Kjartan Thor Wikfeldt

The inhomogeneous structure of water at ambient conditions

Small-angle X-ray scattering (SAXS) is used to demonstrate the presence of density fluctuations in ambient water on a physical length-scale of ≈1 nm; this is retained with decreasing temperature while the magnitude is enhanced. In contrast, the magnitude of fluctuations in a normal liquid, such as CCl4, exhibits no enhancement with decreasing temperature, as is also the case for water from molecular dynamics simulations under ambient conditions. Based on X-ray emission spectroscopy and X-ray Raman scattering data we propose that the density difference contrast in SAXS is due to fluctuations between tetrahedral-like and hydrogen-bond distorted structures related to, respectively, low and high density water. We combine our experimental observations to propose a model of water as a temperature-dependent, fluctuating equilibrium between the two types of local structures driven by incommensurate requirements for minimizing enthalpy (strong near-tetrahedral hydrogen-bonds) and maximizing entropy (nondirectional H-bonds and disorder). The present results provide experimental evidence that the extreme differences anticipated in the hydrogen-bonding environment in the deeply supercooled regime surprisingly remain in bulk water even at conditions ranging from ambient up to close to the boiling point.

Ultrafast X-ray probing of water structure below the homogeneous ice nucleation temperature

Water has a number of anomalous physical properties, and some of these become drastically enhanced on supercooling below the freezing point. Particular interest has focused on thermodynamic response functions that can be described using a normal component and an anomalous component that seems to diverge at about 228 kelvin (refs 1,2,3 ). This has prompted debate about conflicting theories that aim to explain many of the anomalous thermodynamic properties of water. One popular theory attributes the divergence to a phase transition between two forms of liquid water occurring in the ‘no man’s land’ that lies below the homogeneous ice nucleation temperature (TH) at approximately 232 kelvin and above about 160 kelvin, and where rapid ice crystallization has prevented any measurements of the bulk liquid phase. In fact, the reliable determination of the structure of liquid water typically requires temperatures above about 250 kelvin. Water crystallization has been inhibited by using nanoconfinement, nanodroplets and association with biomolecules to give liquid samples at temperatures below TH, but such measurements rely on nanoscopic volumes of water where the interaction with the confining surfaces makes the relevance to bulk water unclear. Here we demonstrate that femtosecond X-ray laser pulses can be used to probe the structure of liquid water in micrometre-sized droplets that have been evaporatively cooled below TH. We find experimental evidence for the existence of metastable bulk liquid water down to temperatures of  kelvin in the previously largely unexplored no man’s land. We observe a continuous and accelerating increase in structural ordering on supercooling to approximately 229 kelvin, where the number of droplets containing ice crystals increases rapidly. But a few droplets remain liquid for about a millisecond even at this temperature. The hope now is that these observations and our detailed structural data will help identify those theories that best describe and explain the behaviour of water.

Modeling Molecular Interactions in Water: From Pairwise to Many-Body Potential Energy Functions

Almost 50 years have passed from the first computer simulations of water, and a large number of molecular models have been proposed since then to elucidate the unique behavior of water across different phases. In this article, we review the recent progress in the development of analytical potential energy functions that aim at correctly representing many-body effects. Starting from the many-body expansion of the interaction energy, specific focus is on different classes of potential energy functions built upon a hierarchy of approximations and on their ability to accurately reproduce reference data obtained from state-of-the-art electronic structure calculations and experimental measurements. We show that most recent potential energy functions, which include explicit short-range representations of two-body and three-body effects along with a physically correct description of many-body effects at all distances, predict the properties of water from the gas to the condensed phase with unprecedented accuracy, thus opening the door to the long-sought “universal model” capable of describing the behavior of water under different conditions and in different environments.

Spatially inhomogeneous bimodal inherent structure of simulated liquid water.

In the supercooled regime at elevated pressure two forms of liquid water, high-density (HDL) and low-density (LDL), have been proposed to be separated by a coexistence line ending at a critical point, but a connection to water at ambient conditions has been lacking. Here we perform large-scale molecular dynamics simulations and demonstrate that the underlying potential energy surface gives a strictly bimodal characterization of the molecules at all temperatures and pressures, including the biologically and technologically important ambient regime, as spatially inhomogeneous either LDL- or HDL-like with a 3 : 1 predominance for HDL under ambient conditions. The Widom line in the supercooled regime, where maximal structural fluctuations take place, coincides with a 1 : 1 distribution. Although our results are based on molecular dynamics force-field simulations the close agreement with recent analyses of experimental X-ray spectroscopy and scattering data indicates a unified description also of real liquid water covering supercooled to ambient conditions.

Diffraction and IR/Raman data do not prove tetrahedral water

We use the reverse Monte Carlo modeling technique to fit two extreme structure models for water to available x-ray and neutron diffraction data in q space as well as to the electric field distribution as a representation of the OH stretch Raman spectrum of dilue HOD in D(2)O; the internal geometries were fitted to a quantum distribution. Forcing the fit to maximize the number of hydrogen (H) bonds results in a tetrahedral model with 74% double H-bond donors (DD) and 21% single donors (SD). Maximizing instead the number of SD species gives 81% SD and 18% DD, while still reproducing the experimental data and losing only 0.7-1.8 kJ/mole interaction energy. By decomposing the simulated Raman spectrum we can relate the models to the observed ultrafast frequency shifts in recent pump-probe measurements. Within the tetrahedral DD structure model the assumed connection between spectrum position and H-bonding indicates ultrafast dynamics in terms of breaking and reforming H bonds while in the strongly distorted model the observed frequency shifts do not necessarily imply H-bond changes. Both pictures are equally valid based on present diffraction and vibrational experimental data. There is thus no strict proof of tetrahedral water based on these data. We also note that the tetrahedral structure model must, to fit diffraction data, be less structured than most models obtained from molecular dynamics simulations.

