In the investigation of the optical and magnetic properties of the semiconductors containing transition-metal ions, the one-electron orbital cannot be treated with a pure d orbital because of a strong covalence. This paper presents the energy matrix of the d* 8 and d* 2 (d* means a modified d function͒ system, in which the covalence is described by two covalent factors. The differences between the matrix diagonal elements of the t 2 m e n term of the d* 8 system and the t 2 6Ϫm e 4Ϫn term of the d* 2 system vary with m and n. The d N electron system can be explained with the d 10ϪN hole system because the difference between the energy matrix of the d N and d 10ϪN systems has a fixed value. However, this kind of simple relation does not exist for the d* N and d* 10ϪN systems when the covalence is considered. A numerical calculation shows that the variation of the energy levels with the covalence for Ni 2ϩ in the d* 8 electron system is larger than that in the d* 2 hole system. The calculated energy levels obtained from the d* 8 matrix are in good agreement with the experimental data of the Ni 2ϩ ion for ZnS:Ni and ZnSe:Ni. This suggests that the d* 8 electron system instead of the d* 2 hole system should be used in the investigation of optical and magnetic properties of semiconductor containing Ni 2ϩ ions. ͓S0163-1829͑99͒05904-4͔