The deviation of QM/DIM results from full QM results for small metal clusters, however, can be partially resolved. By incorporating the term that incorporates the first-order nonlinear polarizability of Au clusters and the dipole (or electric field) derivatives of the probe molecule, we can capture the non-negligible three-virtual-photon process of Raman scattering within this hybrid method. With this correction, the Raman spectra for the short-distance configurations of the Py-Au clusters calculated using QM/DIM are improved. We thus suggest that the atomic (distributed) hyperpolarizability of metal atoms should be parameterized within the hybrid QM/DIM method to enable it to describe Raman scat-FIG. . Corrected Raman spectrum of Py-Au 18 -V (3 Å) complex by QM/DIM with PBE0/6-31+G(d)/LanL2DZ. (a-c) variations of QM/DIM method use Eq. ( ) with different distance R AB while (d) and (e) correspond to Eq. ( ) without and with QM induced fields, respectively. TABLE V. Charge populations on the pyridine molecule within the different Py-Au complexes calculated from the Mulliken, ChElPG, ESP, and FBH tering spectra more accurately. Besides, as investigated by Schatz and the coworker, the other high-order properties such as dipole-quadrupole and dipole-magnetic-dipole polarizabilities may also play a rule in the Raman intensity if the electric field derivatives are comparable with the field strength.