Glossary:

3D-electron density contour diagram:
Diagrams of the electron density (the square of the wavefunction) in a single MO or complete molecule contoured at an appropriate electron density level to visualise the "shape" of the orbital or total electron density of the molecule.

Allowed, forbidden reactions:
Allowed and forbidden reactions were defined by Woodward and Hoffman as those that proceed without and with a change in the orbital occupancies, respectively. This simple picture is only strictly applicable within point groups that do not allow the two orbitals to interact, but is still a good interpretative framework.

Anomeric effect:
The stabilising interaction of a lone pair donor orbital on a heteroatom (usually oxygen) with a s*-orbital of an a,b-bond to an electronegative element (again, usually oxygen). The anomeric effect is equivalent to negative hyperconjugation and the reverse of hyperconjugation.

Atomic Orbital (AO):
Strictly speaking, atomic orbitals are only applicable to the atom itself. Within the LCAO-approximation, however, AOs are combined to make up the molecular orbitals, MOs.

"Banana" bond:
"Banana", or bent, bonds are found in strained compounds, especially cyclopropanes, where they are caused by the Walsh orbitals. They are characterised by the fact that, in contrast to normal s-bonds, the centre of the electron density associated with the orbital lies outside the line connecting the two atoms.

Character table:
Table of symmetry elements, irreducible representations, characters of the individual irreducible representations and assignments of vector and tensor properties for a given point group.

Conrotatory, disrotatory:
In an electrocyclic reaction, the conrotatory process is the one in which the two end groups that rotate to form the new bond do so in the same direction. For the disrotatory process, they rotate in opposite directions.

Degenerate orbitals:
A set of two molecular orbitals belonging to an E-, three belonging to a T-, four belonging to a G- or five belonging to an H-irreducible representation. The orbitals in a degenerate set have exactly the same energy and can be combined to give an alternative representation of the degenerate set with no energetic consequences.

Dipole moment:
The dipole moment, µ, of two equal charges, ±Q, of opposite sign at a distance r is given by:

For an array of charges, such as a molecule consisting of i atoms each with a net charge Q_i:

This definition can be extended to the nuclear charges and electron density of the molecule within a quantum mechanical treatment.

Electrocyclic reaction:
An electrocyclic reaction is one in which a p-system consisting of n p-bonds interconverts with a cyclic system with (n-1) p-bonds and one extra s-bond.

Electronegativity, electropositive:
The electronegativity of an element is its tendency to accumulate electrons (negative charge). The higher the electronegativity, the more negative the element is likely to be in a molecule. There are many different electronegativity scales. Electropositive elements are those (such as metals) with low electronegativities.

Frontier orbital theory:
The frontier orbitals are the HOMO and LUMO. Frontier orbital theory uses only these orbitals to treat reactivity problems by assuming that the two-electron interaction between HOMOs and LUMOs is likely to be the strongest between two interacting molecules. This is justified by the fact that the energy gap between HOMO and LUMO is smaller than between any other occupied and virtual orbitals.

Global minimum:
Depending on the definition of a molecule - either as a collection of atoms with a given total formula or as a given bonding pattern - the global minimum is the most stable minimum energy structure that exists. Finding the gobal minimum for large molecules is a largely unsolved problem. Less stable minima than the global minimum are known as local minima.

Group theory:
A group is defined as a collection of elements (in the case of symmetry groups, symmetry operations) that are related to each other by a given set of rules. Group theory allows us to apply manipulations such as multiplication, definition of subgroups and classes, etc.

Group orbital:
A group orbital is an orbital that is assigned to a given fragment or group within a molecule. Usually group orbitals resemble the MOs of the given fragment closely. MOs for larger molecules can be built up qualitatively as linear combinations of group orbitals.

Highest Occupied Molecular Orbital (HOMO):
The HOMO is simply the doubly occupied orbital with the highest energy. It is one of the frontier orbitals.

Hückel theory:
Hückel theory was the first LCAO-MO approach to calculating the electronic structure of molecules. Hückel theroy considers only the p-orbitals perpendicular to a planar p-system, does not include electron-electron repulsion and assumes that all bonding overlaps are equal and all nonbonding zero.

Hyperconjugation:
Hyperconjugation is the stabilising interaction between an occupied s-MO and an empty acceptor orbital on the adjacent atomic center. It is the reverse of the anomeric effect.

