Energy-conserving molecular dynamics is not energy conserving

Molecular dynamics (MD) is a widely-used tool for simulating molecular and materials properties. It is common wisdom that molecular dynamics simulations should obey physical laws and, hence, lots of effort is put into ensuring that molecular dynamics simulations are energy conserving. The emergence of machine learning (ML) potentials for MD leads to a growing realization that monitoring conservation of energy during simulations is of low utility because the dynamics is often unphysically dissociative. Other ML methods for MD are not based on a potential and provide only forces or trajectories which are reasonable but not necessarily energy-conserving. Here we propose to clearly distinguish between the simulation-energy and true-energy conservation and highlight that the simulations should focus on decreasing the degree of true-energy non-conservation. We introduce very simple, new criteria for evaluating the quality of molecular dynamics by estimating the degree of true-energy non-conservation and we demonstrate their practical utility on an example of infrared spectra simulations. These criteria are more important and intuitive than simply evaluating the quality of the ML potential energies and forces as is commonly done and can be applied universally, e.g., even for trajectories with unknown or discontinuous potential energy. Such an approach introduces new standards for evaluating MD by focusing on the true-energy conservation and can help in developing more accurate methods for simulating molecular and materials properties. Molecular dynamics is often simulation-energy conserving but the quality of calculations is still unsatisfactory. It is more conducive to focus on evaluating and improving the theoretical best estimate of total-energy time evolution.