The computation of the spin-orbit coupling contributions implemented in CERES includes five steps: (i) evaluation and storage of the Cholesky representation for the 2e-SOC integrals as presented in ref. , (ii) evaluation of F I ab in eq. ( ) by direct contraction of the inactive density matrix with the Cholesky vectors (eq. ( )) and transformation on the molecular basis (iii) transformation of the Cholesky vectors on the molecular basis within the chosen active space and construction of the 2e-SOC integrals (iv) evaluation of the effective one-electron integrals in eq. ( ) via eq. ( ) (v) update and diagonalization of the CI-SOC matrix.