Valence bond theoryIn chemistry, valence bond (VB) theory is one of the two basic theories, along with molecular orbital (MO) theory, that were developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of the dissociated atoms combine to give individual chemical bonds when a molecule is formed. In contrast, molecular orbital theory has orbitals that cover the whole molecule. In 1916, G. N. Lewis proposed that a chemical bond forms by the interaction of two shared bonding electrons, with the representation of molecules as Lewis structures.
Organoboron chemistryOrganoboron chemistry or organoborane chemistry is the chemistry of organoboron compounds or organoboranes, which are chemical compounds of boron and carbon that are organic derivatives of borane (BH3), for example trialkyl boranes. . Organoboron compounds are important reagents in organic chemistry enabling many chemical transformations, the most important ones being hydroboration and carboboration. Reactions of organoborates and boranes involve the transfer of a nucleophilic group attached to boron to an electrophilic center either inter- or intramolecularly.
Zero-energy buildingA Zero-Energy Building (ZEB), also known as a Net Zero-Energy (NZE) building, is a building with net zero energy consumption, meaning the total amount of energy used by the building on an annual basis is equal to the amount of renewable energy created on the site or in other definitions by renewable energy sources offsite, using technology such as heat pumps, high efficiency windows and insulation, and solar panels. The goal is that these buildings contribute less overall greenhouse gas to the atmosphere during operations than similar non-ZNE buildings.
Enantioselective synthesisEnantioselective synthesis, also called asymmetric synthesis, is a form of chemical synthesis. It is defined by IUPAC as "a chemical reaction (or reaction sequence) in which one or more new elements of chirality are formed in a substrate molecule and which produces the stereoisomeric (enantiomeric or diastereomeric) products in unequal amounts." Put more simply: it is the synthesis of a compound by a method that favors the formation of a specific enantiomer or diastereomer.
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.
EtherIn organic chemistry, ethers are a class of compounds that contain an ether group—an oxygen atom connected to two alkyl or aryl groups. They have the general formula , where R and R′ represent the alkyl or aryl groups. Ethers can again be classified into two varieties: if the alkyl or aryl groups are the same on both sides of the oxygen atom, then it is a simple or symmetrical ether, whereas if they are different, the ethers are called mixed or unsymmetrical ethers.
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.
Boron trifluorideBoron trifluoride is the inorganic compound with the formula . This pungent, colourless, and toxic gas forms white fumes in moist air. It is a useful Lewis acid and a versatile building block for other boron compounds. The geometry of a molecule of is trigonal planar. Its D3h symmetry conforms with the prediction of VSEPR theory. The molecule has no dipole moment by virtue of its high symmetry. The molecule is isoelectronic with the carbonate anion, .
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.
