**Glossary of terms used in theoretical
organic chemistry **

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

[N] [O] [P]
[Q-R] [S] [T]
[U-V] [W-Z]

# **N**

**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* c*i*(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.

REED, WEINSTOCK, and WEINHOLD (1985).

**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 :

s_{AB} = *c*_{A}h_{A}
+ *c*_{B}h_{B}

where h_{A} and h_{B} 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.

REED, WEINHOLD, and CURTISS (1988).

**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 =
*a*_{ij}f_{i}^{*}f_{j}

where the coefficients *a*_{ij} are a set of numbers
which form the density matrix. The NOs reduce the density matrix
r to a diagonal form:

r =
*b*_{k}f_{k}^{*}f_{k}

where the coefficients *b*_{k} 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, *n*_{i}(A) are the occupancies
of the natural atomic orbitals. These rigorously satisfy the *Pauli*
*exclusion principle*:
0 < *n*_{i}(A) <2. The population of an atom *n*(A)
is the sum of natural populations

*n*(A) = *n*_{i}(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 n_{p}-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
C_{6}H_{6}^{2+}, **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[2.1.0.0^{1,3}.0^{2,5}]pentane
(pyramidane), **4**, the structure of which corresponds to a local
minimum on the C_{5}H_{4} 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**.

** **BORDEN, IWAMURA, and BERSON
(1994); LONGUET-HIGGINS (1950).

**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.