Molecular dynamics simulation with finite electric fields using Perturbed Neural Network Potentials

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.