Combinatorics of chiral and stereo isomers of substituted nanotubes: applications of Eulerian character indices and comparison with bondonic formalism

Abstract

Combinatorial techniques are outlined through generalization Sheehan’s version of Pόlya’s theorem extended to all irreducible representations of the dihedral point group aimed at applications to nanotube enumerations. Furthermore we invoke the Euler Totem function for a cylindrical nanotube of any length and circumference. General expressions for the generalized character cycle indices are derived in order to enumerate chiral, achiral and stereo isomers of polysubstituted nanotube of any length and circumference. Remarkable connection with bondonic theory and its implications in potential tree enumeration is also originally initiated here. We have constructed the combinatorial enumeration tables for heterosubstituted nanotubes up to 100 vertices on the circular cross section and up to 100 tube length. The heterosubstituted nanotubes composed of carbon and nitrogen or tubes made of boron and nitrogen are of considerable interest due to their important optical properties, energy storage and in applications as high energy novel materials. Thus the developed techniques could have applications in the development of these materials and in the generation of combinatorial libraries of heteronanotubes.