Spectra of Conic Carbon Radicals

Abstract

Conic carbon radicals with non-trivial automorphism groups are topologically possible when the curvature originates from 1, 3 or 5 pentagons in the otherwise hexagonal graphene sheet. By splitting determinants of quotient graphs, we determine the bonding nature of the last occupied and first unoccupied Huckel orbitals of the radicals constituting the three infinite series with the most plausible topologies. Each member of the series with three pentagons at the tip has one electron in the first anti-bonding orbital, each member of the series with one or five pentagons at the tip has one vacancy in the last bonding orbital, and none of the radicals have any un-bonding orbital. Within the limits of the Huckel model, this implies, respectively, stable conic cations and anions. The quotient graphs also give the collected Huckel energy for each of the one-dimensional irreducible representations of the point groups.