Properties and applications of the average interparticle distance
The first and second moment operators are used to define the origin invariant shape and size of a molecule or functional group, as well as expressions for the distance between two electrons and the distance between an electron and a nucleus. The measure of molecular size correlates quite well with an existing theoretical measure of molecular volume calculated from isodensity contours. Also, the measure of size is effective in predicting steric effects of substituents which have been measured experimentally. The electron-electron and electron-nuclear distances are related to components of the Hartree-Fock energy. The average distance between two-electrons can model the Coulomb energy quite well, especially in the case of localized molecular orbitals. The average distance between an electron and a nucleus is closely related to the electron-nuclear attraction energy of a molecule.
Steric Interactions in Organic Chemistry: Spatial Requirements of Substituents
From the very extensive factual material available on steric interactions in organic chemistry, the present paper reviews the investigations that provide information about the “size” (“spatial requirement”) of the substituents. After an introductory section on the results obtained with the aid of spectroscopic data and by analysis of chemical reactions, attention is turned to conformational processes, including hindered rotation in ethanes, in the biphenyl system, in butadienes, multiply substituted arenes, molecular propellers, and triptycenes. The main emphasis is placed on the explanation of sterically hindered ring inversions in bridged arenes, a class of compounds particularly suitable for the study of steric interactions. The results obtained by variation of the parameters in this system are also discussed with respect to the spatial requirements of organic substituents.
Investigations of dielectric gratings using electrodynamic models based on volume integral equations
Eigenmodes of planar and cylindrical dielectric gratings (DGs) and electromagnetic wave scattering from multiplayer DGs are investigated. The DG characteristics are calculated using numerical-analytical solution of integral equations (IEs).