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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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Narcissistic reaction - The degenerate transformation in which the structure of the products can be viewed as a reflection of the structure of the reactants in a mirror plane, which is a symmetry element absent in both the reactants and the products. An example is the pyramidal inversion of ammonia

SALEM (1971).

Natural atomic orbital (NAO) - A valence-shell atomic orbital whose derivation involves diagonalizing the localized block of the full density matrix of a given molecule associated with basis functions ci(A) on that atom. A distinguishing feature of NAOs is that they meet the simultaneous requirement of orthonormality and maximum occupancy. For isolated atoms, NAOs coincide with natural orbitals. In a polyatomic molecule the NAOs (in contrast to natural orbitals that become delocalized over all nuclear centers) mostly retain one-center character, and thus are optimal for describing the molecular electron density around each atomic center.


Natural bond orbital (NBO) - The orbital which is formed from natural hybrid orbitals. For a localized s-bond between atoms A and B, the NBO is :

sAB = cAhA + cBhB

where hA and hB are the natural hybrids centered on atoms A and B. NBOs closely correspond to the picture of localized bonds and lone pairs as basic units of molecular structure, so that is possible to conveniently interpret ab initio wavefunctions in terms of the classical Lewis structure concepts by transforming these functions to NBO form.


Natural hybrid orbital (NHO) - Symmetrically orthogonalized directed hybrid orbital derived through unitary transformation of natural atomic orbitals centered on a particular atom.

Natural orbital - The orbitals defined (P. Löwdin) as the eigenfunctions of the spinless one-particle electron density matrix. For a configuration interaction wavefunction constructed from orbitals f, the electron density function, r, is of the form:

r = aijfi*fj

where the coefficients aij are a set of numbers which form the density matrix. The NOs reduce the density matrix r to a diagonal form:

r = bkfk*fk

where the coefficients bk are occupation numbers of each orbital.The importance of natural orbitals is in the fact that CI expansions based on these orbitals have generally the fastest convergence. If a CI calculation was carried out in terms of an arbitrary basis set and the subsequent diagonalization of the density matrix aij gave the natural orbitals, the same calculation repeated in terms of the natural orbitals thus obtained would lead to the wavefunction for which only those configurations built up from natural orbitals with large occupation numbers were important. LÖWDIN (1955); PILAR (1968).

Natural population analysis (NPA) - The analysis of the electron density distribution in a molecular system based on the orthonormal natural atomic orbitals. Natural populations, ni(A) are the occupancies of the natural atomic orbitals. These rigorously satisfy the Pauli exclusion principle: 0 < ni(A) <2. The population of an atom n(A) is the sum of natural populations

n(A) = ni(A).

A distinquished feature of the NPA method is that it largely resolves the basis set dependence problem encountered in the Mulliken population analysis method. REED and SCHLEYER (1990); REED, WEINHOLD, and CURTISS (1988).

Negative hyperconjugation - The effect of donation of electron density from filled p or np-orbitals to the symmetry adapted s*-orbital(s) of s-bond(s) of a molecular entity resulting in building p-character into bonds that nominally possess only s-character. The consequences of the effect are, for example, in elongation of the C-F bond in the b-fluoroethyl anion and stabilization of the antiperiplanar conformation of fluoromethylamine.

REED and SCHLEYER (1990); SCHLEYER and KOS (1983).

Nodal plane - A plane of a system in which the value of the orbital wavefunction equals zero. This plane defines a region of zero electron density for the orbital.

Nonadiabatic reaction - Synonymous with Diabatic reaction.

Nonbonding molecular orbital - A molecular orbital whose occupation by electrons does not contribute (or contributes insignificantly) to the binding energy of the molecule. Generally, a nonbonding MO represents the highest occupied molecular orbital of a molecule

Nonclassical structure - The structure of molecules or molecular ions that escapes description in terms of conventional rules of valency and stereochemistry. Nonclassical structures are characteristic of carbonium ions with hypercoordinated (see hypercoordination) carbon atoms, e.g. the ion methanium 1, pyramidal dication C6H62+, 2 (isomeric to benzene dication), and the molecular species whose structure cannot be adequately represented by the equilibrium (2-norbornyl cation, 3) or resonance of two or more classical structures. From the stereochemical point of view, those structures are assigned to the nonclassical type for which all tetracoordinate carbon bonds extend into a single hemisphere, i.e. the valence angle of a carbon atom is greater than 180o. A hypothetical example is tetracyclo[,3.02,5]pentane (pyramidane), 4, the structure of which corresponds to a local minimum on the C5H4 potential energy surface.


BROWN (1977); MINKIN, MINYAEV, and ZHDANOV (1987).

Noncrossing rule - Energy levels of orbitals of the same symmetry cannot cross each other along a reaction coordinate. The rule is applied also to the energy variation of electronic states. SALEM (1982); WOODWARD and HOFFMANN (1969).

Nonempirical quantum mechanical methods - see Ab initio quantum mechanical methods.

Non-Kekulé molecules - Molecules that are fully conjugated, but each of whose Kekulé structures contains at least two atoms that are not p-bonded. Examples of non-Kekulé hydrocarbons are trimethylenemethane (2-methylidenepropane-1,3-diyl) 1, m-benzoquinodimethane (benzene-1,3- diyldimethyl) 2, and 1,2,4,5-tetramethylenebenzene (benzene-1,2,4,5-tetrayltetramethyl) 3.


Normalization - A mathematical procedure which ensures that the integral of the square of modulus of a wavefunction over all space equals 1. The constant required to ensure that a wavefunction is normalized is termed the normalization constant.

[A] [B] [C] [D] [E] [F] [G] [H] [I] [J-K] [L] [M]
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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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