Abstract: It is proved that by employing the ten spin-d-orbitals matched for group chain (SO₃⊃D_n⊃C_n) ×SU(2), the Slater functions of the direct product for the single electron can be used as the basic vectors of the irreducible representations of dⁿ ion or the direct summation representations of two one-dimensional representation.The related matrix element expressions and the calculation of EPRparameters are systematically derived to realize computation on a mini-computer for all dNion in pentagonal field.

Key words: dⁿ Configuration, Pentagonal ligand field, Basic vectors of spinor