Application of angular momentum theory to constructing basis functions of irreducible representations of icosahedral group

A new method based on angular momentum theory was proposed to construct the basis functions of the irreducible representations (IRs) of point groups. The transformation coefficients, i.e., coefficients S, are the components of the eigenvectors of some Hermitian matrices, and can be made as real numbers for all pure rotation point groups. The general formula for coefficient S was deduced, and applied to constructing the basis functions of single-valued irreducible representations of icosahedral group from the spherical harmonics with angular momentum jless than or equal to7.