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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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Many body perturbation theory (MBPT) - In quantum mechanics, methods of perturbation theory which use an independent particle approximation to obtain the zero-order wavefunction.

Marcus equation - A relationship correlating free activation energy, DG#, with the standard free energy, DGo of a reaction in the particular solvent

DG# = wr + l(1 + DGo’/l)2/4

where DGo’ = DGo + wp - wr , wr (or wp) is the work required to bring the reactants (or products) together to the mean separation distance in the transition state structure, and the vertical reorganization energy , l, is equal to the fourfold intrinsic barrier. Originally developed for treatment of outer-sphere electron transfer reactions, the Marcus equation has later been found to be applicable to proton transfer and group-transfer reactions. MARCUS (1964); SHAIK, SCHLEGEL, and WOLFE (1992).

Maximum hardness, principle of - A chemical system at a given temperature will evolve to a configuration of maximum absolute hardness, h, provided that the potential due to the nuclei, plus any external potential and the electronic chemical potential remain constant. In terms of molecular orbital theory, the highest value of h reflects the highest possible energy gap between the lowest unoccupied and highest occupied molecular orbitals; this value correlates with the stability (see structural stability, electronic stability, thermodynamic stability and kinetic stability) of a system. PEARSON (1987); PARR and CHATTARAJ (1991).

Mesomeric effect (synonymous with Resonance effect) - The intramolecular polarization of a conjugated molecular system brought about by a substituent whose pp or p-orbitals overlap with the p-MOs of the conjugated moiety. A distinctive feature of the mesomeric effect, as compared with the inductive effect, is that it causes alternation of the electron density in the conjugated chain or ring to which the mesomeric substituent is attached. Electron-releasing substituents with lone electron pairs (e.g. hydroxy, amino groups) are said to exert positive mesomeric effects, whereas substituents with low-lying lowest unoccupied molecular orbitals are characterized by negative mesomeric effects.

Metropolis algorithm - see Monte Carlo, method of.

Microscopic reversibility, principle of - For a system in thermodynamic equilibrium not only the total number of molecules leaving a given quantum state in unit time will equal the number arriving in the state in unit time, but also the number leaving by any one particular path will be equal to the number arriving by the reverse of that path. The principle was widely applied to the analyses of reaction mechanisms, in particular of substitution reactions. In the case of SN2 reactions at tetrahedral centers implying a formation of the trigonal bipyramid transition state (or intermediate) structure, the original formulation of the principle was extended in the following way: if a molecule or reactant enters a trigonal bipyramid at an apical position, this (or another) molecule or reactant must likewise leave the trigonal bipyramid from an apical position. TOLMAN (1934); WESTHEIMER (1968).

Minimal basis set - see Basis set.

Minimum energy reaction path (MERP) - The trajectory orthogonal to the equipotential contours of a potential energy surface, which connects the energy minima through a common saddle point (transition state) from which it slopes downward along the steepest descent lines in 3N - 6 configurational space (N is the number of nuclei in the reacting system). The methodology of MERP allows one to transform the large number of nuclear coordinates needed to specify the geometry of a polyatomic system to a unique coordinate. The remaining coordinates vary smoothly between their values at each end point of the MERP. DEWAR (1975).

Möbius system - A cyclic p-conjugated ribbon-like (see Ribbon delocalization) delocalized molecular system whose basis atomic orbitals are organized in a Möbius strip. In contrast to Hückel systems, whose orbital basis sets of a ring have zero or even number of phase inversions, Möbius type systems are characterized by an odd number of nodes. The electron counting rule for the stability of Möbius systems is opposite to the Hückel rule: the 4n electron Möbius systems have a closed electron shell, while the shell of the (4n+2) electron Möbius systems is open. HEILBRONNER and BOCK (1976); ZIMMERMAN (1971).

Molecular dynamics (MD), method of - A method of computational modeling of the static (equilibrium) and dynamic (kinetic) properties of many-particle systems by solving numerically the classical Newtonian equation assuming a predetermined force potential and a protocol for preparation of the system from a rational starting configuration to monitor the movement of molecules in liquid  or solution, define the phase trajectories and then average over time, and obtain the magnitudes of the functions examined. OHMINE and TANAKA (1993); SIMKIN and SHEIKHET (1995).
See also Monte Carlo, method of.

Molecular electrostatic potential (MEP) - see Electrostatic potential.

Molecular entity - A general term applied to any constitutionally or isotopically distinct atom, molecule, ion, ion pair, radical, radical ion, complex, conformer etc., identifiable as a separately distinguishable entity. IUPAC PHYSICAL ORGANIC CHEMISTRY GLOSSARY (1994)

Molecular graph - The graph with differently labeled (colored) vertices (chromatic graph) which represent different kinds of atoms and differently labeled (colored) edges related to different types of bonds. Within the topological electron distribution theory, a complete network of the bond paths for a given nuclear configuration.

Molecular graph theory - The theory which deals with analyses of all consequences of connectivities inherent in molecular structure and chemical transformations. The theory does not produce numerical data but uses available data and searches for regularities that can be attributed to combinatorial and topological origins. BALABAN (1976); KING (1983)
See also Molecular graph, Reaction graph.

