where |Φ i ⟩ and |Φ f ⟩ are the wavefunctions of the initial and final vibronic states, respectively, ω is the frequency of the external radiation. Ĥ′ denotes the perturbation and can be written as Ĥ′ = -⃗ µ • ⃗ f + TN + ĤSO , where the first, second and third operators correspond to the matter-field interaction, the nuclear kinetic energy, and spin-orbit interaction, respectively.