where ψ 0 and ψ j represent the ground and jth excited state wavefunctions, µ α is the electric dipole operator, m β is the magnetic dipole operator, ω j0 is the jth excitation frequency, and ω is the frequency of the impinging radiation. Greek letter indexes represent Cartesian coordinates. This sum-over-state (SOS) formulation of β is not convenient for fast calculations, which are commonly performed using linear response (LR) theory .