In the investigation of optical and magnetic properties of semimagnetic semi-conductors containing transition-metal ions, one electronic d-orbital should not be treated as a pure d-orbit, instead of a mixed orbit t2g or eg because of strong covalence. In consequently, two covalent factors Nt and Ne should be introduced according to it. The energy matrix constructed on the mixed wave functions and including the covalent factors is called generalized energy matrix. We constructed the generalized energy matrices (45×45) for the d2/d8 electron systems. In the generalized forms, Racah electrostatic parameter A is no longer an additive constant, and d8 electron system is not identical to d2 hole system because their energy matrices are different. Furthermore, though Nt and Ne are the two different covalent factors belonging to different wave functions, their difference in numerical values should be small, because Racah electrostatic parameter A plays a great role in the calculation of energy levels when the covalence effect is considered. It means that the conventional BCΔ scheme is a good approximation. These conclusions are then extended to the application of the d-d transitions of ZnS:Ni2+, the calculated results agree well with the experimental values.