**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]

# **W-Z**

**Wade's rules **- The *electron-counting
rules* for prediction of stable structures of polyhedral inorganic,
organometallic, and organic compounds. So-called "skeletal" electrons,
i.e. valence electrons of atoms positioned in the vertices of a
molecular polyhedron that form bonding electron pairs of the framework
bonds, are taken into account, their number being determined as follows

Main-group elements *k* = *v* + *x* - 2

Transition metals *k* = *v* + *x* - 12

where *v* is the full number of valence electrons of an atom or
group in a vertex and *x* is the number of one-electron ligands.
For deltahedral *closo* (closed) structures (characterized by triangle
faces) with *m* vertices there exist (*m*+1) *bonding
molecular orbitals* which may be filled with not more than
2*m*+2 skeletal electrons (*m* = 4, 5 ...). For *nido*
(nest-like) structures derived from the *closo*-forms through
truncation of one apex there are (*m*+2) bonding MOs which may
be occupied with not more than 2*m*+4 skeletal electrons. For *arachno*
(web-like) structures derived from *nido*-forms through truncation
of one apex, there are (m+3) bonding MOs that may be occupied by
2*m*+6 electrons.The extension of Wade’s rules is the
*polyhedral skeletal electron pair* *approach* that
makes allowance for the total electron count in condensed polyhedra
derived by the condensation of smaller tetrahedral, octahedral,
and trigonal-prismatic fragments. The total electron count in a
condensed polyhedron is equal to the sum of the electron counts for
the parent polyhedra A and B minus the electron count characteristic
of the atom, pair of atoms, or face of atoms common to both polyhedra.
MINGOS (1984); WADE
(1976).

**Walsh diagram **(also called* Walsh-Mulliken
diagram*) -** **A molecular orbital diagram where the *orbitals*
in one reference geometry are correlated in energy with the orbitals
of the deformed structure.

**Walsh's rules **-** **The summaries
of observations that the shapes of molecules in a given structural class
are determined by the number of valence electrons. The most important
rule states that a molecule adopts the structure that best stabilizes
its *highest occupied molecular
orbital.* If the HOMO is unperturbed by the structural change
under consideration, the occupied MO lying closest to it governs
the geometric preference.

**Wavefunction
**- A mathematical expression whose form resembles the wave equations
of physics, supposed to contain all the information associated with
a particular atomic or molecular system,. When a wavefunction is
operated on by certain quantum mechanical operators, a theoretical evaluation
of physical and chemical observables for that system (the most important
one being energy) can be carried out.

**Wave vector** - The vector which appears
in the expression of a *crystal orbital*
as a result of the application of the periodic boundary conditions
to the *wavefunction* of a solid. It
determines the symmetry and nodal properties of the crystal orbital.
Given the periodic nature of the Bloch orbitals, all the non-equivalent
wavefunctions are generated by the components of the wave vector with
values within the* Brillouin zone*.

**Wigner rule **(also known as* spin-conservation
rule*)** **-** **During an elementary chemical step, electronic
and nuclear magnetic moments conserve their orientation.

**Woodward-Hoffmann rules **-**
***Electron-counting rules*
allowing predictions of thermally and photochemically driven *symmetry
allowed *and *symmetry
forbidden concerted reactions*.

**Zero differential overlap (ZDO)
approximation **-** **An approach to the systematic neglect of
the small-in-value electron repulsion integrals which is used in
a number of approximate *self- consistent
field* molecular orbital schemes. It means that all the products
of *atomic orbitals* c_{m}c_{n}
are set to zero and the *overlap
integral* *S*_{mn} = d_{mn}
(where d_{mn} is the Kronecker delta).
The ZDO approximation greatly simplifies the computation of* wavefunctions*
by eliminating many of two-electron integrals. At the ZDO approximation
all three- and four-centered integrals vanish.

**Zero-order wavefunction**
- Commonly, the *wavefunction* used
as a starting point to include
*electron correlation* effects. Very often the zero-order wavefunction
is a single determinant SCF wavefunction as in MP2, coupled cluster
and CI methods, but it can be a multideterminant wavefunction as in
the MRCI approach.

**Zero-point energy** **(ZPE)** - synonymous with*
zero-point vibrational energy.*

**Zero-point vibrational energy
(ZPVE)** - The energy of vibration of a molecule at absolute zero
(0 K). It is given by

*E*_{vib}(0) = (1/2)*h* n_{i}

where n_{i}
is a normal-mode vibrational frequency. Even for a small molecule, the
total ZPE can amount to several tens of kcal/mol. ZPE is a quantum
mechanical effect which is a consequence of the *uncertainty
principle.*