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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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Pariser-Parr-Pople (PPP) method - A semiempirical quantum mechanical method of calculation of the properties of conjugated molecules and ions from self-consistent-field theory and the p-electron approximation.

Pauli exclusion principle - A rule, complementary to the aufbau principle, of building up the electronic configuration of atoms and molecules: a maximum of two electrons can occupy an orbital and then only providing that the spins of the electrons are paired, i.e. opposed. The principle demands that the wavefunction for a many-electron system must be asymmetric with respect to the permutation of the space-spin coordinates for every pair of electrons.

Pauling’s bond order - see Fractional bond number.

Peierls distortion - The distortion of a regular one-dimensional structure with a partially occupied band to give bond alternation, eventually leading to dimerization or oligomerization. The degree of oligomerization l depends on the electronic population of the conduction band indicated by wave vector of the Fermi level, kF:

l = 2p/kF

A Peierls distortion opens a gap at the Fermi level, producing a net stabilization of the distorted structure. The Peierls distortion for chain compounds is analogous to the Jahn-Teller effect for molecules. The prototypical example of the Peierls distortion in organic chemistry is the bond alternation present in polyacetylene.

Perfect pairing - The term used to describe corollaries of the Coulson-Rushbrooke pairing theorem for alternant hydrocarbons: (a) the molecular orbitals of an even alternant hydrocarbon occur on pairs with energies a Em , a being the Coulomb integral for carbon; (b) the coefficients at atomic orbitals of the paired molecular orbitals are numerically the same, but their signs at atomic orbitals of starred atoms are reversed in going from one molecular orbital to the other; (c) in an odd alternant hydrocarbon, with the total number of molecular orbitals odd, all but one of the molecular orbitals is paired. The odd molecular orbital has energy a (see nonbonding molecular orbital) and is confined to the starred atoms.

Pericyclic reaction - Reactions in which all first-order changes in bonding relationships take place in concert on a closed curve, i.e. throughout a cyclic array of continually bonded atoms forming a fully conjugated cyclic transition state. An example of a pericyclic reaction is the 3,3-sigmatropic (Cope) rearrangement of hexa-1,5-diene.


Permutation group of the set of n objects - The set of all possible permutations that can be applied to a given set of objects, together with the composition operation. For example for a set of three objects (vertices of a graph, atomic centers etc.) the permutation group consists of six permutations: id, ((1,2)), ((1,3)), ((2,3)), ((1,2,3)), ((1,3,2)), where id is the permutation which leaves each object fixed.

Permutational isomerization - see Automerization.

Perturbation theory - Along with variational method, the second major quantum-mechanical approximation method. The methods of perturbation theory are based on representation of the Hamiltonian of a system under study, H, through the Hamiltonian,H0, of a system, whose Schroedinger equation is solvable, and its relatively small perturbation H' : H = H0+ H'. Numerous techniques are derived allowing one to relate the unknown eigenvalues and eigenfunctions of the perturbed system to the known eigenvalues and eigenfunctions of the unperturbed system. As distinct from the variational method, the methods of perturbation theory are applicable to all the electronic states of an atom or molecule. When H' is time-dependent, the perturbed system does not have stationary states. In this case time-dependent perturbation theory, which is the method of approximate calculation of the expansion of wavefunctions of the perturbed system over wavefunctions of stationary states of the unperturbed system must be employed. The applications of this method are associated mostly with studies of light emission and absorption by atoms and molecules. See also MØller-Plesset (MP) Perturbation Theory.

Phonon - A quantized vibration of a crystalline lattice. In contrast to photons, phonons are quasiparticles.

Photon - The quantum of electromagnetic energy at a given frequency.

Pi (p) electron approximation - The assumption that in planar unsaturated molecular entities, whose p-molecular orbitals do not mix with s-molecular orbitals, the molecular wavefunction is rigorously separated into Y = YsYp .The s-electron shell serves as a nonpolarizable core (see core approximation) merely providing part of the effective potential for the motion of p-electrons, i.e. Ys remains the same for any state of the p-system.

Point group - see Symmetry point group.

Polarizability (static dielectric polarizability) - A measure of the linear response of the electronic cloud of a chemical species to a weak external electric field. For isotropic molecules, the dipole moment, mi, produced by a field, E, of unit strength

mi = aE

In the general case, the polarizability is anisotropic, i. e. dependent on the position of the molecule with respect to the field and a is replaced by a function (symmetrical tensor) which defines the induced dipole moment for each possible direction of the electric field. The polarizability defined on an experimental basis is the average polarizability, i. e. the sum of polarizabilities (bi) in three principal directions, b1 being collinear with the external field.

aave = (1/3) (b1 + b2 + b3)

BÖTTCHER (1973), EXNER (1975)

Polarization - The readjustment of a charge distribution when it experiences an external electrostatic potential. Polarization, p, is usually measured as the dipole moment induced in a unit volume

p = NdaE/M

where a is polarizability, M/d is the molar volume (M is the molecular mass and d is density), and E is applied electric field.

Polarized basis set - see Basis set.

Polarizable continuum model (PCM) - A self-consistent reaction field method to treat solvation effects, which employs a van der Waals surface type cavity instead of a spherical cavity in the standard SCRF procedures.

Polyhedral skeletal electron pair approach - see Wade’s rules.

Potential Energy Surface (PES) - Within the adiabatic approximation, the function of the total energy of a molecular system (minus kinetic energy of the nuclei) of the coordinates of all nuclei which this system contains.
See also Energy hypersurface.

Predissociation - Dissociation of a molecule occurring through its excitation to a certain bound state which is coupled to a dissociative continuum. Predissociation is caused by interaction between discrete levels of a given electronic state and the dissociative continuum of another electronic state. Predissociation manifests itself by the appearance of line broadening, a decrease in lifetime, an abrupt decrease of fluorescence quantum yield and generation of dissociation products. KATO and BABA (1995).

Prereactive complexes - Weakly bound complexes with a potential minimum that precedes the activation barrier along the reaction path. In contrast with the van der Waals complexes which fall apart reversibly into their constituents, the prereactive complexes may undergo a vigorous reaction to form different products. BÜRGER (1997)

Prochirality - The property of an achiral object to acquire chirality through a single desymmetrization step, e.g. addition to it of a new atom or achiral group or substitution of an existing atom or achiral group by different ones.

Proton affinity ( of a given base Z) - The negative of the enthalpy change at 298K for the gas phase reaction of an atomic or molecular entity with a proton

H+ + Z HZ+

Pseudo Jahn-Teller effect (synonymous with Second-order Jahn-Teller effect) - see Jahn- Teller effect.

Pseudopericyclic reaction - A reaction from the subset of pericyclic reactions for which there is no cyclic orbital overlap. An example of pseudopericyclic orbital topology is given by the reaction of decarbonylation of furan-2,3-dione to give 4-oxoprop-2-enal.


ROSS, SEIDERS, and LEMAL (1976); BIRNEY, HAM, and UHRUH (1997).

Pseudopotential approximation - see Core approximation.

Pseudorotation - A conformational change resulting in a structure that appears to have been produced by rotation of the entire initial molecule and is superimposable on the initial one, unless different positions are distinguished by substitution or isotopic labeling. No angular momentum is generated by this motion; this is the reason for the term. An example is the facile interconversion of the envelope and twist conformers of cyclopentane. A particular case is the Berry pseudorotation.

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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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