  A quantitative descriptor of local atomic environments is often required for
the analysis of atomistic data. Descriptors of the local atomic environment
ideally provide physically and chemically intuitive insight. This requires
descriptors that are low-dimensional representations of the interplay between
atomic geometry and electronic bond formation. The moments of the local density
of states (DOS) relate the atomic structure to the electronic structure and
bond chemistry. This makes it possible to construct electronic structure based
descriptors of the local atomic environment that have an immediate relation to
the binding energy. We show that a low-dimensional moments-descriptor is
sufficient as the lowest moments, calculated from the closest atomic
neighborhood, carry the largest contributions to the local bond energy. Here,
we construct moments-descriptors that project the space of local atomic
environments on a 2-D map. We discuss in detail the separation of various
atomic environments and their connections in the map. The distances in the map
may be related to energy differences between local atomic environments as we
show by analytic considerations based on analytic bond-order potentials (BOP)
and by numerical assessment using TB and density-functional theory
calculations. Possible applications of the proposed moments-descriptors include
the classification of local atomic environments in molecular-dynamic
simulations, the selection of structure sets for developing and testing
interatomic potentials, as well as the construction of descriptors for
machine-learning applications.
