Adaptive dimensionality reduction for accelerated calculations of ionic conductivity in correlated electrolytes

Molecular dynamics (MD) computation of the ionic conductivity of correlated electrolytes does not allow for the use of the familiar mean square displacement, instead requiring to collect statistics on the total ionic flux fluctuations, which leads to the need of much longer trajectories to obtain converged results. We propose a way to systematically reduce the noise in the conductivity and diffusivity calculations from MD in regimes of moderate correlation (Haven ration 0.5-2). For systems with a time-independent correlation structure, we use spectral decomposition of the short-time position covariance matrix to learn the optimal set of diffusion eigenmodes and perform the analysis of the full MD trajectory in that basis. The proposed method allows to significantly decrease the uncertainty of conductivity estimates.