  Explicit-electron force fields introduce electrons or electron pairs as
semi-classical particles in force fields or empirical potentials, which are
suitable for molecular dynamics simulations. Even though semi-classical
electrons are a drastic simplification compared to a quantum-mechanical
electronic wavefunction, they still retain a relatively detailed electronic
model compared to conventional polarizable and reactive force fields. The
ability of explicit-electron models to describe chemical reactions and
electronic response properties has already been demonstrated, yet the
description of short-range interactions for a broad range of chemical systems
remains challenging. In this work, we present the electron machine learning
potential (eMLP), a new explicit electron force field where the short-range
interactions are modeled with machine learning. The electron pair particles
will be located at well-defined positions, derived from localized molecular
orbitals or Wannier centers, naturally imposing the correct dielectric and
piezoelectric behavior of the system. The eMLP is benchmarked on two newly
constructed datasets: eQM7, a extension of the QM7 dataset for small molecules,
and a dataset for the crystalline $\beta$-glycine. It is shown that the eMLP
can predict dipole moments, polarizabilities and IR-spectra of unseen molecules
with high precision. Furthermore, a variety of response properties, e.g.
stiffness or piezoelectric constants, can be accurately reproduced.
