Computing the Kirkwood $\textit{g}$-Factor by Combining Constant Maxwell Electric Field and Electric Displacement Simulations: Application to the Dielectric Constant of Liquid Water

In his classic 1939 paper, Kirkwood linked the macroscopic dielectric constant of polar liquids to the local orientational order as measured by the $\textit{g}$-factor (later named after him) and suggested that the corresponding dielectric constant at short-range is effectively equal to the macroscopic value just after “a distance of molecular magnitude” [Kirkwood, J. Chem. Phys., 1939, 7, 911]. Here, we show a simple approach to extract the short-ranged Kirkwood $\textit{g}$-factor from molecular dynamics (MD) simulation by superposing the outcomes of constant electric field ${\bf E}$ and constant electric displacement ${\bf D}$ simulations [Zhang and Sprik, Phys. Rev. B: Condens. Matter Mater. Phys., 2016, 93, 144201]. Rather than from the notoriously slow fluctuations of the dipole moment of the full MD cell, the dielectric constant can now be estimated from dipole fluctuations at short-range, accelerating the convergence. Exploiting this feature, we computed the bulk dielectric constant of liquid water modeled in the generalized gradient approximation (PBE) to density functional theory and found it to be at least 40% larger than the experimental value.The research fellowship (Grant ZH 477/1-1) awarded to C.Z. by the Deutsche Forschungsgemeinschaft (DFG) is gratefully acknowledged. Computational resources were provided by the UK Car−Parrinello (UKCP) consortium funded by the Engineering and Physical Sciences Research Council (EPSRC).This is the final version of the article. It first appeared from the American Chemical Society via http://dx.doi.org/10.1021/acs.jpclett.6b0112