Interchange Symmetry. I. Molecules, Crystals, and Excitons

Abstract

The interchange-symmetry concept for molecules and crystals is introduced. In a molecule it is the minimal symmetry establishing the physical equivalence among a given set of its constituent fragments (nuclei or collections thereof). In a crystal it is a minimal symmetry establishing the physical equivalence among a set of constituents (atoms or molecules) within the unit cell. The chief application of the interchange symmetry in this paper is for the classification of eigenstates and the interpretation of spectroscopic data encountered in investigations of molecular crystals. The existence of n-1 pure, inequivalent, interchange elements in ideal crystals is proven group theoretically, where n is the number of molecules or atoms per primitive unit cell. The relations among interchange symmetries and interchange groups, site groups, unit cell groups, translation groups and space groups are discussed. These are related to crystal splittings, intermolecular coupling constants (including signs), selection rules and exciton theory (including k≠0). Examples: the benzene molecule (Höckel theory), the benzene, naphthalene, and anthracene crystals (exciton coupling constants and their signs), methyl halides, N2, CO, and CO2 crystals (interchange splittings), and the CS2 crystal (ground and distorted excited state). Nonhexagonal benzene and its energy splittings is the example in a separate chapter on isotopically substituted molecules that get distorted in excited states and/or in condensed phases like matrices and crystals.