In this work, we report the derivation and implementation at DFT level of the magnetic dipole and electric quadrupole integrals for PBC calculations. These integrals are used to evaluate the mixed polarizability tensors β and A that form the full OR tensor B for oriented systems. The implementation is tested in section IV, where we show that the B tensor is origin invariant, see Tables I-II. We also show that the PBC calculations match the results for model cluster calculations for all tensor elements, see Figures . A preliminary analysis indicates that the choice of density functional, basis set, and gauge affects the tensor values in decreasing order, similar to molecular calculations. However, while the use of diffuse functions is necessary to obtain accurate results for molecules, it may be problematic in periodic systems, and this aspect should be investigated more thoroughly. Finally, a comparison with experimental measurements of OR for the tartaric acid crystal shows reasonable agreement considering the level of theory employed. These simulations highlight the importance of comparing the full B tensor to experimental data rather than the β tensor alone. This work now offers the opportunity to study the OR of chiral crystalline materials with general purpose quantum chemistry methods, which in turn may help us understand the role of intermolecular interactions on this sensitive electronic property.