Analytical irreducible representation bases of the single and double icosahedral groups and their applications

An equivalent basis of icosahedral molecules is introduced in which the bas is functions can be transformed under the operations in the icosahedral gro up (Ih) In this equivalent basis, the irreducible representation basis (IRB ) of Ih, including the double-valued IRE of I-h(*), is deduced analytically based on the method introduced in the literature [J. Comput. Chem. 17, 851 (1996)]. Therefore the concepts of symmetry-matrix and symmetry-supermatri x can be used in the single- and multiconfiguration self-consistent field m ethods (including relativistic effects) to reduce the storage of two-electr on integrals and calculations of Fock matrix during iterations by a factor of ca. 10,000. In addition, the equivalent basis of Ih can also be used to reduce the calculations of atoms and representations of rank greater than o r equal to 2 tensors. (C) 2000 John Wiley & Sons, Inc.