By defining this alternative chiroptical response tensor, one can easily compute the specific rotation for light traveling in an arbitrary direction relative to the oriented material . The evaluation of polarizability tensors using the sumover-states formulas in Eqs. 2-5 is impractical, and linear response theory is used instead. This requires the evaluation of a perturbed density as the solution of coupled-perturbed Kohn-Sham (CPKS) equations for one of the multipole moments, which is then contracted with the integrals of the paired perturbation for a specific tensor. For PBC calculations, we use the CPKS implementation for the length gauge electric dipole µ L from Scuseria and coworkers. Therefore, extending β and A (and consequently B) to periodic systems reduces to the problem of defining µ V , m, and Θ operators that are translation invariant (i.e., consistent with periodic boundary conditions) that can be evaluated over an AO basis. The evaluation of µ V is trivial, as it amounts to a Fourier transform to k-space of the real-space ∇ r integrals over the central and replicated cells, which already have the proper translational symmetry. The only complication is the extension of the periodic CPKS algorithm to handle anti-Hermitian matrices that are stored in lower-triangular form. For the derivation of the equations for m, and Θ V , we follow the approach used for µ L . This is a different approach than that used in Ref. 37 for m, although the final expression is the same. Once the PBC dipole integrals are available, it is sufficient to evaluate the perturbed density for the dipole operator P µ (with either choice of gauge) and contract it with the magnetic dipole integrals to form β and with the electric quadrupole integrals to form A.