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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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Back donation (also known as the Dewar-Chatt-Duncanson model) - A description of the bonding of p- conjugated ligands to a transition metal which involves a synergic process with donation of electrons from the filled p-orbital or lone electron pair orbital of the ligand into an empty orbital of the metal (donor-acceptor bond), together with release (back donation) of electrons from an nd orbital of the metal (which is of p-symmetry with respect to the metal-ligand axis) into the empty p*-antibonding orbital of the ligand.

Band orbital - see Crystal orbital.

Basis function - A one-electron function used in the expansion of the molecular orbital function. Basis functions are commonly reperesented by atomic orbitals (see also Slater-type orbital or Gaussian-type orbital) centered on each atom of the molecule.

Basis set - In quantum chemistry, a set of basis functions employed for the representation molecular orbitals. One may distinguish the minimal basis set (includes one basis function for each SCF occupied atomic orbital with distinct principal and angular momentum quantum numbers); split valence basis set (includes two or more sizes of basis function for each valence orbital); double zeta DZ) basis set (a split valence basis set that includes exactly twice as many functions as the minimal basis set); extended basis set (the set larger than the double zeta basis set); polarized basis set (incorporates basis functions of higher angular quantum number beyond what is required by the atom in its electronic ground state; allows orbitals to change not only a size, but also a shape); basis set with diffuse functions and others. DAVIDSON and FELLER (1986); FORESMAN and FRISCH (1996); HEHRE, RADOM, SCHLEYER, and POPLE (1986); SCHAEFER (1972).

Basis set superposition error (BSSE) - An artfactual increase in calculated stability of the supersystem (the system formed by noncovalent interaction between two or more molecular entities, e.g. hydrogen bond system) resulting from the basis set of the supersystem being larger than for the component subsystems. The BSSE arises from a lowering of the quantum mechanical energy when the electron density of each subsystem spreads into the basis functions provided by the other subsystems. DAVIDSON and FELLER (1986).

Bent's rule - In a molecule, smaller bond angles are formed between electronegative ligands since the central atom, to which the ligands are attached, tends to direct bonding hybrid orbitals of greater p character towards its more electronegative substituents. BENT (1961).

Berry pseudorotation - A mechanism for the interconversion of trigonal bipyramid structures (1a and 1b ) through an intermediate (or transition state ) tetragonal pyramid structure 2. It may be visualized as two synchronized bending motions by which a pair of apical ligands (1 and 2) exchange their positions with a pair of equatorial ones (3 and 4), whereas one equatorial ligand (5) described as "pivotal" remains unchanged. This process results in an apparent rotation (pseudorotation) of the actual trigonal bipyramid structure.

For the majority of five-coordinate main-group and transition metal compounds the energy difference between the trigonal bipyramid (1) and tetragonal pyramid (2) structures is sufficiently low, so that Berry pseudorotation represents a widespread mechanism of stereochemical nonrigidity. The same type of intramolecular rearrangement is characteristic also of four- coordinate bisphenoidal structures, a lone pair always playing the role of the pivotal phantom-ligand. BERRY (1960); MISLOW (1970).
See also Pseudorotation.

Bethe lattices - The infinite connected graphs (a graph is connected if each pair of its points is joined by a path) not containing cycles, all vertices of which are equivalent and have equal numbers (n) of neighbours. Although Bethe lattices with arbitrary n cannot be realized in three-dimensional space, this model is useful in the electronic theory of disordered systems.

Bifurcation - Branching of the minimum energy reaction path into two different paths at a certain point (bifurcation point) on the potential energy surface.

Binding energy - The difference between the total energy of a molecular system and the sum of the energies of its isolated p- and s-bonds. The value of binding energy depends upon the geometrical arrangement of the isolated subunits (molecules). According to another definition, the term to be substracted from the total energy is the sum of the energies of the separate atoms in the corresponding valence states, which compose the molecule. PAULING (1960).

Biradical - An even-electron molecular entity with two (in some cases delocalized) radical centers which act almost independently of each other. The lowest-energy triplet state of a biradical lies below or at most only a little above its lowest singlet state.The states of those biradicals whose radical centers interact particularly weakly are described in terms of a pair of local doublets. BORDEN (1982); IUPAC PHOTOCHEMICAL GLOSSARY (1988);

Biradicaloid - A biradical displaying a strong coupling between the radical centers.

