Water Dielectric Function at Finite Wavelength and the Convergence of Its Large Wavelength Limit (Static Dielectric) by Fluctuation Formulas

We provide a general analysis of the longitudinal dielectric function ε_<i>l</i>(<i>k</i>) via fluctuation formulas at finite wavelength <i>k</i>, including the static dielectric constant ε_<i>w</i> = ε_<i>l</i>(<i>k</i> → 0), and analyze the different sources of errors, deriving explicit formulas. Simulations with the SPC/E water model show that the convergence of fluctuation formulas to compute the static dielectric constant is slow and requires long simulations. The analysis of ε_<i>l</i>(<i>k</i>) allows us to identify the long- and short-wavelength limits and provide a precise determination of the location of the poles as well as the zeros in the complex plane, which determine the short-distance form of the electrostatic (Coulomb) interaction among charged particles.