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Pure Appl. Chem., Vol. 71, No. 10, pp. 1919-1981, 1999

Glossary of terms used in theoretical organic chemistry

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Ab initio quantum mechanical methods (synonymous with nonempirical quantum mechanical methods) - Methods of quantum mechanical calculations independent of any experiment other than the determination of fundamental observables. The methods are based on the use of the full Schrödinger equation to treat all the electrons of a chemical system. In practice, approximations are necessary to restrict the complexity of the electronic wavefunction and to make its calculation possible. In this way methods of density functional theory are usually considered as ab initio quantum mechanical methods.

Absolute electronegativity - The property of a chemical system derived from density functional theory defined as

c = - m = -( E/ N)v @ (I + A)/2

where m is the electronic chemical potential , vis the potential due to the nuclei, and N is the number of electrons, I and A are respectively the ionization potential and electron affinity of the chemical system in its ground state ( in contrast to a similar relationship for the Mulliken electronegativity where I and A refer to the valence state). The "absolute"part of the term comes from the relationship to the electronic chemical potential, m . The absolute scale is essentially a measure of the chemical reactivity of a free atom, molecule, radical or ion, whereas the Pauling scale of electronegativity has no meaning with regard to molecules or ions. The scales are, therefore, comparable only for atoms and radicals where these are roughly parallel. Absolute electronegativity serves as a measure of bond polarity. For the species composed of two entities X and Y, the difference cX- cY is positive when X-Y has the polarity X- - Y+. PARR and YANG (1989); PEARSON (1991).

Absolute hardness - The resistance of the electronic chemical potential, m of a chemical system to a change in the number of electrons as measured by the curvature of the plot of energy E versus number of electrons.

h = (1/2)( m/ N)v = (1/2)( 2E/ N2)v @ (1/2)(I -A)

where I and A are respectively ground state ionization potential and electron affinity, and v is the potential due to the nuclei. In molecular orbital theory, the absolute hardness is measured by the energy gap between the lowest unoccupied and highest occupied molecular orbitals.

h = (eLUMO - eHOMO)/2

A high value of the absolute hardness is, thus, an indication of high stability and low reactivity. Absolute softness is defined as the reciprocal of the hardness. PARR and YANG (1989); PEARSON (1991).

Absolute softness - The reciprocal of absolute hardness. s = 1/h

Active space - Set of active orbitals in the formalism of Multiconfigurational SCF method, see also Complete active space.

Adiabatic approximation - see Born-Oppenheimer approximation.

Adiabatic electron affinity - see Electron affinity.

Adiabatic ionization potential - see Ionization potential.

Adiabatic reaction - Within the Born-Oppenheimer approximation, a reaction that occurs on a single potential energy surface.

Adjacency matrix of a graph - the matrix which consists of entries aij = 1 for adjacent vertices, and aij = aii = 0 otherwise. The matrix is isomorphic to the bonds drawn in simple molecular representation.

Aggregate - An assembly of molecules stabilized by noncovalent interactions (hydrophobicinteractions, p-p interactions, ionic and hydrogen bonds). In contrast to stable molecules, aggregates are equilibrated mixtures of several associates corresponding to certain thermodynamic minima. WHITESIDES, SIMANEK, MATHIAS, SETO, CHIN, MAMMEN and GORDON (1995).

Agostic interaction - The manner of interaction (termed according to the Greek "to hold or clasp to oneself as a shield") of a coordinatively unsaturated metal center with a bond of a ligand. This results in an attraction between the metal and and the bond and thus often in structural distortions of the whole complex. Initially described for a C - H -Metal bond interaction where M is a transition metal  complex, it has been commonly used to describe M...YZ interaction. It is thought to be determining in the activation of a bond, notably C-H. BROOKHART and GREEN (1983).

Alternancy symmetry - A topological property of the molecular graphs of alternant hydrocarbons which allows the carbon atoms to be divided into two subsets in such a way that no two atoms of the same subset are adjacent. A consequence of this property is the symmetrical arrangement of the energy levels of bonding and antibonding Hückel MOs relative to the level of a nonbonding orbital (energy level of the p AO of a carbon atom).

Alternant hydrocarbon - A conjugated hydrocarbon whose molecule does not contain odd-membered rings, so that it is possible to divide the carbon atoms into two sets, "starred" atoms and "unstarred" atoms in such a way that no two atoms of the same set are linked by a bond.

