As discussed in the Introduction, approximate calculations with incomplete basis sets lead to an unphysical static limit in the velocity gauge formulation, which is explicitly calculated and subtracted out in the MVG method, although the results are intrinsically origin invariant. Conversely, approximate LG calculations lead to origin-dependent OR values; these can be made origin-independent using GIAOs with variational methods. However, GIAOs are not useful with methods where the orbital response is not included in the LR calculation, as for standard CC methods. Alternatively, origin independence can be achieved with the LG(OI) approach, which works for variational and non-variational methods. The origin dependence of the β tensor in the LG is due to the off-diagonal elements of the mixed length-velocity gauge electric dipole-electric dipole polarizability tensor α (L,V ) , which is non-symmetric for approximate methods. In LG(OI), α (L,V ) is diagonalized with a singular value decomposition (SVD):