Rotational Memory Function of SPC/E water

TL;DR

This study computes memory functions for both single-dipole and collective dipolar relaxation in SPC/E water using MD simulations. By inverting a Volterra memory equation, it shows the single-dipole memory m(t) closely matches the short-time derivative correlation φ_ω(t), with a memory time τ_m ≈ 0.8–0.9 fs and a rotational frequency ω_r set by equipartition. Remarkably, the collective memory m_M(t) derived from the total dipole moment M(t) tracks m(t) as well, yielding near-equality m_M(t) ≈ m(t) ≈ φ_ω(t) and supporting the KKM relation in practice. Consequently, the frequency-dependent dielectric function ε(ω) can be predicted from single-particle correlations, with static dipole cross-correlations providing only minor corrections; this solidifies the link between microscopic rotational dynamics and macroscopic dielectric response in SPC/E water at 300 K. The findings have implications for interpreting dielectric spectroscopy and for using single-particle spectra to infer collective dipolar relaxation in polar liquids.

Abstract

Memory effects are essential for dynamics of condensed materials and are responsible for non-exponential relaxation of correlation functions of dynamic variables through the memory function. Memory functions of dipole rotations for polar liquids have never been calculated. We present here calculations of memory functions for single-dipole rotations and for the overall dipole moment of the sample for SPC/E water. The memory functions for single-particle and collective dipole dynamics turn out to be nearly identical. This result validates theories of dielectric spectroscopy in terms of single-particle time correlation functions and the connection between the collective and single-particle relaxation times through the Kirkwood factor. The dielectric function in this formalism contains no new dynamic information that does not exist in the single-dipole correlation function. A short memory time, $\lesssim 1$ fs, justifies the use of rotational diffusion model to describe dynamics of a single molecular dipole moment in bulk water.

Figures (5)

• Figure 1: (a) $\dot\phi(t)$ averaged over 900 SPC/E water molecules. (b) $\phi(t)$ (blue), $\phi_\omega(t)$ (red), and $m(t)$ (black) calculated from the same set of trajectories.
• Figure 2: Normalized memory functions $m(t)$ (Eq. \ref{['6']}) (a) and normalized correlation functions $\phi_\omega(t)$ (Eq. \ref{['4']}) (b) calculated with integration steps of 0.25 fs (blue), 0.5 fs (red), and 2.0 fs (black).
• Figure 3: Normalized time correlation functions $\phi_\omega(t)$ and $\Phi_\omega(t)$ (a) and time derivative correlation functions $g_K^{-1}\dot{\phi}(t)$ and $\dot{\Phi}(t)$ (b).
• Figure 4: Memory functions of the system dipole $m_M(t)$ (Eq. \ref{['24']}) compared to the approximate result from Eq. \ref{['26']} and to $m(t)$ for single-dipole rotations according to Eq. \ref{['6']}.
• Figure 5: Real, $\epsilon'(\nu)$, (a) and imaginary, $\epsilon"(\nu)$, (b) parts of $\epsilon(\nu)$ ($\nu=\omega/(2\pi)$) calculated from Eq. \ref{['32']} (solid lines) and Eq. \ref{['33']} with $\zeta_K=g_K$ (dashed lines) for SPC/E water ($\epsilon_s=71$DMjml2:22 and $\epsilon_\infty=1$).