Distinguishing Weak and Strong Hydrogen Bonds in Liquid Water—A Potential of Mean Force-Based Approach

Abstract

The ability to form hydrogen bonds is one of the most important factors behind water’s many anomalous properties. However, there is still no consensus on the hydrogen bond structure of liquid water, including the average number of hydrogen bonds in liquid water. We use molecular dynamics simulations of the polarizable iAMOEBA water model for investigating the hydrogen bond characteristics of liquid water over a wide range of temperatures and pressures. Geometric definitions of a hydrogen bond often use a rectangular region on the plane of hydrogen bond distances and angles. In this work, we find that an elliptical region is more appropriate for the identification of hydrogen bonds, based on statistically favorable molecular configurations. The two-dimensional potential of mean force (PMF) landscape along the hydrogen bond distance (O–H) and angle (O–H–O) is calculated for identifying the statistically favored molecular configurations, which is then used for defining hydrogen bond formation as well as the strength of a hydrogen bond. We further propose a new approach to characterize the hydrogen bonds as strong when the PMF is lower than −2 kT. Using this definition, a consistent explanation for the different average numbers of hydrogen bonds in water is obtained in agreement with the literature. Simulations are also performed with the rigid and nonpolarizable TIP4P/2005 water model. Both water models are qualitatively consistent in predicting the distribution of double-, single-, and non-donor configurations, in line with experimental data, while the iAMOEBA water model yields more quantitatively precise results, including a 10–15% double-donor fraction at 90 °C and 1 atm. The method is also demonstrated to be applicable to the recent, and more general, three-dimensional PMF-based definition of hydrogen bonds.

Multiple insights call for revision of modern thermodynamic models to account for structural fluctuations in water

“…exhibit geometries similar to that of ice I h (the hexagonal crystalline form of ice). Hydrogen bonds defined by this criterion were also observed 66 to show statistics similar to that of strong hydrogen bonds reported by Wernet et al 9 Therefore, hydrogen bonds that lie in the region PMF ≤ À2 kT were distinguished as "ice-like" or "strong" hydrogen bonds. 66 Interested readers are referred to our previous work for more details.…”

“…Here, kT is the magnitude of thermal fluctuations in the system at temperature T. We reported that this region could be well captured by a partial ellipse. 66 This method is also capable of identifying hydrogen bond configurations that lie deeper inside the PMF wells. We showed that hydrogen bonds which lie deeper inside the PMF well (PMF ≤ À2 kT)…”

Structural characteristics of low-density environments in liquid water

“…Two molecules are defined to be hydrogen bonded if the oxygen-hydrogen (O-H) distance and the oxygenhydrogen-oxygen (O-H-O) angle lie in the statistically favourable region on the distance-angle plane, defined by PMF ≤ 0 kT. We also reported that a vast majority of hydrogen bonds formed in the ice I h crystal lie in a smaller sub-region on the PMF landscape, defined by PMF ≤ -2 kT [73]. We used these PMF based definitions of hydrogen bonds to compare the tetrahedrally hydrogen bonded fraction of liquid water with the LFTS fractions estimated from other methods.…”

“…We also compared the fraction of LFTS molecules estimated by θ avg with the fraction of tetrahedral environments indicated by hydrogen bond formation. In a recent work [73], we used Potential of Mean Force (PMF) landscapes to distinguish 'ice-like' hydrogen bonds in liquid water. Two molecules are defined to be hydrogen bonded if the oxygen-hydrogen (O-H) distance and the oxygenhydrogen-oxygen (O-H-O) angle lie in the statistically favourable region on the distance-angle plane, defined by PMF ≤ 0 kT.…”

“…where ∆(i; k, t) is r i+1 − r i and r i is the distance of molecule i from the central molecule k when they are arranged in the ascending order of distances from k. We compared the distribution of LSI parameters for 4 strongly hydrogen bonded water molecules [73] to the structured component of LSI as reported by Shiratani and Sasai. We find that the distribution of structured component of LSI is similar to the distribution of LSI parameters for four strongly hydrogen bonded water molecules as shown in Fig.…”