New Approaches to Degenerate Interconversions of Organic Structures: 1. Levels of Structural Degeneracy and Computer-aided Search for Degenerate Rearrangements*

The general methodology of systematic search for degenerate interconversions must be based on a certain hierarchy of degeneracy. The levels and sublevels of the proposed hierarchy are represented by topological and structural types and subtypes of degeneracy, which correspond to specific equations and to graphs identifying them. Graph operations that enable an efficient search for arbitrary types of organic reactions are formulated, and problems specific to generation of degenerate transformations are considered. In conclusion, results of computer-aided search (using the ARGENT–1 software) for new heteroderivatives and structural analogs of the Cope reaction are discussed. Many of the rearrangements thus found (especially [3,3]-shifts in cations and anions, which have not been studied to date) can be subjects of experimental investigations

Continuous symmetry of C60 fullerene and its derivatives

Conventionally, the Ih symmetry of fullerene C60 is accepted which is supported by numerous calculations. However, this conclusion results from the consideration of the molecule electron system, of its odd electrons in particular, in a close-shell approximation without taking the electron spin into account. Passing to the open-shell approximation has lead to both the energy and the symmetry lowering up to Ci. Seemingly contradicting to a high-symmetry pattern of experimental recording, particularly concerning the molecule electronic spectra, the finding is considered in the current paper from the continuous symmetry viewpoint. Exploiting both continuous symmetry measure and continuous symmetry content, was shown that formal Ci symmetry of the molecule is by 99.99% Ih. A similar continuous symmetry analysis of the fullerene monoderivatives gives a reasonable explanation of a large variety of their optical spectra patterns within the framework of the same C1 formal symmetry exhibiting a strong stability of the C60 skeleton.Comment: 11 pages. 5 figures. 6 table