Orbital Contributions at the Strong-Field limit

hi there exists the respective three-fold spatial degeneracies 

For the cubic-field (octahedral or tetrahedral) subshells g(g), there is spatial degeneracy for e(g) but not for eQy Nevertheless, neither of these configurations give rise to an orbital contribution to the magnetic moment. The conditions for orbital contributions to arise in strong-field configurations are that the orbitals must be 

Orbital angular momentum associated with the dj, and dy orbitals as a pair. 

The orbitals d. and dy can be expressed in terms of the complex forms di and whose angular parts are given by the spherical harmonics and respectively. The matrix of orbital angular momentum about the z axis in the complex basis is 

---