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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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Canonical molecular orbital (synonymous with self-consistent field orbitals) - The molecular orbitals which produce a Fock matrix in the canonical (diagonal) form. These orbitals are delocalized over the whole molecule and form the basis for an irreducible representation of the point group defined by the symmetry of the molecule.

Characteristic polynomial - is defined for an arbitrary square matrix A of order n as

Pn(x) = det(xEn - A)

where En is the unit matrix of order n and det stands for the determinant of the matrix. The chemical term equivalent to characteristic polynomial is a secular polynomial.

Charge decomposition analysis (CDA) - A fragment molecular orbital partioning scheme for analyzing the electronic interactions between closed-shell fragments A and B in terms of donation A B, backdonation A B, and repulsive polarization A B. The three terms are given by the mixing of the occupied orbitals of the fragments (donation and backdonation), and by mixing of the occupied orbitals of both fragments (repulsive polarization). The rest term D, which is given by the mixing of the unoccupied orbitals of the fragments, is a probe which shows if A-B may be considered a donor-acceptor bond. DAPPRICH and FRENKING (1995).

Charge density - see Electron density.

Charge-transfer complex - A ground state adduct which exhibits an observable charge transfer absorption band. IUPAC PHYSICAL ORGANIC CHEMISTRY GLOSSARY (1994).

Chemical bond - When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. PAULING (1960); RUEDENBERG (1962), SUTCLIFFE (1992).
See also Coordination, Covalent bond, Dative bond, Hydrogen bond, Ionic bond, Van der Waals systems.

Chirality - The property of an object due to which it cannot be superimposed on its mirror image by translation or rotation. A molecule is chiral if it lacks Sn mirror-rotational axes. The notion of chirality has also been extended to displacements in space and other processes. A chiral process consists of successive states all of which are chiral.

Chromatic graph - see Molecular graph.

Closed shell molecular systems - Even-electron atomic or molecular systems whose electron configurations consist of doubly occupied orbitals.

Complete Active Space (CAS) - A computational scheme employed in Multiconfiguration SCF methods especially suitable for studies of excited states. The wavefunction is defined by selecting a set of active orbitals, and is constructed as a linear expansion in the set of configuration functions that can be generated by occupying the active orbitals in all ways consistent with an overall spin and space symmetry (full Configuration Interaction). ROOS (1987)

Complete active space Self-consistent field second-order perturbation theory (CASPT2) - Theoretical scheme that in the first step takes electron correlation into account only to a certain extent by using a CAS formalism, while the remaining electron correlation is included through the use of of second-order perturbation theory.

Complete basis set (CBS) theory - Set of methods developed for computing very accurate energies. These methods use extrapolations of the Hartree-Fock and the second order correlation energies to the complete basis set limit.

Computational chemistry - Those aspects of molecular research that are expedited or rendered practical by computers. LIPKOWITZ and BOYD (1990).

Concerted reaction - A single step reaction through which reactants are directly transformed into products, i.e. without involvement of any intermediates. WOODWARD and HOFFMANN (1969).

Configuration interaction (CI) - The mixing of many-electron wavefunctions constructed from different electronic configurations to obtain an improved many-electron state. In the CI method, an n-electron wavefunction is expanded as a linear combination of Slater determinants. CI proceeds by constructing other determinants through replacing one or more occupied orbitals within the Hartree-Fock determinant (see Hartree-Fock method) with a virtual orbital. In the full CI method, the wavefunction Y is represented by a linear combination of the Hartree- Fock determinant Y0 and all possible substitutions Yi . The ci are the set of coefficients to be solved for by minimizing the energy of the resultant wavefunction.

Y = c0Y0 +

In practical calculations, CI methods are usually used which augment the HF method by only a limited set of substitutions: the CIS method adds single excitations to the HF determinant, CID adds double excitations, CISD adds single and double excitations, and so on. FORESMAN and FRISCH (1996); SCHAEFER (1972).

Conical intersection (synonymous with the term "funnel") - An n-2 dimensional subspace of n nuclear coordinates in which two electronic states are degenerate. Such type potential energy surface crossings of two singlet (or two triplet) surfaces or singlet-triplet surface intersections provide a very efficient channel for radiationless transition or for chemical transformation occurring from the lowest excited state of polyatomic molecular systems, even in the case when two electronic states possess the same symmetry (contrary to the noncrossing rule, which is rigorously valid only for diatomics). BERNARDI, OLIVUCCI, and ROBB (1996); TELLER (1969).

Conjugation - In a topological sense, the indication that each pair of multiple (double or triple) bonds in a polyunsaturated molecule is separated by one single (or double) bond. In a conjugated system one multiple bond can be replaced by a centre with a fully or incompletely occupied orbital, (i. e. an atom with a lone pair, an unpaired electron, or a vacant orbital). The term conjugation was extended to orbital language to describe particular orbital interactions (p-conjugation, s-conjugation) given by the topology of the molecule. Conjugation implies an alternation between stronger and weaker orbital interactions leading to a corresponding alternation of the resonance integrals. CREMER (1988).

Conservation of orbital symmetry - The orbital symmetry control of concerted reactions; this requires transformation of the molecular orbitals of reactants into those of products to proceed continuously by following a reaction path along which the symmetry of these orbitals remains unchanged. Reactions which adhere to this requirement are classified as symmetry allowed reactions, and those which do not as symmetry forbidden reactions. WOODWARD and HOFFMANN (1969).

