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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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ECW model for donor-acceptor interaction - An approach to obtaining a quantitative scale of bond strengths of Lewis acid-base complexes. Each acid is characterized by electrostatic, EA, and covalent, CA, enthalpy parameters as is each base (EB and CB) which are combined according to the equation


to produce the enthalpy of formation of the AB complex.The E, C parameters are chosen in such a way as to have minimal contributions from solvation or lattice energies. The W term incorporates any constant contribution to the reaction of a particular acid (or base ) that is independent of the base (acid) it reacts with. DRAGO, WONG, BILGRIEN, and VOGEL (1987); VOGEL and DRAGO (1996).

Effective Atomic Number (EAN) rule - see 18-Electron rule.

Effective Hamiltonian - A model Hamiltonian, Heff used for an approximate description of a certain part of the total electronic system of a molecular entity, e.g. valence electrons or pp- electrons. It is related to the exact Hamiltonian, H, for the same problem by means of a factorizing similarity transformation: Heff = W-1HW such that Heff has the same eigenvalues as H (usually for a small subset of the eigenvalues of H), but much simpler eigenfunctions. In the Hartree-Fock method Heff replaces electron-electron repulsion by an average over occupied orbitals.The Hückel MO theory can be interpreted as a method based on Heff. KUTZELNIGG (1988).
see also Kohn-Sham orbitals.

Effective molecular symmetry group - The appropriate group in which the energy levels of molecules undergoing rearrangements on a given experimental time scale are to be classified. The operations of the molecular symmetry group of such molecules consist of permutations of identical nuclei amongst themselves, and permutation-inversions, where a permutation is combined with the inversion of all particle coordinates through the origin of a space-fixed axis system. The complete nuclear permutation-inversion group contains all such operations, which all commute with the full molecular Hamiltonian. LONGUET-HIGGINS (1963); BUNKER (1979).
See also Symmetry point group, Symmetry operation.

Electron affinity - The energy (AX) released upon attachment of an electron to an atom or a molecule (X) resulting in the formation of the negative ion X-, i.e.

X + e- X- + AX

As with the case of ionization potential, there may be defined adiabatic electron affinity and a vertical electron affinity. The adiabatic AX is equal to the difference between the total energies of a neutral system (X) and the corresponding anion (X-). The vertical AX is equal to the difference between total energies of X and the anion X- in the equilibrium geometry of X.

Electron correlation - The adjustment of electron motion to the instantaneous (as opposed to time- averaged) positions of all the electrons in a molecular system,i. e. the tendency of electrons to correlate their motions in order to keep as far apart as possible because of the restrictions set by the Pauli exclusion principle (exchange correlation) and because of the electrostatic repulsions (coulombic correlation).
See also Correlation energy.

Electron-counting rules - Rules establishing correspondence between the topology of a molecular structure and the number of electrons which may be placed into its bonding molecular orbitals. In the origin of various electron-counting rules lies a general assumption that the completeness of the valence electron shell of a molecular entity belonging to a certain structural type serves as the major criterion of structural stability.
See 18-Electron rule, Hückel rule, Lewis octet rule, Wade's rules, Woodward- Hoffmann rules.

Electron deficient compounds - Molecules or ions that contain too few electrons to allow their bonding to be described exclusively in terms of two-center, two-electron, i.e.covalent, bonds. Such molecules or certain fragments in these are often held together by the multicenter bonds. The compounds containing atoms with incompletely filled but spin-paired electron shells (carbenes, carbenium ions) may also be regarded as electron deficient ones.

Electron density - (synonymous with charge density), see Electron density function.

Electron density function - The electron probability distribution function, r defined as

r(r) = n y*[r(1), r(2) ...r(n)] y [r(1) r(2) ...r(n)] dr(2)...dr(n)

where y is an electronic wavefunction and integration is made over the coordinates of all but the first electron of n. The physical interpretation of the electron density function is that rdr gives the probability of finding an electron in a volume element dr, i.e. electron density in this volume.

18-Electron rule - for mononuclear transition metal complexes the electron-counting rule derived from the fact that transition metals have nine valence AOs which can be used either for metal-ligand binding or for accommodating non-bonding electrons. An extension of the rule to transition metal cluster compounds is known as the effective atomic number rule.

Electron transfer (ET) reaction - A redox process in which the overall change that has occurred is the transfer of one or more electrons.

Electronegativity - The power of an atom in a molecule to attract electrons. The two widespread empirical scales of electronegativity are those developed by L. Pauling and R. Mulliken. The Pauling scale is thermochemical; it is based on the values of bond energies of type X-Y, X-X and Y-Y molecules from which the ionic contribution to the X-Y bond is defined as

DXY = EXY - (1/2)(EXX + EYY)

From this value the relative electronegativity of X with respect to Y is defined (in eV1/2 units) as

cX - cY (DXY)1/2

The Mulliken electronegativity ( in eV units) is given by the equation:

cX = (1/2) (IX + AX)

where IX and AX are respectively ionization potential and electron affinity in a suitable valence state (see valence state ionization potential, valence state electron affinity). both scales are linearly interrelated. These are useful for estimating bond polarities and strengths of bonds between different atoms. Many other scales of electronegativity are known, among which that of A. Allred and E. Rochow , where electronegativity is defined as the electrostatic force between the nucleus and its valence electrons, is most frequently used. Accounting for the observation that the position of bond points relates to the polarity of a bond, a scale of atomic and group electronegativities, which are comparable in magnitude to the Pauling values, was derived (R. Boyd) on the basis of topological properties of the electron density distributions in model hydrides R-H. ALLEN (1994); ALLRED and ROCHOW (1958); BERGMANN and HINZE (1996); BOYD and BOYD (1992); MULLIKEN (1934); PAULING (1932).
See also Absolute electronegativity, Equalization of electronegativity.

Electronic chemical potential - The quantity that measures the escaping tendency of electrons from a species in its ground state. It is the negative of the absolute electronegativity. PARR, DONNELLY, LEVY, and PALKE (1978).

Electronic configuration - The allocation of electrons within an atom or a molecule to a set of correspondingly atomic or molecular orbitals complying with the Pauli exclusion principle. One electronic configuration may give rise to several electronic states with different multiplicities. A wavefunction for a given electronic configuration which is an eigenfunction of the electron spin operators S2 and Sz represents an electronic state of the the atom or molecule.

Electronic state - An arrangement allowed by the laws of quantum mechanics of electrons within an atom, molecule (or system of molecules) .
See also Electronic configuration.

Electronic stability - Unavailability of another electronic structure (different electronic state ) of lower energy with the same number of electrons.

Electrostatic potential - A physical property equal in magnitude to the electrostatic energy between the static charge distribution, r(r), of an atomic or molecular system (in the latter case the term molecular electrostatic potential is commonly used) and a positive unit point charge located at r. The electrostatic potential V(r) that is produced at any point r by the electrons and nuclei (A) of the system is given by

V(r) = ZA/|RA-rA| - r(r')dr'/|r'-r|

POLITZER (1981); SCROCCO and TOMASI (1973).

Energy gradient - First derivatives of the total energy with respect to nuclear coordinates, i.e. negative values of forces on the nuclei. Evaluation of energy gradient plays a central role in searching potential energy surfaces for stationary points. A widespread technique is based on the minimization of the gradient norm (the square of energy gradient). SCHLEGEL (1989).

Energy hypersurface (synonymous with potential energy surface, PES) - The notion of hypersurface is used to stress the multidimensionality of PESs. In a molecular system consisting of N atomic nuclei, the number of the independent coordinates that fully determine the PES is equal to 3N-6 (or 3N-5 if the system is linear).

MEZEY (1987).

Energy profile - A schematic plot of the energy of a reacting system as a function of the reaction coordinate. The term energy may refer to enthalpy, free energy or internal energy. Energy profiles are intended to illustrate the energies of reactant, intermediate, transition and product states of the system in the order in which they are formed; they are useful for depicting reaction mechanisms.

Equalization of electronegativity, principle of - The postulate that in a molecule all the constituent atoms should have same electronegativity value, which would be the geometric mean of the electronegativities of isolated atoms. SANDERSON (1951).

Equilibrium geometry - Molecular geometry that corresponds to the true minimum on the respective potential energy surface. While information relating to the equilibrium geometry is provided by calculations within the adiabatic approximation (minimization of the total energy with respect to any independent geometrical parameter), various experiments yield some effective geometries for the molecule which are averaged over molecular vibrations.
See also Bond length.

Exchange integral - see Exchange repulsion.

Exchange repulsion - The correction to the Coulomb repulsion between two electrons in orbitals yi and yj for the case when the electrons possess parallel spins. It is to be substracted from the Coulomb repulsion to give the total energy of the electron-electron interaction. In the Hartree- Fock theory the magnitude of the exchange repulsion is given by the exchange integral

Kij = yi*(r1)yj*(r1)( e2/r12)yi(r2)yj(r2)dr1dr2 = < ij|ji >

For the case of electrons with opposite spins Kij vanishes.

Excimer - A dimer stable only in the electronically excited state formed by the interaction of an excited molecular entity with a ground state partner of the same structure.

Exciplex - An electronically excited complex stable only in the electronically excited state formed by the interaction of an excited molecular entity with a ground state partner of a different structure.

Excited configuration - An electronic configuration that makes a predominant contribution to the quantum mechanical description of an excited state of a system.

Excited state - An electronic state other than the lowest energy state of a system.

Exciton - A quasiparticle invoked to describe the migration through the crystal lattice of the excitation of one molecule in the crystal. The rate of the migration depends on the width of the band orbital: the wider bands provide for faster migration.The migration of the excitation is analogous to the migration through the crystal of a spin-free particle. FRENKEL (1931); MURRELL (1963).

Exclusion principle - see Pauli exclusion principle.

Extended basis set - see Basis set.

Extended Hückel MO method (EHMO) - A semiempirical all-valence electron quantum mechanical method which uses the same approximations, apart from p-approximation and neglect of overlap integrals, as those of the Hückel molecular orbital theory. The method reproduces relatively well the shapes and the order of energy levels of molecular orbitals. The account for overlap makes it possible to describe the net destabilization caused by interaction of two doubly occupied orbitals, which effect is not reproduced by HMO theory. HOFFMANN (1963).

Extended transition state method (ETS) - An energy partioning scheme of the bond energy DE between two atoms of fragments A and B into four different terms:

DE (A-B) = DEprep + DEelst + DEex + DEorb

where DEprep is the energy which is necessary to promote the fragments A and B from the respective equilibrium geometry in the electronic ground state to the geometry and electronic reference state in the molecule A-B. The three terms DEelst, DEex, and DEorb give the interaction energy DEint. They are calculated in three subsequent steps. DEelst is the electrostatic interaction energy which is calculated in the first step with a frozen electron density of the fragments. DEex then gives the repulsive energy caused by exchange repulsion, which is calculated when the frozen wavefunction of step one becomes orthogonalized and antisymmetrized. DEorb is calculated in the third step. It gives the stabilization which comes from the orbital interaction when the wavefunction is completely relaxed. The latter term can be broken down into orbital contributions with different symmetry. The ETS method is similar to Morokuma analysis. ZIEGLER and RAUK (1977).

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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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