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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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Saddle point - A point of lowest maximum energy on a valley (reaction path) connecting two minima on the potential energy surface. In mathematical terms, the stationary point on the PES in which the Hessian matrix has only one negative eigenvalue is assigned to the saddle point of the first rank. The saddle point is associated with the transition state structure.

Scaling factor - A variational parameter (see variational method) used as a multiplier of each nuclear Cartesian and electronic coordinate chosen to minimize the variational integral and to make a trial variation function to satisfy the virial theorem. In practical calculations, the numeral factor to scale computed values, e.g. vibrational frequencies, to those found in experiments.

Second-order Jahn-Teller (SOJT) effect - see Jahn-Teller effect.

Secular equation - In molecular orbital theory, the determinant of matrix elements whose solution leads to the set of energy levels of molecular orbitals for a given system.

Selection rule - A rule which states whether a given transition or process is allowed or forbidden (i.e. its intensity is high or zero, or close to zero) on the basis of the symmetry or spin of the wavefunctions of the initial and final states.

Self-Consistent Field (SCF) method - see Hartree-Fock method.

Self-Consistent Reaction Field (SCRF) methods - Methods designed to treat solvation effects which incorporate the essential elements of the reaction field theory in the conventional SCF approach. The classical reaction field is treated as a perturbation, so that the hamiltonian is given by


Semiempirical quantum mechanical methods - Methods which use parameters derived from experimental data to simplify computations. The simplification may occur at various levels: simplification of the Hamiltonian (e.g. as in the Extended Hückel method), approximate evaluation of certain molecular integrals (see, for example, Zero differential overlap approximation), simplification of the wavefunction (for example, use of a Pi (p) electron approximation as in Pariser-Parr-Pople method) etc. MURRELL and HARGET (1972); POPLE and BEVERIDGE (1970).

Singly occupied molecular orbital (SOMO) - see Frontier orbitals.

Size consistency - A property which guarantees that the method scales properly with the number of particles, i.e., when doubling the size of the system investigated and keeping the particle density constant, the energy of the system should double.

Slater determinant - The determinantal representation of many-electron wavefunction Y which conforms to the requirement of the antisymmetry principle.

Slater type atomic orbital (STO) - The exponential function centered on an atom; its radial dependence is given by Nrn-1exp(-zr), where n is the effective principal quantum number and z is the orbital exponent (screening constant) derived from empirical considerations. The angular dependence is usually introduced by multiplying the radial one by a spherical harmonic glm(qF).

Soliton - Vibration coupled with longitudinal sound waves propagated as localized quasiparticles. From a chemical point of view, a soliton can be regarded as a migrating region of conformational change.

Solvation energy - The change in Gibbs energy when an ion or molecule is transferred from a vacuum (or the gas phase) to a solvent. The main contributions to the solvation energy come from: (a) the cavitation energy of formation of the hole which preserves the dissolved species in the solvent; (b) the orientation energy of partial orientation of the dipoles; (c) the isotropic interaction energy of electrostatic and dispersion origin; and (d) the anisotropic energy of specific interactions, e.g. hydrogen bonds, donor-acceptor interactions etc.

Spin conservation rule - see Wigner rule.

Spin contamination - In unrestricted Hartree-Fock method, the wavefunctions obtained are eigenfunctions of the Hamiltonian and the spin projection Sz operators, but not eigenfunctions of the S2 operator. As a result, the wavefunctions of the doublet systems are spin contaminated to some extent by admixtures of quartet, sextet, and higher spin states. The eigenvalues of the S2 operator are given as a measure of the spin contamination. LÖWDIN (1966).

Spin crossover - A type of molecular magnetism that is the result of electronic instability (see electronic stability) caused by external constraints (temperature, pressure, or electromagnetic radiation), which induce structural changes at molecular and lattice levels. The phenomenon is most characteristic of first-row transition metal complexes, e. g. those of Fe(II). An example of spin- crossover complexes (the term of spin-state isomers is also used) is [Fe(2-pic)3]Cl2 . EtOH (2-pic = 2-picolylamine). At the Fe-N distance of 203.2 pm (115K), the complex has an electronic low-spin state (1A1), whereas stretching the bond up to 219.9 pm at 227 K induces the transition to a high-spin state (5T2). GÜTLICH, GOODWIN, and HENDRICKSON (1994).

Spin density - The excess of the electron density related to the electron with a spin over that of the electron with b spin (see spin-orbital) at a given point of an open-shell system. For a closed-shell system spin density is zero everywhere.

Spin polarization - Static and dynamic spin polarization effects are distinguished. The static polarization of an electron spin occurs in the C-H bonds of aromatic radicals where the s-electron closest to an unpaired p-electron tends to have its spin parallel to that of the p-electron. Likewise, static spin polarization arises in the p-system of conjugated radicals: the electron of the doubly occupied molecular orbital prefers to take a closer spatial position to the odd one, which spin is parallel to the latter. The effect reflects the energy unfavourable situation if an electron of opposite spin were to come nearby. The dynamic spin polarization is the instantaneous electron correlation effect occurring in biradicals (e.g. in 90o-twisted ethene, cyclobuta-1,3-diene) leading to correlation of spins of electrons in inner-shell orbitals with those of odd electrons. Essentially, a molecule seeks out a local (p,s) or (p,p) triplet configuration at each center (as is the case of static spin polarization) to decrease the overall coulomb repulsion energy of singlet states. The effect is termed dynamic since spin-polarized electron configuration has a counterpart where all the spins are reversed. BORDEN (1982).