Consistent Force Field (CFF) - A force field for calculating structures, energies and vibration frequencies of both small organic molecules and large biomolecular systems, including peptides, proteins, nucleic acids, carbohydrates and lipids. The CFF differs from empirical force fields in that its force constants are derived from a rigorous quantum mechanical procedure. MAPLE (1998).

Coordination - The bonding of a Lewis base to a Lewis acid via a dative or coordinate covalent bond.

Coordination number of an atom - The number of atoms by which that atom is directly surrounded, and to each of which it is attached by the direct sharing of electrons.

Core approximation (synonymous with Pseudopotential approximation) - The approximation treating atoms as being subdivided into a core composed of a nucleus and tightly bound inner electrons (which form a cloud of negative charge representing the time averaged motion of inner electrons) and a valence shell of electrons that are less tightly bound and may be delocalized over a molecular entity. This simplification allows one to greatly reduce the number of electrons that must be taken into account in the calculation of molecular properties. It is used in all semiempirical quantum mechanical methods and in some of ab initio quantum mechanical methods.

Correlation consistent basis sets - Sets of contracted gaussian functions specially designed to account as much as possible for the correlation energy of valence electrons. DUNNING, PETERSON, and WOON (1998)

Correlation diagram - A diagram which shows the relative energies of orbitals, configurations, valence bond structures or states of reactants and products of a reaction as a function of molecular geometry or another suitable parameter.

Correlation energy - The difference between the energy of a system calculated as the minimal value within the Hartree-Fock approximation (see Hartree-Fock limit) and the exact nonrelativitistic energy of that system. The correlation energy arises because the Hamiltonian in the Hartree-Fock method includes an averaged interelectronic potential which does not account for the electron correlation in a molecular system.

Coulomb integral (see Coulomb repulsion). In the Hückel molecular orbital theory , is treated as an empirical parameter supposed to have a value am characteristic of the AO fm and the atom of which it is an AO, and independent of the rest of molecule. In the HMO theory, it is usually assumed that am is equal to ionization potential of an electron occupying the AO fm of the corresponding atom. DEWAR (1969)

Coulomb repulsion - The potential energy component corresponding to the electrostatic interaction between each pair of charged particles:

where eo is the permittivity of a vacuum, Drij is the distance between the two particles, and ei and ej are the charges on particles i and j. In molecular orbital theory, the electrostatic repulsion between the two electrons occupying the orbitals yi and yj. In the Hartree-Fock method the mean Coulomb repulsion is determined by the value of the Coulomb integral

See also Exchange repulsion.

Counterpoise correction - Approximate method to estimate the value of the basis set superposition error. For a complex A-B formed by two interacting monomers, A and B, the BSSE is estimated as the difference between monomer energies with the regular basis set of each monomer and the energies calculated with the full basis functions for the whole complex. The latter energies for each monomer are calculated by adding to the normal basis set the basis functions of the other monomer located at the corresponding nuclear positions, but without the nuclei present. These additional basis are called ghost orbitals.

Coupled cluster (CC) method - An ab initio quantum mechanical method in which electron correlation effects are introduced by acting with the exponential operator exp(T) on the zero-order wavefunction, and where T consists of the sum of all possible excitation operators. A CCSD(T) calculation provides for a higher-level treatment of electron correlation beyond MP4 (see M ller-Plesset Perturbation Theory). FORESMAN and FRISCH (1996).

Covalent bond - A type of bonding associated with the sharing of two electrons usually between two atomic centers of a molecular entity. The mechanism of covalent bonding that causes decrease in the total potential energy of a molecule as its constituent atoms move towards each other is orbital contraction, which increases the localization of the electrons around the nuclei and decreases the accumulated charge in the bonding region(s). BACSKAY, REIMERS, and NORDHOLM (1997); RUEDENBERG (1962).

Crystal field - The average static electric field experienced by an ion, molecule or atom in a crystal generated by all the other surrounding atoms, molecules, or ions. The concept introduced by Becquerel and developed by Bethe has been extended to refer to the field generated by the ligands (anions or neutral species) surrounding a transition metal ion in a coordination compound. With the understatement that some covalency (see Covalent bond) may exist in the metal-ligand bond, it is often referred to as ligand field.

Crystal orbital (synonymous with band orbital) - One-electron function extended throughout a crystal. Typically a linear combination of Bloch orbitals:

The Bloch orbitals incorporate the translational symmetry by application of boundary conditions:

where cm(r) is the n-th atomic orbital at the unit cell defined by the translation vector r. The different values adopted by the wave vector k determine the symmetry and nodal properties of the crystal orbital.

Crystal orbital overlap population (COOP) - The overlap population weighted density of states. For a solid, COOP serves as the differential version of the bond order concept. The integral of the COOP curve up to the Fermi level is the total overlap population of the specified bond in a solid, whereas the value of COOP(E)dE represents the contribution to the total overlap population of those crystal orbitals whose energy levels lie in the range of E and E+dE. HOFFMANN (1988).

Curve-crossing model - Model of organic reactivity that generates a reaction profile from curves that describe the energies of reactant, product, and intermediate electronic configurations (or, alternatively, reactant, product and intermediate electronic states) as a function of the reaction coordinate. The crossing reflects the electronic reorganization that accompanies the transformation of reactants and products. PROSS (1995); PROSS and SHAIK (1983), SHAIK (1981).

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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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