Finitary relationIn mathematics, a finitary relation over sets X1, ..., Xn is a subset of the Cartesian product X1 × ⋯ × Xn; that is, it is a set of n-tuples (x1, ..., xn) consisting of elements xi in Xi. Typically, the relation describes a possible connection between the elements of an n-tuple. For example, the relation "x is divisible by y and z" consists of the set of 3-tuples such that when substituted to x, y and z, respectively, make the sentence true. The non-negative integer n giving the number of "places" in the relation is called the arity, adicity or degree of the relation.
Hückel methodThe Hückel method or Hückel molecular orbital theory, proposed by Erich Hückel in 1930, is a simple method for calculating molecular orbitals as linear combinations of atomic orbitals. The theory predicts the molecular orbitals for π-electrons in π-delocalized molecules, such as ethylene, benzene, butadiene, and pyridine. It provides the theoretical basis for Hückel's rule that cyclic, planar molecules or ions with π-electrons are aromatic.
Molecular machineMolecular machines are a class of molecules typically described as an assembly of a discrete number of molecular components intended to produce mechanical movements in response to specific stimuli, mimicking macromolecular devices such as switches and motors. Naturally occurring or biological molecular machines are responsible for vital living processes such as DNA replication and ATP synthesis. Kinesins and ribosomes are examples of molecular machines, and they often take the form of multi-protein complexes.
HyperconjugationIn organic chemistry, hyperconjugation (σ-conjugation or no-bond resonance) refers to the delocalization of electrons with the participation of bonds of primarily σ-character. Usually, hyperconjugation involves the interaction of the electrons in a sigma (σ) orbital (e.g. C–H or C–C) with an adjacent unpopulated non-bonding p or antibonding σ* or π* orbitals to give a pair of extended molecular orbitals. However, sometimes, low-lying antibonding σ* orbitals may also interact with filled orbitals of lone pair character (n) in what is termed negative hyperconjugation.
Converse relationIn mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the converse of the relation 'child of' is the relation 'parent of'. In formal terms, if and are sets and is a relation from to then is the relation defined so that if and only if In set-builder notation, The notation is analogous with that for an inverse function. Although many functions do not have an inverse, every relation does have a unique converse.
Molecular symmetryIn chemistry, molecular symmetry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a fundamental concept in chemistry, as it can be used to predict or explain many of a molecule's chemical properties, such as whether or not it has a dipole moment, as well as its allowed spectroscopic transitions. To do this it is necessary to use group theory. This involves classifying the states of the molecule using the irreducible representations from the character table of the symmetry group of the molecule.
Conformational isomerismIn chemistry, conformational isomerism is a form of stereoisomerism in which the isomers can be interconverted just by rotations about formally single bonds (refer to figure on single bond rotation). While any two arrangements of atoms in a molecule that differ by rotation about single bonds can be referred to as different conformations, conformations that correspond to local minima on the potential energy surface are specifically called conformational isomers or conformers.
Radical polymerizationIn polymer chemistry, free-radical polymerization (FRP) is a method of polymerization by which a polymer forms by the successive addition of free-radical building blocks (repeat units). Free radicals can be formed by a number of different mechanisms, usually involving separate initiator molecules. Following its generation, the initiating free radical adds (nonradical) monomer units, thereby growing the polymer chain. Free-radical polymerization is a key synthesis route for obtaining a wide variety of different polymers and materials composites.
Stacking (chemistry)In chemistry, pi stacking (also called π–π stacking) refers to the presumptive attractive, noncovalent pi interactions (orbital overlap) between the pi bonds of aromatic rings. However this is a misleading description of the phenomena since direct stacking of aromatic rings (the "sandwich interaction") is electrostatically repulsive.
Molecular geometryMolecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule. It includes the general shape of the molecule as well as bond lengths, bond angles, torsional angles and any other geometrical parameters that determine the position of each atom. Molecular geometry influences several properties of a substance including its reactivity, polarity, phase of matter, color, magnetism and biological activity. The angles between bonds that an atom forms depend only weakly on the rest of molecule, i.
