As we are interested in the polarization dependence in both static and dynamical RIXS spectra, we extract the transition dipole moments between |0 , |i and |f , which denotes the electronic ground state, the core-excited intermediate state and final valence-excited states respectively, and based on these transition dipole moments µ 0i = 0| r|i and µ if = i| r|f , we computed the po-larization dependent RIXS.