where i/f represent the initial and final electronic states with transition frequency ω if , and Greek letters refer to Cartesian coordinates (repeated indexes imply a summation over all values). For ECD, i is the ground state and f is an excited state, while for CPL i is typically the first excited state (because of Kasha's rule) and f is the ground state. However, given the symmetry of the tensors, the CPL rotatory strength is the same as that for the ECD from the ground to the first excited state at the optimized geometry of the first excited state. The transition moment between the initial and final states for the electric dipole is µ if α = ⟨i|μ α |f ⟩, and similarly for the magnetic dipole m if α and the electric quadrupole Θ if δα . For a beam along a given direction n, the quantity corresponding to the measured observable is: 31