where cdf(ω 0 ) is the fraction of particles with resonant frequency ω res,i ≥ ω 0 . The resonant frequency distributions predicted for our model nanoparticles using MPM systematically redshift to lower frequencies as structuring is enhanced due to either increases in η or U 0 (Figure ). The distribution broadens with increasing U 0 and also nonmonotonically with increasing η, attaining the widest distribution of resonant frequencies at intermediate packing fractions. Similarly, including quadrupoles in the MPM calculation (Figure ) redshifts and broadens the particle-level resonance frequency distribution. These trends are identical to those observed for the ensemble extinction spectrum. In fact, as we discuss further below, the distribution of individual particle resonant frequencies determines the far-field optical properties of the ensemble.