Modeling electronic response properties with an explicit-electron machine learning potential

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.