Ab initio calculations on icosahedral molecules: I. The implementation of symmetry reduction in calculation exemplified by B12H 2−12

The symmetry reduction of icosahedral group has been carried out by means of projective operator method. The irreducible bases and matrices were tabulated for generators C2, C3 and C5 which would be sufficient for the implementation of ab initio or other computations in terms of symmetry-adapted linear combinations of atomic orbitals. As an initial application, the borane dianion B12H2-12 with Ih symmetry has been calculated with a flexible s, p set, (9s5p/4s) being contracted into [3s2p/2s]. The electron counting rule was then analyzed.