Since the origin dependent terms for SMVG-M ia and SMVG-E ia are equal in magnitude but opposite in sign, they cancel in the average, leaving SAvg ia origin invariant. SAvg ia still satisfies Eq. 8, which means it can still be used as an interpretive tool to understand which occupied to virtual orbital transitions are driving the OR. However, while SMVG-M ia and SMVG-E ia each have associated electric/magnetic dipole and perturbed density vectors describing the flow of charge during the i → a transition, see Eq. 9, SAvg ia does not have an associated set of vectors. This is because simply averaging the MVG-M and MVG-E electric/magnetic vectors and taking their dot product is not equivalent to averaging the MVG-M and MVG-E dot products from Eqs. 7b and d, as is done in Eq. 12.