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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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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 2m+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 2m+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 2m+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 cmcn are set to zero and the overlap integral Smn = dmn (where dmn 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

Evib(0) = (1/2)h ni

where ni 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.

[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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