A local approach based on an $\mathrm{sp}$-electron tight-binding Hamiltonian is used to calculate the electronic properties of stable fullerenelike arrangements exhibiting high topologies (from genus 5 to genus 21). The structures studied consist of closed networks possessing only hexagons and heptagons, no pentagonal rings, no positive Gaussian curvature, and no dangling bonds. These structures exhibit closed interconnected shells with channels, and may be regarded as finite zeolites. Remarkably, an overall local metallic behavior is found which depends upon curvature, symmetry, and topology (number of heptagons). The role of nonagonal rings of carbon is also studied, and potential applications of these structures are discussed.

• Received 5 June 1997

DOI:https://doi.org/10.1103/PhysRevB.56.12143