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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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Landau-Zener model - A semiclassical model for the probability, P, of a diabatic reaction occurring by hopping from a potential energy surface for one electronic state to that of another at an avoided crossing.

P = exp (-4p2e212 / hV|s1 - s2|)

where e is the energy gap between the two adiabatic electronic states at the crossing point, |s1 - s2| is the difference in slopes between the intesecting potential curves at this point, and V is nuclear velocity along the reaction coordinate. SALEM (1982).

Laplacian of the electron density - A characteristic used to reveal the distribution of electrons in molecular systems and crystals. It is defined as the sum of the three principal curvatures of the electron density function at each point in space, that is

2r(r) = 2r/x2 + 2r/y2 + 2r/z2

When 2r(r) < 0, the value of r at point r is greater than its average value at neighboring points, and when 2r(r) > 0, r at r is less than its average value at neighboring points. Thus, the Laplacian of the electron density identifies regions of molecular space where r(r) is locally concentrated or depleted; this information can be used to study directions of electrophilic and nucleophilic attacks. A negative value of 2r(r) in the internuclear region indicates the formation of covalent bond, while a positive value characterizes the interaction between closed-shell molecular (or atomic) systems. BADER (1990).

Least motion, principle of - The statement that those elementary reactions are the most favored which exhibit the fewest possible alterations in the positions of the atomic nuclei and in the electronic configuration. The most frequently used mathematical formulation of the principle rests on a mechanical model of a molecule in which the energy of structural deformation, when reactants (r) turn into products (p), is assumed to be proportional to the sum of the squares of the changes in the positions of the nuclei common to both reactants and products

E = fi (qpi - qri)2

where fi is the force constant (in many applications set equal to unity). The equation coincides with the relationship for the potential energy of small vibrations, hence it is valid only at a very early stage of a reaction. This is one of the reasons why many reactions violate the principle of least motion. HINE (1977).

Lennard-Jones potential - see van der Waals interactions.

Lewis octet rule - A classical rule for describing the electronic configuration of atoms in molecules: the maximum number of electron pairs that can be accommodated in the valence shell of a first-row element is four. For the second and subsequent row elements there are many exceptions to this rule. See Hypervalency.

Ligand field - see Crystal field.

Linear Combination of Atomic Orbitals (LCAO) - The approximation of the molecular orbital function as a linear combination of atomic orbitals chosen as the basis functions.

Localized molecular orbitals (LMO) - The molecular orbitals located on certain fragments of a molecular system and spatially separated from each other as much as possible. The LMOs are derived from the electron occupied canonical molecular orbitals by subjecting them to a unitary transformation determined by an appropriate physical criterion, e.g. by maximizing the sum of squares of the centroids of occupied MOs (the Foster-Boys procedure) or by minimizing the sum of the exchange (or Coulomb) repulsion integrals between the occupied MOs (the Edmiston- Ruedenberg procedure). FOSTER and BOYS (1950); EDMISTON and RUEDENBERG (1963).

Low-spin state - When the separation between the highest occupied and the lowest unoccupied molecular orbitals is not large, two alternative electronic states may be considered. The state with two electrons paired up in the HOMO is called a low-spin state. The low-spin state is the ground state when the one-electron energy needed to promote an electron to the LUMO is larger than the Coulomb and exchange repulsion energies required to pair up two electrons in the HOMO.
See also High-spin state.

Lowest Unoccupied Molecular Orbital (LUMO) - see Frontier orbitals.

[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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