  It is a generally accepted idea that the particle size distribution strongly
affects the optical spectra of colloidal plasmonic nanoparticles. It is often
quoted as one of the main reasons while explaining the mismatch between the
theoretical and experimental optical spectra of such nanoparticles. In this
work, these aspects are critically analyzed by means of a bottom up statistical
approach that considers variables such as mean, standard deviation and skewness
of the nanoparticle size distribution independently from one another. By
assuming normal and log-normal distributions of the particle size, the effect
of the statistical parameters on the Mie analytical optical spectra of
colloidal nanoparticles was studied. The effect of morphology was also studied
numerically in order to understand to what extent it can play a role. It is our
finding that the particle polydispersity, skewness and surface morphology in
fact only weakly impact the optical spectra. While, the selection of suitable
optical constants with regard to the crystallinity of the nanoparticles is a
far more influential factor for correctly predicting both the plasmon band
position and the plasmon bandwidth in theoretical simulations of the optical
spectra. It is shown that the mean particle size can be correctly estimated
directly from the plasmon band position, as it is the mean that determines the
resonance wavelength. The standard deviation can on the other hand be estimated
from the intensity distribution data obtained from dynamic light scattering
experiments. The results reported herein clear the ambiguity around particle
size distribution and optical response of colloidal plasmonic nanoparticles.
