The introduction of SOC to DFT theory has been done either by variational or perturbative approaches. Although there have been significant efforts of implementing the relativistic full four-component (4c) Dirac-Kohn-Sham formalism such as the recent linear damped response (LD)-TDDFT, the four-component relativistic Hamiltonian is impractical for large systems. On the other hand, various transformation schemes, e.g., Pauli, Douglas-Kroll, elimination of small components, infinite-order two-component, etc., are available to reduce the relativistic Hamiltonian to a two-component (2c) form, which can be separated to a spin-independent ( Ĥ0 ) and a spin-dependent part. ( ĤSOC )