Effects of quadrupole moments. To understand the consequences of truncating the moment expansion in eq (13) for MPM at the dipole (p-truncation) level, we compare the predictions with results obtained including quadrupolar terms (Q-truncation). The number of unknowns, and therefore the computational expense, for MPM increases with the number of included moments, so it is advantageous to include the fewest number of moments required to capture the physics of interest. For an isolated pair of closely-spaced particles with large |α| (e.g., silver) oriented parallel to the E 0 polarization of light, a very large number of moments must be included to accurately describe the extinction spectrum. However, truncation at the dipole level was sufficiently accurate to describe an isotropic and disordered coresatellite configuration of closely-spaced particles. The optimal truncation level depends Comparison between MPM predictions with p-and Q-truncations for the extinction spectra of Drude hard-sphere dispersions shows that the inclusion of quadrupoles can result in quantitative, but not qualitative, differences (Figure ). At low η, there are no significant quantitative differences between the two truncation levels. As η increases, the p-and Q-level extinction lineshapes remain qualitatively similar, but quadrupoles change the resonant frequencies and spectral linewidths. Including quadrupoles redshifts ω res to lower frequency, broadens the linewidth W , and increases the deviation of MPM from mean-field predictions.