Structural information in the form of radial distribution curves can be derived from scattering data by Fourier transformation of the measured intensity curve as a function of the momentum transfer, Q, to give the molecular centers distribution function of water. But before this transformation, it is necessary to correct the experimental data for several factors. The new data from Berkeley spans work over the last two years, in which the group was able to gather high-quality x-ray scattering data for water over a range of temperatures relevant to most life processes. The error estimates for the data were smaller than the discrepancies between data sets collected in past x-ray experiments. This achievement was due to the use of a highly monochromatic source (the ALS), a well-characterized polarization correction, a Compton scattering correction that includes electron correlation effects, and better resolution and more accurate intensities from a modern CCD detector.

X-ray scattering pattern of liquid water at room temperature and pressure. Structural information can be extracted from the pattern either by Fourier transformation or by comparing it directly with patterns calculated from models of water.

Getting a Hold on Water

Scientists believe life began in water. Biologists sometimes model the cells in our bodies as bags of water. The 200,000 cubic kilometers of fresh water that fall on the Earth each year as rain and snow are vital to the agriculture that provides our food. But for all its importance to our very existence, water continues to evade complete scientific understanding. Its structure (where the atoms are) is a case in point. In the main form of solid water (ice), each water molecule is bonded to four water neighbors in a rigid structure made up of connected hexagonal rings. When the ice melts, owing to motion of the water molecules, there is a broader distribution of bonding configurations, including a variety of polygons of varying sizes and degrees of puckering or distortion, that make the structure of liquid water more difficult to determine. The venerable technique of x-ray scattering (in which an x-ray beam shining on a sample emerges with different intensities at various directions) has long been used to study the structure of liquid water. Hura et al. have not only improved this technique, but they have combined it with a comparison of measured scattering patterns with those calculated from theoretical models of liquid water to determine the best model over a wide range of biologically relevant temperatures.

In addition to gathering data over a range of temperatures important to water, the group introduced a new approach to interpreting the data. The common practice has been to report both the intensity curve and radial distribution functions extracted from it, but the proper extraction of the real-space pair-correlation functions from scattering data is very difficult because of uncertainty introduced in the experimental corrections, the proper weighting of oxygen-oxygen, oxygen-hydrogen, and hydrogen-hydrogen contributions, and numerical problems of Fourier transforming data truncated in Q-space. Instead, the group undertook the alternative strategy of directly calculating the x-ray scattering spectra from electron densities derived from density functional theory (DFT) based on real-space configurations generated with classical water models. The model providing the most accurate simulation of the experimental intensity was then used to calculate the real-space pair-correlation functions.

Comparison of ALS experiments (gray lines) with older x-ray experiments (red lines) at three temperatures from 2°C (left) to 77°C (right) shows a qualitative difference that lies outside the error bars of the ALS experiment.

Water models start with "normal" ice (at least 13 other structures are known), in which a water molecule is hydrogen-bonded to four water neighbors in a tetrahedral structure, resulting in a crystal comprising connected hexagonal rings. In liquid water, the greater translational and rotational motion of the water molecules yields a broader distribution of hydrogen-bonded configurations. As temperature and pressure are increased or decreased, the structure of the three-dimensional hydrogen-bonded network of water changes, giving rise to the well-known anomalous properties of liquid water. These altered water properties expand the functional versatility of the liquid solvent.

Real-space pair-distribution functions from the TIP4P-Pol2 model, which best reproduces the experimental x-ray scattering intensity curves for oxygen-oxygen (left) and oxygen-hydrogen (right) at 2°C (red), 25°C, (gray), and 77°C (dashed).

Models of the structure of water range from those derived from empirical force fields, to more recent models that incorporate many-body effects through polarizability, and finally to first-principles molecular dynamics studies based on well-defined approximations to the Schrödinger equation. The researchers found that among the models showing very good agreement with the experimental intensities, the polarizable water model TIP4P-Pol2 show quantitative agreement over the full temperature range. The resulting radial distribution functions calculated from TIP4P-Pol2 provide the current best benchmarks for real-space water structure over the biologically relevant temperature range studied in these experiments.

Research conducted by G. Hura, D. Russo, R.M. Glaeser, and T. Head-Gordon (University of California, Berkeley, and Berkeley Lab); M. Krack (Swiss Center for Scientific Computing, Manno, Switzerland); and M. Parrinello (ETH-Zurich, Switzerland).

Research funding: National Institutes of Health, National Science Foundation, and Berkeley Lab Laboratory Directed Research and Development. Operation of the ALS is support by the U.S. Department of Energy, Office of Basic Energy Science.

Publication about this research: G. Hura, D. Russo. R.M. Glaeser, T. Head-Gordon, M. Krack, and M. Parrinello, "Water structure as a function of temperature from x-ray scattering experiments and ab initio molecular dynamics," Phys. Chem. Chem. Phys. (PCCP) 5, 1981 (2003) and T. Head-Gordon and G. Hura, "Water structure from scattering experiments and simulation," Chem. Rev. 102, 2651 (2002).