Site projection operator and its application: electronic structures and stability rules of tetrahedral fullerenes

Abstract

For a quantized subgroup of the symmetry group of the Hamiltonian, a site projection operator is defined to produce symmetry-adapted wave functions from the functions with the symmetry of the subgroup. The method, which is based on the site projection operator and proposed to factorize the single-particle Hamiltonian into irreducible representations of symmetry groups of π-conjugate systems, was used to study the electronic structures and deduce the stability rules for tetrahedral fullerenes. From the calculated results, a conclusion is derived, as a special case of the leapfrog rule, that a tetrahedral fullerene without atoms on three-fold axes must be the leapfrog of another fullerene with the same symmetry and has a closed-shell electronic structure.