International Union of Pure and Applied Chemistry Organic Chemistry Division Commission on Physical Organic Chemistry Glossary of Terms Used in Theoretical Organic Chemistry

The glossary contains de®nitions and explanatory notes for more than 450 terms used in the context of multidisciplinary research and publications related to applications of modern theoretical concepts, computational and graph-theoretical methods to investigation into structure, reactivity, spectroscopic and other physical and physicochemical properties of organic, organometallic and metal coordination compounds. The aim of the glossary is to provide guidance on terminology used in theoretical organic chemistry and to contribute to the elimination of inconsistencies and ambiguities in the meanings of terms in the area. GENERAL REMARKS Recent years have seen a deep penetration of the language, concepts and methods of quantum chemistry, statistical mechanics and graph theory into the conceptual system of organic chemistry and cognate ®elds. The terminology of modern quantum chemistry interlaces with that of classical electronic and resonance theories, and the use of new technical terms, methodologies and acronyms proliferated. This process necessitates examination of the terms used in theoretical organic chemistry for meaning, utility and consistence. Although theoretical organic chemistry cannot be separated from theoretical chemistry itself, it constitutes a signi®cant part of the latter representing the domain of physical organic chemistry associated with theoretical modeling of reaction mechanisms, computational studies of structural, thermodynamic, spectroscopic and other physical properties of organic compounds, and has grown tremendously. A need has, therefore, been recognized for providing an organic chemist, who uses in the research modern methodologies or is interested in their comprehension, with the relevant operational de®nitions or explanations of frequently employed notions and concepts. For this purpose, concise introductory descriptions and leading references (to original sources, important reviews or monographs) are given for a number of important terms. The Glossary may be considered as a supplement to the comprehensive compendium [38] of terminology traditionally established in physical organic chemistry. Therefore, the styles of the presentation of the material in both Glossaries are basically similar. The general criteria adopted for inclusion of a term into the Glossary were: (a) its wide use in the literature; (b) uncertainty or ambiguity in its current use. There is almost no overlap in included terms between the two Glossaries. This Glossary is supplemented by a list of most frequently encountered (about 200) acronyms used in the literature on theoretical organic chemistry (appendix). This list is intentionally much shorter than that of the parallel project `Acronyms used in Theoretical Chemistry' [Pure Appl. Chem. 68(2), 387±456 (1996)] developed by the Physical Chemistry Division which includes a giant number (about 2500) of speci®c acronyms and abbreviations, e.g. those of numerous program packages, and covers areas of application far beyond those of primary interests of organic and physical organic chemists. The Commission considers it necessary to emphasize that the primary objective of the Glossary is to serve as an update and consistent reference to terminology used in theoretical organic chemistry and cognate ®elds. There is no intention to impose any restrictions or rules on the use of the recommended terminology. The Commission and the Working Party gratefully acknowledge important contributions of many scientists who helped by proposing or de®ning certain terms as well as providing useful criticisms and advice. The following names are to be mentioned: A. Dneprovskii, E. Eliel, E. Halevi, R. Hoffmann, A. Katritzky, A. Levin, I. Stankevich, R. Thummel, M. Yanez. The work was coordinated with that of Working Party on Theoretical and Computational Chemistry in the Physical Chemistry Division. 1920 COMMISSION ON PHYSICAL ORGANIC CHEMISTRY q 1999 IUPAC, Pure Appl. Chem. 71, 1919±1981 ARRANGEMENT The arrangement is alphabetical. Italicized words in the body of a de®nition, as well as those given at the end, point to relevant cross-references. No distinction is made between singular and plural in crossreferencing. Capitalized names indicate references which are either those where the term was originally de®ned or pertinent review articles or monographs where it is used. FUNDAMENTAL PHYSICAL CONSTANTS USED IN THE GLOSSARY* Atomic mass constant (uni®ed atomic mass unit) muˆ 1uˆ 1.6605402(10) ́ 10 kg Bohr radius a0ˆ 4pe0(h/2p) /mee 2 ˆ 5.29177249(24) ́ 10 m Electron rest mass meˆ 9.1093877(54) ́ 10 kg Elementary charge eˆ 1.60217733(49) ́ 10 C Energy in hartrees Ehˆ (h/2p) /mea0 2 ˆ 4.3597482(26) ́ 10 J Permittivity of vacuum e0ˆ 8.854187816 ́ 10 F m Speed of light in vacuum c0ˆ 299792458 m s ÿ1 (de®ned) Plank constant hˆ 6.6260755(40) ́ 10 J s Boltzmann constant kˆ 1.380658(12) ́ 10 J K Avogadro constant NAˆ 6.0221367(36) ́ 10 mol Ab initio quantum mechanical methods (synonymous with nonempirical quantum mechanical methods)ÐMethods 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 SchroÈdinger 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 electronegativityÐThe property of a chemical system derived from density functional theory de®ned as x ˆ ÿm ˆ ÿ…¶E=¶N†n > …I ‡ A†=2 where m is the electronic chemical potential, n is the potential due to the nuclei, and N is the number of electrons, I and A are respectively the ionization potential and electron af®nity 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 xX±xY is positive when X ± Y has the polarity X ±Y [1,2]. Absolute hardnessÐThe 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 ˆ …1=2†…¶m=¶N†n ˆ …1=2†…¶ E=¶N†n > …1=2†…IÿA† where I and A are respectively ground state ionization potential and electron af®nity, and n is the potential Glossary of terms used in theoretical organic chemistry 1921 q1999 IUPAC, Pure Appl. Chem. 71, 1919±1981 * I Mills, T. Cvitas, K. Homann, N. Kallay, K. Kuchitsu. Quantities, Units and Symbols in Physical ChemistryÐThe Green Book. 2nd edn, Blackwell Science (1993). 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 ˆ …eLUMOÿeHOMO†=2 A high value of the absolute hardness is, thus, an indication of high stability and low reactivity. Absolute softness is de®ned as the reciprocal of the hardness [1,2]. Absolute softnessÐThe reciprocal of absolute hardness: sˆ 1/h. Active spaceÐSet of active orbitals in the formalism of Multicon®gurational SCF method, see also Complete active space. Adiabatic approximationÐsee Born±Oppenheimer approximation. Adiabatic electron af®nityÐsee Electron af®nity. Adiabatic ionization potentialÐsee Ionization potential. Adiabatic reactionÐWithin the Born±Oppenheimer approximation, a reaction that occurs on a single potential energy surface. Adjacency matrix of a graphÐthe matrix which consists of entries ai jˆ 1 for adjacent vertices, and ai jˆ aiiˆ 0 otherwise. The matrix is isomorphic to the bonds drawn in simple molecular representation. AggregateÐAn assembly of molecules stabilized by noncovalent interactions (hydrophobic interactions, p±p interactions, ionic and hydrogen bonds). In contrast to stable molecules, aggregates are equilibrated mixtures of several associates corresponding to certain thermodynamic minima [3]. Agostic interactionÐThe 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 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 [4]. Alternancy symmetryÐA 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 HuÈckel MOs relative to the level of nonbonding orbital (energy level of the p AO of a carbon atom). Alternant hydrocarbonÐA 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). 1922 COMMISSION ON PHYSICAL ORGANIC CHEMISTRY q 1999 IUPAC, Pure Appl. Chem. 71, 1919±1981 Angular Overlap Model (AOM)ÐA 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-, pand d-types and parametric equations of the type estab;j ˆ F ej ÿ …F 2 † fj edestab;j ˆ ÿ‰F ej ÿ …F 2 † fjŠ 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 S 2 and S respectively and depend on the identity of atoms A and B as well the A±B distance. Similar equations are derived for the pand 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 [5,6]. Antiaromaticity (antithetical to aromaticity)ÐThose cyclic molecules for which cyclic electron delocalization provides for the reduction (in some cases loss) of thermodynamic stability compared to acyclic structural analogues are classi®ed 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 ̄uxional behavior (see ̄uxional 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 ®eld induces a paramagnetic electron current. Whereas benzene represents the prototypical aromatic compound, cyclobuta-1,3-diene exempli®es the compound with most clearly de®ned antiaromatic properties [7,8]. Antibonding molecular orbitalÐThe 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)ÐThe 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 antisymmetry wavefunctions, and all particles with zero or integral spin (bosons) are described by symmetric wavefunctions. ApicophilicityÐIn trigonal bipyramidal structures with a ®ve-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 threecoordinate 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) [9,10]. AromaticityÐThe 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 Glossary of terms used in theoretical organic chemistry 1923 q1999 IUPAC, Pure Appl. Chem. 71, 1919±1981 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 ®eld 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 un®lled. The notion of aromaticity is applied also to transition states [8,11,12]. See also Electron counting rules, HuÈckel rule. Atom-atom polarizabilityÐA 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: