Efficient simulations of mobility matrices for electrolytes by applying forces

Ion drift velocities in response to electric fields are a critical attribute of battery electrolytes. Accurately predicting species mobilities in such systems is an important challenge for atomistic simulations. In this work, we investigate two organic liquid electrolytes: LiPF₆ dissolved in (a) dimethyl carbonate (DMC) and (b) a mixture of DMC and ethylene carbonate (EC). We compare two approaches to measure mobilities: observing center of mass diffusion with no forces applied, and observing species drift in response to external forces. The two approaches are related by the fluctuation-dissipation theorem, but they are not equally efficient computationally. We argue that statistical errors of the two methods scale differently with system size and simulation run time. In a head-to-head test, we apply both methods to LiPF₆ in DMC in multiple simulations with the same size and run time. The drift method gives a much smaller variance in repeated measurements than the diffusion method, and should be preferred in practice.