The same model system is used to compare PBC and large molecular cluster calculations, which helps to verify that the implementation is correct. The SVWN5/cc-pVQZ model chemistry was employed as in Ref. 37, and the PBC calculation used a 1000 k-point mesh. We consider two molecular cluster sizes with 39 and 37 H 2 O 2 units. The "unit cell" tensors are then obtained as the average of the 39-unit calculation and as the averaged difference between the 39 and 37-unit calculations. For this comparison, using a geometry with the origin in the center of the O-O bond is convenient because the unit cell in the PBC calculation matches the central unit in the cluster calculations. The results for the fully relaxed density with MVG and LG(OI) are shown in Figures and, respectively. The figures include the tensor elements and the spatially averaged trace (all in a.u.) for the full B tensor as well as for the β and A contributions. The isotropic OR values (in units of deg L dm -1 mol -1 ) are reported in Table III and all the tensor elements are reported in Tables S2-S4 of the SI. LG(OI). Data are reported for the periodic chain (PBC), for the average of the 39-unit molecular cluster (39/39), and for the averaged difference between the 39 and 37-unit molecular clusters [(39-37)/2]. The data in Figures show very good agreement between the molecular cluster and PBC calculations for all the elements of the B tensor, irrespective of the choice of gauge. The largest difference is found for the xz element: 9-11% for MVG and 15-17% for LG(OI). The discrepancy is likely due simultaneously to the limited size of the cluster models and the lack of the ∇ k P µ terms in the PBC expressions in Eqs. 34 and 35, respectively. In this case, these effects are small but they need to be investigated further. The MVG and LG(OI) results also match each other for the isotropic OR (see the Trace values in the figures and the results in Table ). This indicates that this basis set is close to completeness for this system and the calculations approach gauge invariance. The PBC-MVG value in Table is in very good agreement with the value reported in Ref. 37: 36.1 deg L dm -1 mol -1 (the small discrepancy is due to the extreme sensitivity of this property to unavoidable differences in numerical thresholds between different implementations). The differences in the individual elements of the B tensor between MVG and LG(OI) is due to the fact the SVD transformation in the latter corresponds to a rotation of the system; 3 repeating the MVG calculation at this rotated geometry would lead to matching elements. More importantly, the molecular cluster and PBC calculations do not match each other for the β and A contributions to B, as shown in panels b) and c) of Figures . The yy and zz elements of the β contribution are much smaller in the PBC case compared to the molecular cluster case; simultaneously, the corresponding elements of the A contribution have the opposite sign. It is only in the full B tensor that these contributions combine properly to provide the same picture.