where ω if is the transition frequency and σ is the broadening parameter and they are expressed in the same units, and R if n is expressed in cgs units of 10 -40 erg esu cm G -1 . A vibrational progression can be included explicitly with techniques similar to those used for molecules. The review above shows that simulations of ECD and CPL require the evaluation of transition energies and moments for extended systems. Currently, the most general formulation employs PBCs. However, the electric and magnetic dipole operators do not have the correct translational symmetry. An approximate form of the electronic electric dipole operator (µ = -er) that satisfies PBCs has been introduced a few decades ago to compute electric dipole polarizability tensors: r