Irreducible representation, symmetry species:
Within the context of the symmetry groups discussed here, irreducible representations are combinations of symmetry elements that are orthogonal to each other and describe the symmetry species (e.g. vibrations, orbitals, etc.) of the point group. As the name implies, the irreducible representations cannot be reduced to simpler ones.

Koopmans' theorem:
Koopmans' theorem is that the ionisation potential of a molecule is approximately minus the energy of its HOMO.

Lewis structure:
The Lewis structure of a molecule is its bonding pattern described in terms of the octet rule with formal charges, single, double and triple bonds.

Lewis acid:
A Lewis acid is a compound with a low-lying LUMO that allows it to accept electrons from Lewis bases.

Lewis base:
A Lewis base is a compound with a high-lying HOMO that allows it to donate electrons to Lewis acids.

Linear Combination of Atomic Orbitals (LCAO):
The LCAO approximation allows us to build up the MOs of a molecule as linear combinations of a basis set of atomic orbitals assigned to each atom. The approximation provides a simple interpretative framework for the nature of MOs and also has important computational advantages.

Lowest Unoccupied Molecular Orbital (LUMO):
The LUMO is simply the virtual (unoccupied) MO with the lowest energy. It is one of the frontier orbitals.

Mirror plane:
Mirror planes (denoted s) are imaginary planes through a molecule that, when treated as infinitely thin two-sided mirrors, reflect the molecule to give a new structure that is indistinguishable from the starting one.

Molecular Orbital (MO):
Within the context of this book, it is sufficient to define an MO as an orbital belonging to the entire molecule in question. Within the LCAO approximation, these MOs are expressed in terms of contributions from individual AOs.

Negative hyperconjugation:
Negative hyperconjugation is another name for the anomeric effect. It is usually used in connection with anions.

Net atomic charge:
Net atomic charges have no physical significance. They result from some scheme for partitioning the electrons in the molecule to the different atoms and are typically reported in the population analysis.

Normalisation, normalised:
Normalisation is the mathematical process by which the total probablility, for instance of finding an electron in an orbital, is adjusted to be unity.

Orbital correlation diagram:
For concerted reactions, such as those treated by the Woodward-Hoffmann rules, an orbital correlation diagram traces the changes in a given MO from starting point to product.

Orbital interaction diagram:
For bimolecular reactions, orbital interaction diagrams visualise the mixing of the orbitals of the two reacting molecules. Orbital interaction diagrams are often limited to the frontier orbitals.

Orthogonal:
Two species are orthogonal when they cannot interact with each other (i.e. their overlap is zero).

Overlap:
Within the current context, overlap is the interaction between orbitals. Bonding overlap stabilises, antibonding destabilises.

Point group:
Point groups describe the symmetry characteristics of molecules in terms of their symmetry elements.

Population analysis:
A population analysis is a (largely artificial) partitioning of the electrons in the molecule to the individual atoms in order to obtain net atomic charges, bond orders, etc.

Singly Occupied Molecular Orbital (SOMO):
For radicals, triplets, etc. The SOMO(s) are the orbitals that formally contain only one electron.

Strain, strain energy:
A molecule is strained when the sum of the dissociation energies of its bonds is smaller than the corresponding sum of an arbitrary unstrained reference molecule. For instance, the bond dissociations energies of the three CC-bonds in cyclopropane are smaller than three times the "normal" CC-bond dissociation energy. Strain leads to increased reactivity and decreased stability.

Suprafacial, antarafacial:
A suprafacial process is one in which two new bonds are made to the same face of a p-system, or in which a bond is broken and a new one made on the same face. Antarafacial processes involve the two different faces of the p-system.

Symmetry element:
A symmetry element is an operation, such as a mirror plane, that transforms a molecule into a structure that is indistinguishable from the starting one.

Symmetry-adapted combination:
If two atoms, for instance, are symmetrically equivalent, their individual AOs do not have the correct symmetry characteristics to belong to one of the irreducible representations of the point group. In this case, the AOs must be combined to give symmetry-adapted combinations.

Valence bond theory:
Valence bond (or VB) theory is an alternative approach to MO-theory in which resonance hybrids between different Lewis structures can be formed.

Virtual orbital:
A virtual orbital is simply an unoccupied one.

Walsh orbital:
The Walsh orbitals of cyclopropane are its degenerate HOMOs. They are largely responsible for the strain and for the "banana" bond character of the cyclopropane CC-bonds.

Walsh diagram:
Walsh diagrams are a simple MO-technique used to rationalise the structure of simple molecules and fragments by considering the energy changes in the MOs when the structure is distorted.