Bloch orbital - see Crystal orbital.

Bohr magneton - The magnitude of the standard magnetic moment (the negative first derivative of the energy with respect to the magnetic field) for an electron:

mB = eh/4pmec = 0.927408 x 10-23 J T-1 (0.927408 x 10-20 erg G-1)

Bond critical point (synonymous with bond point) - Within the topological electron distribution theory, a (3, -1) critical point (the point of the gradient field of the electron density within a given nuclear configuration in which r (r,q) = 0) which is a local maximum in two directions and is a local minimum in the third, i.e. a saddle point in three dimensions. A bond critical point appears between every pair of neighbouring bonded atoms, its position on the bond path reflecting the polarity of a bond. The location of the bond critical point of bond A-B is shifted toward A and thus, assigns a larger volume of the electronic density to B if B is more electronegative than A. BADER (1990).

Bond ellipticity - Within topological electron distribution theory, the quantity, e, which gives a measure of the deviation of the charge distribution from cylindrical symmetry and thus is correlated with the amount of p-character of a bond

e = l1/l2 - 1

where l1 and l2 are the principal curvatures of the electron density function at the bond point. BADER (1990).

Bond energy - The energy required to break a given type of bond between atoms in certain valence states. An averaged bond energy is commonly derived by dissecting the heat of atomization of a molecule into contributions of individual bonds. For molecules with localized bonds, the heats of atomization (formation) are usually well approximated by the sum of pertinent averaged bond energies. BENSON (1965).

Bond length - The distance between atomic centers involved in a chemical bond. The notion of bond length is defined differently in various experimental methods of determination of molecular geometry; this leads to small (usually 0.01-0.02 Å) differences in bond lengths obtained by different techniques. For example, in gas-phase electron-diffraction experiments, the bond length is the interatomic distance averaged over all occupied vibrational states at a given temperature. In an X-ray crystal structural method, the bond length is associated with the distance between the centroids of electron densities around the nuclei. In gas-phase microwave spectroscopy, the bond length is an effective interatomic distance derived from measurements on a number of isotopic molecules, etc. A number of empirical relationships between bond lengths and bond orders in polyatomic molecules were suggested, see, for example, fractional bond number (the Pauling's bond order).

Bond orbital - A localized molecular orbital related to a certain s-, p-, or d-bond.

Bond order - The electron population in the region between atoms A and B of a molecular entity at the expense of electron density in the immediate vicinity of the individual atomic centers. Different schemes of partitioning electron density give rise to different definitions of bond orders.In the framework of the Mulliken population analysis, bond order is associated with the total overlap population

m n where Pmn and Smn are respectively the elements of the density matrix and overlap matrix (see overlap integral). A large positive value of bond order signifies strong bonding between the atoms of the molecular entity, whereas negative values of qAB imply that electrons are displaced away from the interatomic region and point to an antibonding interaction. In valence bond theory, bond order is given by a weighted average of the formal bond orders (i.e. by the number of electron pairs in a given Lewis structure) between the atoms in the resonance structures (see Resonance hybrid).

Bond path - Within the topological electron distribution theory, the line resulting from the addition of two gradient paths of the electron density function emanating from the bond critical point located between each two neighbouring atomic basins. A bond path can be associated with all types of interatomic interactions, including hydrogen bonds and interactions in van der Waals systems. BADER (1990).

Bond point - see Bond critical point.

Bond resonance energy (BRE) - A quantity that represents the contribution of a given p-bond in a molecule to the topological resonance energy. p-Bonds with large negative BREs are presumed to be antiaromatic (see antiaromaticity) in nature. The greater is the number of such p-bonds in a molecule, the more the molecule becomes reactive and less thermodynamically stable. AIHARA (1995).

