  The interaction of condensed phase systems with external electric fields is
crucial in myriad processes in nature and technology ranging from the
field-directed motion of cells (galvanotaxis), to energy storage and conversion
systems including supercapacitors, batteries and solar cells. Molecular
simulation in the presence of electric fields would give important atomistic
insight into these processes but applications of the most accurate methods such
as ab-initio molecular dynamics are limited in scope by their computational
expense. Here we introduce Perturbed Neural Network Potential Molecular
Dynamics (PNNP MD) to push back the accessible time and length scales of such
simulations at virtually no loss in accuracy. The total forces on the atoms are
expressed in terms of the unperturbed potential energy surface represented by a
standard neural network potential and a field-induced perturbation obtained
from a series expansion of the field interaction truncated at first order. The
latter is represented in terms of an equivariant graph neural network, trained
on the atomic polar tensor. PNNP MD is shown to give excellent results for the
dielectric relaxation dynamics, the dielectric constant and the field-dependent
IR spectrum of liquid water when compared to ab-initio molecular dynamics or
experiment, up to surprisingly high field strengths of about 0.2 V/A. This is
remarkable because, in contrast to most previous approaches, the two neural
networks on which PNNL MD is based are exclusively trained on zero-field
molecular configurations demonstrating that the networks not only interpolate
but also reliably extrapolate the field response. PNNP MD is based on rigorous
theory yet it is simple, general, modular, and systematically improvable
allowing us to obtain atomistic insight into the interaction of a wide range of
condensed phase systems with external electric fields.