Molecular graphics - Rendering a molecule as output by a computer for display. Sometimes molecular properties are also shown.

Molecular mechanics (synonymous with force field method) - Method of calculation of geometrical and energy characteristics of molecular entities on the basis of empirical potential functions (force field) the form of which is taken from classical mechanics. The method implies transferability of the potential functions within a network of similar molecules. An assumption is made on "natural" bond lengths and angles, deviations from which result in bond and angle strain respectively (see Strain energy). In the simplest models, the total potential energy, Vtotal, is broken down into four components:

Vtotal = Vr + VQ + VF + VvdW

where the sums represent respectively contributions due to bond stretching and compression terms, valence angle bending terms, internal rotation or torsional terms and van der Waals interactions. In practice, electrostatic terms and some other terms (improper torsion or out-of-plane bending terms, various cross-terms) are also taken into account. BURKERT and ALLINGER (1982).

Molecular modeling - Generation, manipulation, and/or representation of molecular structures and  associated physicochemical properties on a computer

Molecular orbital (MO) - see Orbital.

Molecular orbital (MO) theory - An approach to molecular quantum mechanics which uses one- electron functions (orbitals) to approximate the full wavefunction.

Molecular Rydberg state - An excited electronic state which is composed primarily of atomic orbitals with principal quantum numbers greater than that of the ground state and the valence excited states. Such electronic states typically have a large polarizability. ROBIN (1974).

MØller-Plesset (MP) perturbation theory - An approach to electron correlation which adds higher excitations to Hartree-Fock method using the technique from many body perturbation theory. Whereas the first perturbation to the HF energy (MP2 method) will always lower the total energy, the higher-level MP orders may be positive. They are also capable of overcorrecting the energy, since the theory is not variational (see Variational principle). FORESMAN and FRISCH (1996).

Monte Carlo (MC), method of - In mathematics, a method originally used for calculating multiple integrals by means of a random sample. The method is used for numerical modeling of many-particle chemical systems, in particular liquids; it is based on the equilibrium statistical mechanics theory. Observables A are calculated as mean values over a great number (@ 105 - 106) of instant configurations as determined by coordinates of the particles.

< A> = 1/N A{ri}

where N is the number of configurations. At the first stage, various configurations are randomly generated and then those energetically unrealizable eliminated. An efficient search for the most probable configurations to be entered into the above expression is provided by the Metropolis algorithm based on the principle of Markov’s chain theory. While being elaborated for the study of equilibrium chemical systems, MC method is also applied to studies of the dynamics of chemical reactions.
See also Molecular dynamics, method of.

Morokuma analysis - An energy partioning scheme for the interaction energy between atoms or  fragments A and B in the molecule A-B. The interaction energy is given as sum of three terms: electrostatic (which gives the interaction between the frozen charge distribution of A and B in the geometry of A-B), exchange interaction and the orbital relaxation energy (the energy change when the orthonormal orbitals of the fragments change into the final MO’s of A-B). The latter term is decomposed further into a polarization term, which arises from the mixing of occupied and empty orbitals of the same fragment, and a charge transfer term which gives the mixing of occupied orbitals of one fragment with the empty orbitals of the other fragment. The Morocuma analysis is similar to the Extended transition state method. MOROKUMA (1977)

Morse potential - The empirical function relating the potential energy of a molecule to the interatomic distance r accounting for the anharmonicity (see harmonic approximation) of bond stretching:

E(r) = De {1 - exp[-a (r - re)]}2

where De is the bond-dissociation energy, re is the equilibrium bond length, and a is a parameter characteristic of a given molecule.

Mulliken population analysis (MPA) - A partitioning scheme based on the use of density and overlap matrixes of allocating the electrons of a molecular entity in some fractional manner among its various parts (atoms, bonds, orbitals). As with other schemes of partitioning the electron density in molecules, MPA is arbitrary and strongly dependent on the particular basis set employed. However, comparison of population analyses for a series of molecules is useful for a quantitative description of intramolecular interactions, chemical reactivity and structural regularities. MULLIKEN (1955); HEHRE, RADOM, SCHLEYER, and POPLE (1986).
See also Atomic charge, Bond order.

Multicenter bond - A type of chemical bonding for which a localized description requires involvement of more than two atomic centers. See also Three-center, two-electron and Three-center, four-electron bonds.

Multiconfiguration SCF (MC SCF) method - The configuration interaction method in which simultaneous optimization of both the shapes of molecular orbitals and contributions from different electronic configurations is carried out by use of the variational method. The MC SCF method with a large enough set of configurations allows better estimation of the correlation energy as compared with the conventional CI method.

Multiplicity - The existence of several degenerate wavefunctions distinguished only by the relative orientation of the angular spin momentum. Defined by the total angular spin momentum S, it is given by 2S+1.

Multi-reference configuration interaction (MRCI) - Configuration interaction method in which the configurations are built by excitations out of a wavefunction obtained by using multiconfiguration SCF method.

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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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