Nuclear quantum effects and hydrogen bond fluctuations in water

Abstract

The hydrogen bond (HB) is central to our understanding of the properties of water. However, despite intense theoretical and experimental study, it continues to hold some surprises. Here, we show from an analysis of ab initio simulations that take proper account of nuclear quantum effects that the hydrogen-bonded protons in liquid water experience significant excursions in the direction of the acceptor oxygen atoms. This generates a small but nonnegligible fraction of transient autoprotolysis events that are not seen in simulations with classical nuclei. These events are associated with major rearrangements of the electronic density, as revealed by an analysis of the computed Wannier centers and (1)H chemical shifts. We also show that the quantum fluctuations exhibit significant correlations across neighboring HBs, consistent with an ephemeral shuttling of protons along water wires. We end by suggesting possible implications for our understanding of how perturbations (solvated ions, interfaces, and confinement) might affect the HB network in water.

Keywords: ab initio liquid water; generalized Langevin equation thermostat; path integral molecular dynamics.

Fig. 1.

Joint probability density P(ν, cosα) of finding an O–H–O′ geometry with a given ν–α configuration in a classical simulation of ab initio water at 300 K and the experimental density, normalized over its maximum P_max. One can clearly identify a cluster of hydrogen-bonded configurations (a) and a cluster corresponding to the other first neighbors of the tagged molecule (b). Features at more negative values of ν are less clear-cut (c). They correspond to farther neighbors and are irrelevant to the present work. The red line marks the dividing surface one should ideally use to define the hydrogen-bonded region, which is obtained by moving away from the saddle point on the probability distribution in the direction of the negative eigenvector of the Hessian.

Fig. 2.

(A) Distribution of the proton-transfer coordinate in ab initio simulations of water at 300 K. The three curves correspond to a classical simulation, to the distribution of the ring polymer beads in a simulation that includes quantum effects, and to the distribution of the centroid of the ring polymer in the quantum simulation. (B) Conditional average of the gyration radius of the ring polymer in the directions parallel and perpendicular to the O–H covalent bond for different values of ν for the centroid.

Fig. 3.

(A) Distribution of the proton-transfer coordinate ν for water at different thermodynamic state points. (B–D) Joint probability distribution of the proton-transfer coordinate and the distance d(O–O′) between the covalently bound and acceptor oxygen atoms: (B) classical nuclei, , ; (C) quantum nuclei, , ; and (D) quantum nuclei, , .

Fig. 4.

Given a tagged H atom, the oxygen atom O it is covalently bound to, and the acceptor atom O′, X and X′ are the Wannier centers of the two O atoms that are closest to H. The plots report the joint probability distribution of ν and of the distances of the Wannier centers to the corresponding O. A classical simulation of liquid water (Upper) and a simulation that includes NQEs (Lower) are shown.

Fig. 5.

Compact illustration of the relation between the instantaneous chemical shift and the structural properties of the O–H bond at three different thermodynamic state points: the liquid at and (blue), supercritical water at and (red), and an isolated gas-phase water molecule at 473 K (black). In all cases, NQEs were included using PIGLET. The continuous lines correspond to conditional averages of the chemical shift as a function of the structural parameter, the dashed lines delimit the area within 1 standard deviation from the mean, and the shading is proportional to the probability distribution of the structural parameter. The dots indicate the means of the structural parameter and the chemical shift. (A) Proton-transfer coordinate ν is used as the structural parameter, the gas-phase molecule corresponding to an asymptotic value of . (B) Covalent bond length is used.