LG(OI) Exp. The choice of gauge is less important than that of the level of theory as the MVG and LG(OI) results are very close to each other. This is also confirmed by the polar plots representation of the OR tensors in Figure -5. In these plots, the unit cell was rotated such that the coordinate system matches the orientation of the tensor, and z coincides with the optic axis. The difference in geometrical orientation between MVG and LG(OI) is small, barely detectable in the figures. The polar plots are also virtually indistinguishable between figures. It is interesting to emphasize that the plots of the β and A contributions to B were scaled down by a factor of 10 compared to the full B plot, to fit within the same picture frame. These results are also in reasonable agreement with those reported in Rérat et al. , which were obtained with the same basis set but a different functional (PBE0). A direct comparison is only possible with the MVG birefringence (δ zx = 0.0916, δ yx = 0.0256 37 ): the better agreement with experiment suggests that long-range exact exchange (absent in HSE06) may play an important role in OR calculations of solids. The angle 2θ is only reported in Ref. 37 as an average value across multiple calculations with different choices of gauge and with/without orbital relaxation (70 ○ ± 10 ○ ), but it is in the same range as the values we report in Table deg/mm, because it is in general origin dependent. Furthermore, it is stated in Ref. 37 that the contribution of the A tensor along the optic axis is zero. This is not the case, because the contributions of A to the diagonal of B are of the type A α,βγ , with α ≠ β ≠ γ (see Eq. 7), and the operators μα and Θβγ can belong to the same irreducible representation. This is also confirmed visually in Therefore, the good agreement with the measured OR reported in Ref. 37 may be fortuitous, and only the full B tensor should be compared directly to experiment. A final comment is warranted for the yx birefringence when the z and optic axes are aligned, which is not as close to zero as it should be even accounting for the numerical precision of the calculations (δ oa yx = -0.0041 for MVG in Table ). The discrepancy is due to the fact the linear relationship between the dielectric tensor and the α tensor in Eq. 36 is only approximate. The Clausius-Mossotti equation would be more accurate, but it is non-linear and more difficult to evaluate. By trial and error we found that the angle that sets δ oa yx = 0 for MVG is 2θ = 62.2 ○ , rather than 66.5 ○ as in the table. However, with this optimal angle the OR along the optic axis is only changed by 0.1 deg/mm (from -5.1 to -5.2 deg/mm). Therefore, this error is negligible compared to other approximations.