where H EOM 0 is a diagonal matrix composed of EOM-EA energies and H BP is the matrix of the Breit-Pauli Hamiltonian in the basis of the EOM-EA states. The resulting energies E SOC are energies of the SOC-perturbed EOM states and matrix U contains the respective eigenstates. This matrix can be used to obtain properties of the SO-perturbed states, such as permanent and transition dipole moments: