In brief, LR replaces the evaluation of the excited states in Eq. 2 with the solution of response equations for one of the multipole perturbations; this produces a perturbed density in the molecular orbital (MO) or atomic orbital (AO) basis, which is then contracted with the MO or AO integrals for the other multipole operator. For variational methods like Hartree-Fock (HF) or DFT, the choice of perturbation for the response equation is immaterial as either choice leads to the same tensor values. For nonvariational methods like CC theory, the symmetric formulation of the response function requires the solution of the response equations for both perturbations while the non-symmetric formulation requires only one perturbation but two sets of perturbed amplitudes. Therefore, both CC-LR formulations are computationally equivalent for the evaluation of β.