“…where the sum goes over the N exc excited states, {c k } are the electronic wave functions of the kth excited state, and c 0 is the electronic ground state wave function. In eqn (4), the terms f À and g + are defined in terms of the energy difference between the ground-state and excited state, o k0 , the frequency of incident light, o, and the life-time of the excitation G. 15,18 Electric dipole moment integrals, for non-periodic calculations, and bulk polarization integrals, for periodic calculations, are not only needed for the calculation of the polarizability, [19][20][21][22] but also for the simulation of vibrational and electronic spectra such as IR spectra, 13,23,24 Vibrational Circular Dichroism (VCD) spectra, 25,26 Raman spectra, 17,[27][28][29][30][31][32] and Raman Optical Activity (ROA) spectra, 15,33 sum frequency generation spectra, 34,35 and two-dimensional IR spectroscopy. 36 For the evaluation of properties that are related to the electric dipole moment and to the polarization, a light-matter interaction Hamiltonian is usually applied.…”