Knowledge Bank

The interchange symmetry concept for molecules and crystals introduced in the 1965 Symposium has been generalized. 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 the 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 is for the classification of eigenstates and the interpretation of spectroscopic data encountered in investigations of molecular crystals. The existence of n-1 pure, nonequivalent, interchange elements in ideal crystals has been 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 have been established and related to crystal splittings, intermolecular coupling constants (including sings), and selection rules (including $k\ne 0$). Examples for application are: the benzene molecule (H""{u}ckel theory); the benzene, naphthalene, and anthracene crystals (exciton couplings and signs); methyl-halides, $N2,CO$, and $CO2$ crystals (interchange splittings); and the $CS2$ crystal (ground and distorted excited states). Nonhexagonal benzene and its energy splittings is an example for a separate treatment, using the interchange concept, for isotopically substituted molecules that get distorted in excited states and/or in condensed phases like matrices and crystals.