Homology groups, symmetry representations and polyhedral clusters
Division of Quantum Chemistry,
University of Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium
2 Department of Chemistry, University of Exeter, Stocker Road, Exeter, EX4 4QD UK
Accepted: 12 November 1996
Physical properties of cages and clusters obey symmetry rules that are extensions of the celebrated Euler-Poincaré theorem on polyhedra. A connection is established between this result and a fundamental topological relationship in the theory of homology groups. The connection allows us to assign symmetry representations to physically relevant topological invariants. The results are illustrated by a derivation of the symmetries of the low-lying empty orbitals in leapfrog fullerenes.
PACS: 02.10.Ws – Category theory and homological algebra / 36.40.-c – Atomic and molecular clusters
© EDP Sciences, 1996