The difference between the two definitions is based on which integrals are contracted first with the response matrix: In Eq. 7a, the response matrix is contracted with the magnetic dipole integrals (MVG-M) to form the perturbed density P M,ω ia in Eq. 7b; conversely, in Eq. 7c, the response matrix is contracted with the electric dipole integrals (MVG-E) to form the perturbed density P E,ω ia in Eq. 7d. The expressions for the static frequency S0 ia are the same, but with D ω replaced by D 0 (the leading factor of ω is retained). Eq. 7 is equivalent to the expressions for MVG-M and MVG-E in Eq. 8 of Ref. 9; we write them here in terms of the response matrix as this makes it easier to present how the origin dependence emerges (and can be removed). We have previously shown that, in general, SMVG-M ia ≠ SMVG-E ia ; however, the Sia values for each choice of perturbation are associated with the same physical process and the relative contribution of this process to the observed OR is roughly the same . A feature of the Sia definition in Eq. 7 is that its values can be visualized as the dot product of two vectors that represent charge transfer (µ) and charge rotation (m). These vectors can be visualized and superimposed to the molecular structure to determine what types of one-electron (1e) transition contribute the most to the OR. This vector analysis holds for the MVG approach because one can define an MVG perturbed density vector that is dotted with the vector of the paired perturbation