In MRSF, the electronic ground and excited states are obtained from the poles of a novel mixed reference (MR) within the linear response (LR) regime. With the help of a novel spinor-like transformation, a hypothetical single reference is constructed from the M S = ±1 components of the restricted open-shell KS determinant, expanding its response space significantly. Consequently, it nearly eliminates the problematic spin-contamination pitfalls of SF-TDDFT. It also considers the singlet ground state and other excited states on the same footing, which not only eliminates the general topological problem 8 of CI 10 by TDDFT but also allows to study open-shell ground singlet states. 14 Furthermore, the one-electron spin-flip excitation from the mixed triplet reference includes the HOMO-to-LUMO doubly excited configuration, which is the main ingredient to properly account for the 2 1 A - g dark states of s-trans-butadiene and s-trans-hexatriene. 9 Thus, MRSF gives a balanced treatment of dynamic and nondynamic electron correlations for both ground and excited states, with the convenience of single determinant orbital optimization. These advantages allow the MRSF to overcome the major limitations of the conventional TDDFT variants, while reliably reproducing the results of the more expensive multi-reference ab initio wave function theories. In a series of studies, 8,12,14-22 it has been demonstrated that the MRSF approach can also yield accurate nonadiabatic coupling matrix elements (NACMEs), enabling reliable non-adiabatic molecular dynamics (NAMD) simulations, a topologically correct description of conical intersections, 8, and accurate values of singlet-triplet gaps. This method has also been successfully used in designing high-performance optoelectronic materials. Given the efficiency and accuracy of the MRSF for both ground and excited states, it is imperative to introduce spin-orbit coupling (SOC) functionality in this scheme for expanding its applicabilities to intersystem crossing (ISC), which is the main subject of the present work. In the following, the basic spin-orbit coupling formulations of MRSF and its applications in some real systems are presented in order.