  Machine Learning (ML) interatomic models and potentials have been widely
employed in simulations of materials. Long-range interactions often dominate in
some ionic systems whose dynamics behavior is significantly influenced.
However, the long-range effect such as Coulomb and Van der Wales potential is
not considered in most ML interatomic potentials. To address this issue, we put
forward a method that can take long-range effects into account for most ML
local interatomic models with the reciprocal space neural network. The
structure information in real space is firstly transformed into reciprocal
space and then encoded into a reciprocal space potential or a global descriptor
with full atomic interactions. The reciprocal space potential and descriptor
keep full invariance of Euclidean symmetry and choice of the cell. Benefiting
from the reciprocal-space information, ML interatomic models can be extended to
describe the long-range potential including not only Coulomb but any other
long-range interaction. A model NaCl system considering Coulomb interaction and
the GaxNy system with defects are applied to illustrate the advantage of our
approach. At the same time, our approach helps to improve the prediction
accuracy of some global properties such as the band gap where the full atomic
interaction beyond local atomic environments plays a very important role. In
summary, our work has expanded the ability of current ML interatomic models and
potentials when dealing with the long-range effect, hence paving a new way for
accurate prediction of global properties and large-scale dynamic simulations of
systems with defects.
