By means of the single electron basis vectors marched for group chain [(O s
uperset of D(4)superset of C-4) X SU (2)], the Slater functions of the dire
ct product for single electron can be used as the basis vectors of the irre
ducible represents of f(N) ions. The Coulomb, Casimir, spin-orbit coupling
and crystal field interacting matrix elements in tetragonal field have been
described.