If the total number of starred and unstarred atoms in an alternant hydrocarbon is even, it is assigned to the even alternant hydrocarbon type. If this number is odd, the hydrocarbon belongs to the type of odd alternant hydrocarbons. The molecular orbitals and energy levels of alternant hydrocarbons are perfectly paired (see Perfect pairing).

Angular Overlap Model (AOM) - A method of description of transition metal - ligand interactions and main-group element stereochemistry, whose basic assumption is in that the strength of a bond formed using atomic orbitals on two atoms is related to the magnitude of overlap of the two orbitals. The interactions between the central-atom and ligand orbitals are usually divided into the s-,  p- and d-types and parametric equations of the type

estab, s = F2es - (F2)2fs

edestab, s = - [F2es - (F2)2fs]

are used, where F is angle-dependent contribution to the overlap integral Sab between the two interacting orbitals, whereas parameters es and fs are proportional to S2 and S4 respectively and depend on the identity of atoms A and B as well the A - B bond distance. Similar equations are derived for the p- and d-type interactions. Neither orbital mixing nor nuclear repulsions are accounted for by the model. Its advantage is in that for simple systems a molecular orbital diagram is easily constructed on the basis of two-orbital interactions and clearly reveals trends in orbital energies on distortion. BURDETT (1980); RICHARDSON (1993).

Antiaromaticity (antithetical to aromaticity) - Those cyclic molecules for which cyclic electron delocalization provides for the reduction (in some cases loss) of thermodynamic stability compared to acyclic structural analogues are classified as antiaromatic species. In contrast to aromatic compounds, antiaromatic ones are prone to reactions causing changes in their structural type, and display tendency to alternation of bond lengths and fluxional behavior (see fluxional molecules) both in solution and in the solid . Antiaromatic molecules possess negative (or very low positive) values of resonance energy and a small energy gap between their highest occupied and lowest unoccupied molecular orbitals. In antiaromatic molecules, an external magnetic field induces a paramagnetic electron current. Whereas benzene represents the prototypical aromatic compound, cyclobuta-1,3-diene exemplifies the compound with most clearly defined antiaromatic properties. BRESLOW (1973); MINKIN, GLUKHOVTSEV and SIMKIN (1994).

Antibonding molecular orbital - The molecular orbital whose occupation by electrons decreases the total bonding (as usual, increases the total energy) of a molecule. In general, the energy level of an antibonding MO lies higher than the average of the valence atomic orbitals of the atoms constituting the molecule.

Antisymmetry principle (synonymous with the Pauli exclusion principle) - The postulate that electrons must be described by wavefunctions which are antisymmetric with respect to interchange of the coordinates (including spin) of a pair of electrons. A corollary of the principle is the Pauli exclusion principle. All particles with half-integral spin (fermions) are described by antisymmetric wavefunctions, and all particles with zero or integral spin (bosons) are described by symmetric wavefunctions.

Apicophilicity - In trigonal bipyramidal structures with a five-coordinate central atom, the stabilization achieved through a ligand changing its position from equatorial to apical (axial). The apicophilicity of an atom or a group is evaluated by either the energy difference between the stereoisomers (permutational isomers) containing the ligand in apical and equatorial positions or the energy barrier to permutational isomerization (see also Berry pseudorotation). In general, the greater the electronegativity and the stronger the p-electron-withdrawing properties of a ligand (as for Cl, F, CN), the higher is its apicophilicity. The notion of apicophilicity has been extended to four-coordinate bisphenoidal and three-coordinate T-shaped structures, which can be viewed as trigonal bipyramidal species where respectively one or two vertices are occupied by phantom ligands (lone electron pairs). TRIPPETT (1974); McDOWELL and STREITWIESER (1985).

Aromaticity - The concept of spatial and electronic structure of cyclic molecular systems displaying the effects of cyclic electron delocalization which provide for their enhanced thermodynamic stability (relative to acyclic structural analogues) and tendency to retain the structural type in the course of chemical transformations. A quantitative assessment of the degree of aromaticity is given by the value of the resonance energy. It may also be evaluated by the energies of relevant isodesmic and homodesmotic reactions. Along with energetic criteria of aromaticity, important and complementary are also a structural criterion (the lesser the alternation of bond lengths in the rings, the greater is the aromaticity of the molecule) and a magnetic criterion (existence of the diamagnetic ring current induced in a conjugated cyclic molecule by an external magnetic field and manifested by an exaltation and anisotropy of magnetic susceptibility). Although originally introduced for characterization of peculiar properties of cyclic conjugated hydrocarbons and their ions, the concept of aromaticity has been extended to their homoderivatives (see homoaromaticity), conjugated heterocyclic compounds (heteroaromaticity), saturated cyclic compounds (s-aromaticity) as well as to three-dimensional organic and organometallic compounds (three-dimensional aromaticity). A common feature of the electronic structure inherent in all aromatic molecules is the close nature of their valence electron shells, i.e. double electron occupation of all bonding MOs with all antibonding and delocalized nonbonding MOs unfilled. Thenotion of aromaticity is applied also to transition state. GARRAT (1986); MINKIN, GLUKHOVTSEV and SIMKIN (1994), SCHLEYER and JIAO (1996).
See also Electron counting rules, Hückel rule.

