  We first develop a descriptor-based representation of atomic environments by
devising two local similarity indices defined from an atom-partitioned
quantum-chemical descriptor. Then, we employ this representation to explore the
size-, shape- and composition-dependent nanocrystal energetics. For this
purpose, we utilize an energy difference {\mu} that is related to the atomic
chemical potential, which enables one to characterize energetic
heterogeneities. Employing first-principles calculations based on the density
functional theory for a set of database systems, namely unary atomic clusters
in the shape of regular polyhedra and the bulk solids of C, Si, Pd and Pt, we
explore the correlations between the energy difference {\mu} and similarity
indices. We find that there exists an interconnection between nanocrystal
energetics and quantum similarity measures. Accordingly, we develop a means for
computing total energy differences from the similarity indices via
interpolation, and utilize a test set comprising a variety of unary
nanocrystals and binary nanoalloys/nanocompounds for validation. Our findings
indicate that the similarity-based energies could be utilized in computer-aided
design of nanoparticles.
