.
