(2) where µ V = -p is the electric dipole operator in the velocity gauge and m = -1 2 (r×p) is the magnetic dipole operator. Greek indices denote Cartesian coordinates, ω is the frequency of the incident electromagnetic radiation while |ψ j ⟩ and ω j are the j th excited state wave function and excitation frequency, respectively. Throughout, we use atomic units unless otherwise specified and denote tensors over Cartesian indices using bold font and matrices over an orbital basis with an underline. This definition is valid for non-resonant optical activity (ω j / ≈ ω) calculations; resonant optical activity is discussed in greater detail elsewhere. The sum-over-states expression for the β tensor in Eq. 2 is impractical for real calculations because the series is slowly converging and it requires the evaluations of hundreds of excited states. Therefore, this tensor is efficiently evaluated through linear response theory as