Increasing correlation length in bulk supercooled H2O, D2O, and NaCl solution determined from small angle x-ray scattering

Using small angle x-ray scattering, we find that the correlation length of bulk liquid water shows a steep increase as temperature decreases at subzero temperatures (supercooling) and that it can, similar to the thermodynamic response functions, be fitted to a power law. This indicates that the anomalous properties of water are attributable to fluctuations between low- and high-density regions with rapidly growing average size upon supercooling. The substitution of H(2)O with D(2)O, as well as the addition of NaCl salt, leads to substantial changes of the power law behavior of the correlation length. Our results are consistent with the proposed existence of a liquid-liquid critical point in the deeply supercooled region but do not exclude a singularity-free model.

On the Range of Water Structure Models Compatible with X-ray and Neutron Diffraction Data

We use the reverse Monte Carlo (RMC) method to critically evaluate the structural information content of diffraction data on bulk water by fitting simultaneously or separately to X-ray and neutron data; the O-H and H-H, but not the O-O, pair-correlation functions (PCFs) are well-described by the neutron data alone. Enforcing at the same time different H-bonding constraints, we generate four topologically different structure models of liquid water, including a simple mixture model, that all equally well reproduce the diffraction data. Although earlier work [Leetmaa, M.; et al. J. Chem. Phys. 2008, 129, 084502] has focused on tetrahedrality in the H-bond network in liquid water, we show here that, even for the O-O-O three-body correlation, tetrahedrality is not strictly defined by the data. We analyze how well two popular MD models (TIP4P-pol2 and SPC/E) reproduce the neutron data in q-space and find differences in important aspects from the experiment. From the RMC fits, we obtain pair-correlation functions (PCFs) that are in optimal agreement with the diffraction data but still show a surprisingly strong variability both in position and height of the first intermolecular (H-bonding) O-H peak. We conclude that, although diffraction data impose important constraints on the range of possible water structures, additional data are needed to narrow the range of possible structure models.

Enhanced small-angle scattering connected to the Widom line in simulations of supercooled water

We present extensive simulations on the TIP4P∕2005 water model showing significantly enhanced small-angle scattering (SAS) in the supercooled regime. The SAS is related to the presence of a Widom line (T(W)) characterized by maxima in thermodynamic response functions and Ornstein-Zernike correlation length. Recent experimental small-angle x-ray scattering data [Huang et al., J. Chem. Phys. 133, 134504 (2010)] are excellently reproduced, albeit with an increasing temperature offset at lower temperatures. Assuming the same origin of the SAS in experiment and model this suggests the existence of a Widom line also in real supercooled water. Simulations performed at 1000 bar show an increased abruptness of a crossover from dominating high-density (HDL) to dominating low-density (LDL) liquid and strongly enhanced SAS associated with crossing T(W), consistent with a recent determination of the critical pressure of TIP4P∕2005 at 1350 bar. Furthermore, good agreement with experimental isothermal compressibilities at 1000, 1500, and 2000 bar shows that the high pressure supercooled thermodynamic behavior of water is well described by TIP4P∕2005. Analysis of the tetrahedrality parameter Q reveals that the HDL-LDL structural transition is very sharp at 1000 bar, and that structural fluctuations become strongly coupled to density fluctuations upon approaching T(W). Furthermore, the tetrahedrality distribution becomes bimodal at ambient temperatures, an observation that possibly provides a link between HDL-LDL fluctuations and the structural bimodality in liquid water indicated by x-ray spectroscopic techniques. Computed x-ray absorption spectra are indeed found to show sensitivity to the tetrahedrality parameter.

Wide-angle X-ray diffraction and molecular dynamics study of medium-range order in ambient and hot water

We have developed wide-angle X-ray diffraction measurements with high energy-resolution and accuracy to study water structure at three different temperatures (7, 25 and 66 °C) under normal pressure. Using a spherically curved Ge crystal an energy resolution better than 15 eV has been achieved which eliminates influence from Compton scattering. The high quality of the data allows for a reliable Fourier transform of the experimental data resolving shell structure out to ~12 Å, i.e. 5 hydration shells. Large-scale molecular dynamics (MD) simulations using the TIP4P/2005 force-field reproduce excellently the experimental shell-structure in the range 4-12 Å although less agreement is seen for the first peak in the intermolecular pair-correlation function (PCF). The Shiratani-Sasai Local Structure Index [J. Chem. Phys. 104, 7671 (1996)] identifies a tetrahedral minority giving the intermediate-range oscillations in the O-O PCF and a disordered majority providing a more featureless background in this range. The current study supports the proposal that the structure of liquid water, even at high temperatures, can be described in terms of a two-state fluctuation model involving local structures related to the high-density and low-density forms of liquid water postulated in the liquid-liquid phase transition hypothesis.

Reply to Soper et al.: Fluctuations in water around a bimodal distribution of local hydrogen-bonded structural motifs

Soper et al. (1) propose that the rise in the structure factor S(Q) at low Q in the small-angle x-ray scattering (SAXS) data reported in ref. 2 is caused by stochastic number fluctuations present in all liquids and that these fluctuations are not qualitatively different for water. Water, however, exhibits enhanced number density fluctuations both at higher and lower temperatures. Clearly, the driving force cannot be the same in both temperature regimes. In ref. 2, we suggest that the balance between minimizing enthalpy (tetrahedral regions) and entropy (disordered regions) provides the driving force dominating at low temperatures and that cooperatively enhanced H bonds associated with lower-density, tetrahedral regions may play an important role.