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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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Dative bond - The coordination bond formed upon interaction between molecular species one of which serves as a donor and the other as an acceptor of the electron pair to be shared in the complex formed, e.g the NB bond in H3NBH3. In spite of the analogy of dative bonds with covalent bonds in that both types imply sharing a common electron pair between two vicinal atoms, the former are distinguished by their significant polarity, lesser strength, and greater length. The distinctive feature of dative bonds is that their minimum-energy rupture in the gas phase or in inert solvent follows the heterolytic bond cleavage path. HAALAND (1989). see also IUPAC PHYSICAL ORGANIC CHEMISTRY GLOSSARY (1994).

Degenerate electronic states - Electronic states whose energies are equal.

Degenerate orbitals - Orbitals whose energy levels are equal in the absence of external fields. Any linear combination of the functions corresponding to a given set of degenerate orbitals serves as an equivalent representation of this set of orbitals.

Degenerate rearrangement - see Automerization.

Delocalization - Redistribution of the valence-shell electron density throughout a molecular entity as compared with some localized models (individual atoms in their valence states, separated bonds or fragments). Different topological modes of the electron delocalization include: (a) ribbon delocalization of either p- or s-electrons (i.e. electrons occupying respectively p- and s-orbitals); (b) surface delocalization of s-electrons occurring through an overlap of radially oriented s-orbitals of a cyclic molecule, as is the case of cyclopropane; and (c) volume delocalization of s-electrons through an overlap of s-orbitals directed inside a molecular polyhedron, as is the case in tricyclo [,4] butane (tetrahedrane). DEWAR (1988); GOLDSTEIN and HOFFMANN (1971).

Delocalization energy (DE) - The difference between the actual p-electron energy of a molecular entity and the p-electron energy of a hypothetical species with a localized form of the p-electron system. These energies are normally evaluated within Hückel molecular orbital theory. See Hückel resonance energy.

Density functional theory (DFT) - A theory which is concerned with a quantum mechanical description of atomic and molecular systems in terms of the electron density. All properties are functionals of it including the electronic kinetic energy T[r] and the electron-electron repulsion energy Vee[r]. The total electronic energy of a given system having N electrons is expressed as a functional of its single particle density r(r)

where v(r) is the potential due to the nuclei, is a minimum when r is the correct ground-state density. In DFT, the exact exchange term for a single determinant is replaced by a more general expression, the exchange-correlation functional, which can include terms accounting for both exchange repulsion energy and the electron correlation which is omitted from the Hartree- Fock method. DFT provides the conceptual basis to a number of important chemical concepts such as electronegativity, absolute hardness and softness, frontier orbital theory etc. HOHENBERG and KOHN (1964); PARR and YANG (1989).

Density matrix - The one-electron density matrix the elements of which are defined as

where subscripts m,n are for basis function, i that of molecular orbitals, ni is the occupation number of the ith orbital. The asterisk denotes complex conjugation (required if the molecular orbitals are not real functions).

Density of states (DOS) - In a solid, the number of energy levels in a given energy interval defined as follows:

DOS (E)dE = number of levels berween E and E+dE

In general, DOS (E) is proportional to the inverse of the slope of the dispersion diagram.The integral of DOS up to the Fermi level is the total number of occupied molecular orbitals in a solid. The DOS curves, therefore, plot the the distribution of electrons in energy in the solid. HOFFMANN (1988).

Dewar resonance energy - see Resonance energy, various types of.

Diabatic reaction - Within the adiabatic approximation, a reaction beginning on one electron state (ground or excited) potential energy surface and ending, as a result of radiationless transition, on another surface.

Diatomics in Molecules (DIM) - A quantum chemical method based on the assumption that the energy  of molecule may be expressed from diatomic contributions. TULLY (1980)
See also Atoms in molecules, theory of.

Differential overlap, neglect of - see Zero differential overlap approximation.

Diffuse functions - Large size versions of s- and p-type atomic orbitals (as opposed to the normal, contracted functions). They allow orbitals to occupy a larger region of space; this makes them important for inclusion into basis sets for systems where electrons are relatively far from the nucleus: molecules with lone pairs, anions, systems in their excited states etc.
See also Basis set.

Dipole hyperpolarizability - see Hyperpolarizability.

Dipole moment - The electric dipole of a molecule, m, is the first derivative of the energy with respect to an applied electric field. It is a measure of the asymmetry in the molecular charge distribution and is defined by the relation

where r is the radius vector of electrons, ra is the vector from the origin to the nucleus of atomic number Za and r (x, y, z) is the electron density. The dipole moment of a complex molecule can be represented approximately in the form of the vectorial sum of the moments belonging to the individual bonds. Dipole moment is independent of origin for a neutral molecule but origin dependent for an ion. LEVINE (1970); MINKIN, OSIPOV, and ZHDANOV (1970)

Dispersion diagram (synonymous with band diagram) - Representation of the energy of the crystal orbitals of a solid as a function of the wave vector. For three-dimensional solids, such representations are given for only a few projections of the wave vector, or symmetry lines of the Brillouin zone.

Dispersion energy - An attractive component of the energy of intermolecular interaction resulting from the interaction between the instantaneous, time-variable dipole of one system and the induced multipole of the second system. This interaction cannot be interpreted in terms of classical electrostatics and corresponds to the intersystem component of the correlation energy. For two neutral atoms, the dispersion energy is proportional to the sixth power of the reciprocal distance:

ED -1/R6.


Distonic ion - An ion with formally separated charge and radical sites. Distonic ions may be divided into two distinct classes: those possessing coordinatively and electronically-saturated charge site (usually of the onium type) and the ionized biradicals with two coordinatively-unsaturated sites containing one or three electrons. YATES, BOUMA, and RADOM (1986).
see also Distonic radical cation (IUPAC PHYSICAL ORGANIC CHEMISTRY GLOSSARY (1994)).

Double zeta (DZ basis set) - see Basis set.

Dynamic reaction path (DRP) - a classical trajectory method based on molecular orbital calculations which determines atomic accelerations, velocities and positions using the energy gradient, and does not require prior knowledge of the potential energy surface. STEWART, DAVIS, and BURGGRAF (1987).

Dynamic spin polarization (see spin polarization)

Dyotropic rearrangement - A class of pericyclic reactions in which migration of two s-bonded groups occurs. Two different types of dyotropic rearrangements are distinguished: (a) those in which two migrating groups interchange their positions [equation (1)] and (b) those which involve migration to new bonding sites in a manner that avoids positional exchange [equation (2)].

[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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