Bond-atom polarizability - A quantity used in perturbation HMO theory as a measure of the change in bond order, p, between the centers r and s caused by a change in electronegativity orcoulomb integral of atom m:

prs,m = prs/ am

Bond-bond polarizability - A quantity used in perturbation HMO theory as a measure of the change in bond order, p, between the centers r and s caused by a change in the resonance integral, b, between the centers m and n:

prs,mn = prs/ bmn

Bond-dissociation energy (BDE) - For a diatomic molecule, the maximum vibrational energy that a molecule can have prior to its decomposition into the ground electronic states of the constituent atoms (spectroscopic bond-dissociation energy, De). The De value is related to the chemical dissociation energy: D0 = De - Evib(0), where Evib(0) is zero-point vibrational energy. This definition is usually extended to the dissociation of polyatomic molecules into certain molecular fragments through homolytic or heterolytic bond cleavages. PILAR (1968), FLISZAR (1994).

Bond-separation reactions - A class of isodesmic reactions of considerable importance for the quantitative characterization of the interaction between neighboring bonds. All formal bonds between heavy (non-hydrogen) atoms are separated into the simplest reference (two-heavy atom) molecules containing these same kind linkages. The set of the molecules involving H, C, N consists of ethane, ethene, ethyne, methylamine, methanimine, hydrogen cyanide, hydrazine and diazene. Stoichiometric balance is achieved by the addition of one heavy atom hydrides (for the H, C, N compounds - methane and ammonia) to the left-hand side of the reaction scheme. A unique bond-separation reaction may be drawn for any molecule with a classical valence structure. The positive bond-separation energy characterizes stabilization of such a structure with respect to the corresponding isolated bonds and the opposite is true for negative values of bond-separation energies. Thus, the bond-separation reactions (1) and (2) reproduce correspondingly the destabilization energy (strain energy) of cyclopropane and stabilization energy (due to the aromaticity) of benzene.

c-(CH2)3 + 3 CH4 3 CH3-CH3 (1)

DHexp = -22.1 kcal/mol (-92.5 kJ/mol); DHcalc(6-31G*) = -26.2 kcal/mol (-110.9 kJ/mol)

C6H6 + 6CH4 3 CH3-CH3 + 3 CH2=CH2 (2)

DHexp = 64.1 kcal/mol (268.2 kJ/mol); DHcalc(MP2/6-31G*) = 67.2 kcal/mol (281.2 kJ/mol)


Bond-stretch isomers - A concept introduced to distinguish molecules (still hypothetical) which differ only in the length of one or several bonds and correspond to minima on the same potential energy surface. A typical example is given by tricyclo[,4] octane ([2.2.2]propellane) in which stretching of the central C-C bond provides for crossing of the electronic states of the same symmetry.

By contrast, in experimentally observed spin-state isomers changes in bond length are associated with changes in spin state. PARKIN (1993); STOHRER and HOFFMANN (1972).

Bonding molecular orbital - A molecular orbital whose occupation by electrons increases the total bonding (usually, lowers the total energy) of a molecule. Generally, the energy level of a bonding MO lies lower than the average of the valence orbitals of the atoms constituting the molecule.

Born - Oppenheimer (BO) approximation - Representation of the complete wavefunction as a product of an electronic and a nuclear part

Y (r,R) = Ye (r,R)YN(R)

where the two wavefunctions may be determined separately by solving two different Schroedinger equations. The validity of the Born-Oppenheimer approximation is founded on the fact that the ratio of electronic to nuclear mass (m/M @ 5 x 10-4) is sufficiently small and the nuclei, as compared to the rapidly moving electrons, appear to be fixed.The approximation breaks down near a point where two electronic states acquire the same energy (see Jahn-Teller effect). The BO approximation m denotes the case when Ye diagonalize theis often considered as being synonymous with the adiabatic approximation. More precisely, the latter ter electronic Hamiltonian. Thus, the adiabatic approximation is an application of the BO approximation.

Brillouin theorem - The theorem that states that there is no nonvanishing configuration interaction matrix elements between the ground-state determinantal wavefunction and those determinants resulting from the excitation of one electron to an empty orbital of the initial SCF calculation

Brillouin zone (usually used as short for the first Brillouin zone) - The set of all values of the wave vector which generate non-equivalent crystal orbitals. It has the form of a polyhedron centered at the G-point, or the center of the Brillouin zone, k = (0,0,0). Its component in,e.g.,the x direction is in the range

- p/a < kx < p/a

for the first Brillouin zone, where a is the repeat distance along that direction.


[A] [B] [C] [D] [E] [F] [G] [H] [I] [J-K] [L] [M]
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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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