Atom-atom polarizability - A quantity used in perturbation HMO theory as a measure of the change in electron density, q, of atom s caused by a change in the electronegativity (or coulomb integral), ar, of atom r:

pSI = qs/ ar

Atom-bond polarizability - A quantity used in perturbation HMO theory as a measure of the change in electron density, q, of atom m caused by a change in the resonance integral, b, of bond rs:

pm,rs = qm/ brs

Atomic basin - Within the topological electron distribution theory, the region of three-dimensional space defined by the gradient paths of the charge density which terminate at each nucleus in a molecule. The atomic basin is an unambiguous definition of an atom in a molecule.

Atomic charge - The charge attributed to an atom A within a molecule defined as z = ZA - qA, where ZA is the atomic number of A and qA is the electron density assigned to A. The method of calculation of qA depends on the choice of the scheme of partitioning electron density. In the framework of the Mulliken population analysis qA is associated with the so-called gross atomic population: where qm is a gross population for an orbital m in the basis set employed defined according to

where Pmn and Smn are the elements of density matrix and overlap matrix respectively (see overlap integral). In the Hückel molecular orbital theory (where Smn = dmn), qm= nmPmm , where nm is the number of electrons in the MO m. HEHRE, RADOM, SCHLEYER, and POPLE (1986).

Atomic orbital - see Orbital.

Atomic units - The units designed to simplify the form of the fundamental equations of quantum mechanics by eliminating from them fundamental constants. The atomic unit of length is the Bohr radius, ao = h2/4p2me2 = 5.291 77249 x 10-11 m (0.529177249 Å). Energy is measured in hartrees, where 1 hartree = e2/ao = 4.359 7482 x 10-18 J. Masses are specified in terms of atomic mass unit, amu = 1.6605402 x 10-27 kg and of the electron mass unit, me = 0.910953 x 10-30 kg. The advantage of atomic units is that if all calculations are directly expressed in such units, the results do not vary with any revision of the numerical values of the fundamental constants. COHEN and TAYLOR (1986).

Atomization energy - synonymous with Heat of atomization.

Atoms in molecules (AIM), theory of - A quantum chemical method based on the assumption that the wavefunction of a molecule can be expressed as a linear combination                                                                              

Y = S ciYi

where Yi are the antisymmetrized products of wavefunctions , … of atoms A, B… in electronic states ai, bi ,…BADER (1990); BADER, POPELIER, and KEITH (1994)
 See also Topological electron distribution theory.

Aufbau principle - A rule for building up the electronic configuration of atoms and molecules. It states that a maximum of two electrons are put into orbitals in the order of increasing orbital energy: the lowest-energy orbitals are filled before electrons are placed in higher-energy orbitals.
See also Pauli exclusion principle and Hund's rule.

Automerization (synonymous with degenerate rearrangement, permutational isomerization, topomerization) - A molecular rearrangement in which the reactant is transformed to the product which differs from reactant only in the permutation of identical atoms. Automerizations may be detectable by the methods which allow one to distinguish individual atoms within a molecule: by isotopic labelling and by dynamic nuclear magnetic resonance technique. An example of an automerization reaction is the photochemical rearrangement of benzene via tricyclo[,6]hex-3-ene (benzvalene).


Avoided crossing - Within the Born-Oppenheimer approximation, when two electronic states change their energy order as the molecular geometry is continuously changed along a reaction path, their energies may become equal at some points (surface crossing) or only come relatively close (the surface crossing is said to be avoided). If the electronic states are of the same symmetry, the surface crossing is always avoided in diatomics and usually avoided in polyatomics. SALEM (1982)
See also Noncrossing rule.


[A] [B] [C] [D] [E] [F] [G] [H] [I] [J-K] [L] [M]
[N] [O] [P] [Q-R] [S] [T] [U-V] [W-Z]

> Abstract
> General remarks
> Arrangement

> Fundamental physical constants used in the glossary
> References
> Appendix. Glossary of acronyms of terms used in theoretical organic chemistry

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