Molecular dynamics study of orientational cooperativity in water

Abstract

Recent experiments on liquid water show collective dipole orientation fluctuations dramatically slower than expected (with relaxation time $>50\mathrm{ns}$) [D.P. Shelton, Phys. Rev. B 72, 020201(R) (2005)]. Molecular dynamics simulations of extended simple point charge (SPC/E) water show a large vortexlike structure of the dipole field at ambient conditions surviving over $300\mathrm{ps}$ [J. Higo et al., Proc. Natl. Acad. Sci. U.S.A. 98, 5961 (2001)]. Both results disagree with previous results on water dipoles in similar conditions, for which autocorrelation times are a few picoseconds. Motivated by these recent results, we study the water dipole reorientation using molecular dynamics simulations of the SPC/E model in bulk water for temperatures ranging from ambient $300\mathrm{K}$ down to the deep supercooled region of the phase diagram at $210\mathrm{K}$. First, we calculate the dipole autocorrelation function and find that our simulations are well described by a stretched exponential decay, from which we calculate the orientational autocorrelation time ${\tau }_a$. Second, we define a second characteristic time, namely, the time required for the randomization of molecular dipole orientation, the self-dipole randomization time ${\tau }_r$, which is an upper limit on ${\tau }_a$; we find that ${\tau }_r\approx 5{\tau }_a$. Third, to check if there are correlated domains of dipoles in water which have large relaxation times compared to the individual dipoles, we calculate the randomization time ${\tau }_{\mathrm{box}}$ of the site-dipole field, the net dipole moment formed by a set of molecules belonging to a box of edge $L_{\mathrm{box}}$. We find that the site-dipole randomization time ${\tau }_{\mathrm{box}}\approx 2.5{\tau }_a$ for $L_{\mathrm{box}}\approx 3\mathrm{\AA }$, i.e., it is shorter than the same quantity calculated for the self-dipole. Finally, we find that the orientational correlation length is short even at low $T$.