Frequency and wave-vector dependent dielectric function of water: Collective modes and relaxation spectra

Abstract

The longitudinal frequency and wave-vector dependent complex dielectric response function χ(k,ω)=1−1/ε(k,ω) is calculated in a broad range of k values by means of molecular dynamics computer simulation for a central force model of water. Its imaginary part, i.e., Im{ε(k,ω)}/|ε(k,ω)|2, shows two main contributions in the region of small k values: Debye-like orientational relaxation in the lower frequency part of the spectrum and a damped librational resonance at the high frequency wing. The Debye relaxation time does not follow a de Gennes-like pattern: τ(k) goes through a maximum at k≈k*≈1.7 Å−1, while the static polar structure factor S(k) peaks at k≈3 Å−1. The resonance frequency ω(k) and the decay decrement γ(k) show a dispersion law, indicative of a decaying optical-like mode, the libron. With an approximate normal mode approach, we analyze the origin of this mode on a molecular level which shows that it is due to a damped propagation of molecular orientational vibrations through the network of hydrogen bonds. At high k the decay, due to dissipation of collective into single particle motions, dominates. The static dielectric function is calculated on the basis of the response function spectra via the Kramers–Kronig relation. In the small k region ε(k) decreases from the macroscopic value ε≈80 to a value ≈15, i.e. it exhibits a Lorentzian-type behavior. This behavior is shown to be determined by higher order multipole correlation functions. In the intermediate and high k range, our results on ε(k) and χ(k) are in excellent agreement with data extracted from experimental partial pair correlation functions: ε(k) exhibits two divergence points on the k axis with a range of negative values in between where a maximum in χ(k) is found with χmax(k)≫1, indicative of overscreening. Consequences of quantum corrections to χ(k) with respect to a purely classical calculation are discussed and consequences are shown for the interaction energy between hydrated ions.