In
recent years, significant progress has been made in the development
of machine learning potentials (MLPs) for atomistic simulations with
applications in many fields from chemistry to materials science. While
most current MLPs are based on environment-dependent atomic energies,
the limitations of this locality approximation can be overcome, e.g.,
in fourth-generation MLPs, which incorporate long-range electrostatic
interactions based on an equilibrated global charge distribution.
Apart from the considered interactions, the quality of MLPs crucially
depends on the information available about the system, i.e., the descriptors.
In this work we show that includingin addition to structural
informationthe electrostatic potential arising from the charge
distribution in the atomic environments significantly improves the
quality and transferability of the potentials. Moreover, the extended
descriptor allows current limitations of two- and three-body based
feature vectors to be overcome regarding artificially degenerate atomic
environments. The capabilities of such an electrostatically embedded
fourth-generation high-dimensional neural network potential (ee4G-HDNNP),
which is further augmented by pairwise interactions, are demonstrated
for NaCl as a benchmark system. Employing a data set containing only
neutral and negatively charged NaCl clusters, even small energy differences
between different cluster geometries can be resolved, and the potential
shows an impressive transferability to positively charged clusters
as well as the melt.