One possible solution, which we adopt in this work, is to antisymmetrize the h SOM F,2e z integrals with respect to the αα and ββ parts and take a trace triplet transition density matrix for SOCs. This operation eliminates the unphysical contribution from the singlet transition densities. By doing so, one can take the h SOM F,2e z integrals out of parenthesis, making the form of the SOMF expression, Eq. ( ), the same as for the one-electron part, Eq. ( ).