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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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Uncertainty (Heisenberg) principle - The statement that two dynamical variables can be simultaneously well defined only if their quantum mechanical operators commute. If, for example the momentum of a particle is known with an uncertainty of Dp, the position of the particle cannot be determined with the precision better than h/Dp:

Dpx Dx h

Unit cell - The cell chosen to represent best the symmetry of a crystal lattice. The entire lattice can be derived from it by translations.The translations selected as the edges of the plane unit cell are denoted as a and b, and for a space lattice as a, b, c called the crystallographic axes. The angles between the edges of the three-dimensional unit cell are a, b and g.

Unitary group - A group which consists of unitary matrices of fixed order with matrix multiplication as the group operation.

Unrestricted Hartree-Fock (UHF) method - see Hartree-Fock method.

Valence bond configuration mixing (VBCM) model - A model that provides a framework for conceptualizing reactivity trends through building up a reaction profile from its constituent VB configurations. Key configurations that are invariably employed are those that best describe reactants YR and products YP. PROSS (1995), PROSS and SHAIK (1983), SHAIK, SCHLEGEL, and WOLFE (1992).
See also Curve-crossing model.

Valence bond (VB) theory - A method of approximating the total wavefunction of a molecule as a linear combination of functions related to certain pairings of electron spins. Each such function is given by a product of the atomic orbitals of the separated atoms. As a first approximation the covalent pairing scheme is employed, in which pairs of electrons between the atoms have their spins paired as much as possible. To account for electron correlation effects, mixing in of functions representing ionic pairing schemes, in which some of the separated atoms are replaced by positive and negative ions, is employed.The VB and MO methods, if carried out with the same basis set of orbitals, are entirely equivalent if all possible ionic structures are included in the VB and all possible configurations in the MO. HIBERTY, KLEIN, and TRINAJSTIC (1990); SHAIK (1989); SLATER (1931).

Valence state electron affinity - The electron affinity of an atom in its particular electron configuration.

Valence state ionization potential (VSIP) - The ionization potential of an atom in its particular electronic configuration.

Valence-shell-electron-pair repulsion (VSEPR) theory - A semiquantitative approach to the prediction of the geometries of compounds of main-group elements. The basic idea of the theory is that the geometric arrangement of the bonds around a central atom depends on the number of electron pairs in its valence shell. A given number of electron pairs adopt that arrangement which keeps them as far apart as possible, as a consequence of the operation of the Pauli exclusion principle. The arrangements of electron pairs are essentially retained independently of whether they are unshared pairs, or form single, double or triple bonds. The theory is concerned with the arrangement of predominantly covalent bonds around a single central atom. It does not apply to the compounds with ionic bonds and to molecules with multicenter bonds. GILLESPIE (1972), GILLESPIE and ROBINSON (1996).

van der Waals complexes - Molecular systems in which the individual parts are held together by forces other than covalent bonds. These include ionic complexes (where the dominant attractive force is of electrostatic origin), complexes with hydrogen bonds, charge-transfer complexes, and true van der Waals molecules for which the dominant attractive contribution is the dispersion energy. HOBZA and ZAHRADNIK (1988).

van der Waals (VDW) interactions - Noncovalent interactions (weak as compared to covalent bonds) due to dipole-induced dipole and dispersion forces (see dispersion energy) acting at molecules and atoms. In molecular mechanics models, the energy contributions from vdW interactions are commonly treated with potential functions of the distance, r, between each pair of nonbonded atoms, like the Lennard-Jones potential:

Vvdw = A/r12 - C/r6

Variational method - See Variational principle.

Variational principle - The principle according to which for a molecular system an approximate wavefunction, when substituted into the Schroedinger equation, will always yield a higher energy than the actual energy of the system. The more precise the wavefunction that is chosen, the closer will the calculated energy be to the true energy. The computational method using this principle to obtain approximations to correct wavefunctions is called the variational method. The method is commonly restricted to the ground state, but can be extended to others provided they are orthogonalized to the (true) ground state.

Variational Transition State - In variational transition state theory, the optimized dividing surface (hypersurface in phase state that separates reactants from products). If not all trajectories passing through the dividing surface and originated at reactants are directed to products transition state theory overestimates the rate. In variational transition state theory one optimizes the location of the dividing surface to minimize the rate. TRUHLAR and GARRET (1984), GARRET and TRUHLAR (1998).

Variational Transition State Theory (VTST) - see Variational Transition State .

Vertical electron affinity - see Electron affinity.

Vertical ionization potential - see Ionization potential.

Vibronic interactions, theory of - An approach to the analysis of molecular properties and molecular transformations which, unlike the Born-Oppenheimer approximation, assumes that electronic states depend strongly on nuclear coordinates. If stationary electronic states (ground, first excited etc.) are obtained as solutions of the Schroedinger equation for fixed nuclei, an accounting for vibronic coupling terms in the Hamiltonian (interaction of electrons with nuclear displacements) mixes these electronic states. This mixing is especially strong in the cases of electronic degeneracy (see Jahn-Teller effect) and pseudodegeneracy (pseudo Jahn-Teller effect). BERSUKER (1984).

Vibronic transition - A transition which involves a change in both the electronic and vibrational quantum numbers of a molecular entity. The transition occurs between two electronic states, but involves a change in both electronic and vibrational energy. IUPAC PHOTOCHEMICAL GLOSSARY (1988).

Virial theorem - Interrelates the kinetic, T, and potential, V, energy of a system in its stationary states. The molecular electronic virial theorem is formulated ( J.Slater ) as follows:

2<Tel> = -<V> - Ra,b(U/Ra,b)

where Rab is the distance between nuclei a and b, U is the potential energy function for nuclear motion and the sum runs over all internuclear distances. The true wavefunctions must satisfy the virial theorem. LEVINE (1970).

Virtual orbital - An orbital from a set of MOs obtained as solutions of the SCF equations (see Hartree- Fock method) whose energies are higher than those of doubly occupied MOs producing the single determinant wavefunction of lowest energy for a given system. The virtual orbitals obtained from SCF calculations are not variationally correct approximations (see variational principle) to the excited state orbitals. Their energies are not related to electron affinities of the molecular system

Volume delocalization - see Delocalization.

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> 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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