Spin projection - A component, MS , of the angular spin moment S along an arbitrary axis (usually chosen as the z-direction). MS can take the values between -S and S: -S, -S+1, ..., S-1, S. The term is also used to denote an operation (spin-symmetry projection) allowing one to eliminate  spin contamination in the cases where wavefunctions are not eigenfunctions of the operator S2.

Spin-coupled (SC) wavefunction - Representation of a wavefunction in the modified valence bond theory. A spin-coupled wavefunction describes a molecular system with a total number of electrons Nt by subdividing these into inactive core electrons placed in doubly occupied orbitals and N active (valence) electrons placed in N distinct, singly occupied, nonorthogonal orbitals, the spins of which are coupled together in all allowable ways to form the required overall resultant S. GERRATT, COOPER, KARADAKOV, and RAIMOND (1997).

Spin-orbit coupling - The interaction of the electron spin magnetic moment with the magnetic moment due to the orbital motion of the electron, and the consequent mixing of electronic states of different multiplicity.

Spin-orbital - The complete one-electron wavefunction given (in the absence or in the case of neglect of spin-orbit coupling) by a product of a spatial function (orbital) and a spin function. An orbital yi(r) may be associated with either a(x) or b(x) spin functions, the spin coordinate x taking on one of two possible values (1/2 or -1/2) that measure the spin angular momentum component along the z-axis in the h/2p units. This gives rise to the spin-orbitals yi(r)a(x) and yi(r)b(x) .

Spin-spin coupling - a small relativistic effect due to interaction between the spin magnetic moments of electrons or nuclei.

Spin-state isomers - see Spin crossover.

Split valence basis set - see Basis set.

Static spin polarization - see Spin polarization.

Stationary point (synonymous with critical point) - On the potential energy surface a point at which the energy gradients with respect to all coordinates vanish.

Stationary state - A state in which the expectation values of properties do not change with time. It is given by a wavefunction representing one of the solutions of the time-independent Schroedinger equation.

Stereochemical nonrigidity - The capability of a molecule to undergo fast and reversible intramolecular isomerization, the energy barrier to which is lower than that allowing for the preparative isolation of the individual isomers at room temperature. It is conventional to assign to the stereochemically nonrigid systems those compounds whose molecules rearrange rapidly enough to influence NMR line shapes at temperatures within the practical range (from –100oC to 200oC) of experimentation. The energy barriers to thus defined rearrangements fall into the range of 5-20 kcal/mol (21-85 kJ/mol). A more general term for this phenomenon is structural nonrigidity. MUETTERTIES (1970); HOLM (1975).
See also Automerization, Fluxional molecules, Pseudorotation.

Steric energy - see Strain energy.

Strain energy -The excess energy due to steric strain of a molecular entity or transition state structure, i.e. distortions relative to a reference (real or hypothetical) "strainless" structure with the standard bond lengths, bond angles and dihedral angles. The strain energy components involve the following destabilizing terms: non-bonded repulsions, bond-angle distortions, bond stretch or compression, rotation around or twisting of double bonds, and electrostatic strain. In general, the contributions of these components are inseparable and interdependent. A quantitative assessment of strain and strain energies can be made by taking the difference between the heat of formation of the substance under consideration and that of a hypothetical strain-free model. Several approaches to the assessment of strain energies have been developed based on the use of energies of isodesmic and homodesmotic reactions and on the so-called "strainless increments", i.e. heats of formation of certain groups (CH3, CH2, CH, C etc). A synonymous term is steric energy. GREENBERG and LIEBMAN (1978).

Structural nonrigidity - see Stereochemical nonrigidity.

Structural stability - Within the Born-Oppenheimer (adiabatic) approximation, this is associated with an energy minimum on a potential energy surface. Structural stability implies that any change in the coordinates of the nuclei can only increase the total energy.

Sudden polarization - The occurrence of a large intramolecular charge separation in the singlet excited state of polyenes and their derivatives twisted about a double bond. Unsymmetrical substitution or geometrical distortion is effective in polarizing the system. An example is the stabilization of the zwitterionic structure of 90o twisted ethene (ethan-2-ylium-1-ide) with one methylene group pyramidalized:

SALEM (1971).

Supermolecule - A discrete oligomolecular species that results from the intermolecular association of its components.

Supramolecular chemistry - A field of chemistry related to species of greater complexity than molecules, that are held together and organized by means of intermolecular interactions. The objects of supramolecular chemistry are supermolecules and other polymolecular entities that result from the spontaneous association of a large number of components into a specific phase (membranes, vesicles, micelles, solid state structures etc.) LEHN (1995).

Surface delocalization - see Delocalization.

Symmetry allowed reaction - see Conservation of orbital symmetry.

Symmetry breaking - Instability of the wavefunction which appears when it has a lower symmetry than the nuclear framework. It is found, for instance, in the allyl radical or in the hydrogen peroxide radical cation. In the former, the nuclear geometry has a C2v symmetry, but the ROHF wavefunction has only Cs symmetry.

Symmetry element - A geometrical entity (mirror plane, proper and improper rotation axes, center of inversion) with respect to which one or more symmetry operations may be carried out. COTTON (1964).

Symmetry forbidden reaction - see Conservation of orbital symmetry.

Symmetry point group - (synonymous with Point group) - All the symmetry operations that leave a particular object (e.g. molecular entity or function) unchanged constitute together the symmetry point group for that object.

Symmetry operation - An operation associated with a symmetry element that is carried out on some object and which leaves the object unchanged.

Synchronous reaction - A concerted reaction in which all the changes in bonding take place in parallel.

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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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