While the total OR computed in the modified velocity gauge is origin invariant regardless of the perturbation used, this is not the case for the individual Sia values, even in the limit of an exact calculation using a complete basis set. The origin dependence of Sia for each choice of perturbation follows directly from that of the full β tensor, which is detailed for instance in Refs. 11,25,26. For a shifted origin O ′ = O + d, displaced by a vector d, the Sia origin dependence can be expressed as