Symmorphy transformations and operators in the repeat spaceX r(q) for additivity problems

A theoretical framework has been presented, which links two diverse molecular problems: the study of symmorphy transformations of molecular shape analysis (further developed in the present paper) and that of additivity of the zero-point vibrational energy of hydrocarbons and the total pi-electron energy of alternant hydrocarbons. The linkage, using fundamental tools of (general) topology and algebra, makes it possible to mutually introduce the methodologies used in fields hitherto separately investigated. By establishing this linkage, topological patterns described by symmorphy groups can be treated by the algebraic methods developed for the above additivity problems. The linkage also brings forth new techniques of topologizing the repeat spaceX _r(q) for the additivity problems. Moreover, this connection paves the way to analyzing molecular homologous series and their properties by means of associating sequences of molecular structures with elements of a repeat space equipped with a topology.On leave from: Institute for Fundamental Chemistry, 34-4 Nishihiraki-cho, Takano, Sakyo-ku, Kyoto 606, Japan.