The standard description of water structure consists of a random tetrahedral network in which every molecule is H-bonded to its four nearest neighbors, an arrangement similar to that in hexagonal ice. In recent years, a number of x-ray absorption spectroscopy (XAS) and related experiments have begun to characterize the H-bond structure in detail by assigning the observed spectral features to specific H-bonding configurations. However, in order for such an analysis to yield a quantitative description of the H-bond structure, it is necessary to establish an experimental definition of what actually constitutes an H-bond, or in other words, what degree of distortion of the H-bond network leads to a measurable change in the XAS.

A liquid microjet about 30 μm in diameter. The nozzle is formed from a fused silica capillary with an inside diameter of 100 μm, which is elongated by means of a commercial CO₂ laser pipette puller in order to obtain the final nozzle diameter.

Previously, only a geometric criterion had been established, which was derived by density functional theory (DFT) calculations of a model cluster [Ph. Wernet et al., Science 304, 995 (2004)]. Applying their theoretical H-bonding criterion to their x-ray Raman measurements, the authors had to invoke a picture of a liquid composed of monocyclic rings and linear chains—radically different from a tetrahedral network—to obtain agreement with theoretical calculations.

This latest experiment begins with injection of a small liquid microjet (10–30 μm diameter) into a high-vacuum chamber. The small size of the volatile sample makes it possible to maintain a relatively good vacuum (10^-5 torr), which enables windowless coupling to both Beamlines 8.0.1 and 11.0.2. Furthermore, such low pressures allow for efficient transport of electrons generated by the x-ray absorption process away from the jet surface to a detector placed about 1 mm away from the interaction region.

The Berkeley group measured x-ray absorption by the total electron yield (TEY) method. To obtain the temperature dependence, they recorded successive TEY spectra as a function of distance from the liquid jet nozzle. The microjet undergoes rapid evaporative cooling upon injection into the high-vacuum chamber, and therefore the liquid jet temperature continually decreases with distance away from the nozzle. The cooling rate had been thoroughly characterized in previous experiments by the group.

Comparison of the TEY x-ray absorption spectra taken at two different temperatures. The solid black curve was recorded at 288 K and the gray curve at 254 K.

Upon cooling, a sizeable decrease in the pre-edge intensity, an XAS spectral feature previously assigned to broken or distorted hydrogen bonding configurations in water, was observed. A simultaneous increase in the post-edge intensity, a spectral feature assigned to highly symmetric ice-like configurations, was also observed. A plot of the logarithm of the ratio of peak areas (I_post-edge/I_pre-edge) vs. inverse temperature should be linear, with a slope proportional to the energy difference between the two configurations (distorted and ice-like). From its temperature dependence measurements, the group found the difference in energy to be 1.5 ± 0.5 kcal/mol. This is the experimentally derived energetic hydrogen bond criterion.

Plots of the log of the ratio of the areas of the post-edge and pre-edge features versus inverse temperature from three separate experiments. The solid lines represent the linear fit with a slope proportional to the difference in energy between the distorted and ice-like H-bonding distributions. The energy difference is determined to be 1.5 ± 0.5 kcal/mol (average of the three measurements).

By this experimental criterion, the x-ray Raman measurements reported by Wernet et al. are consistent with the “standard model” for water after all. The Berkeley group would like to study the nature of the transition from the symmetric ice-like structure to the distorted structure described above via molecular dynamics simulations.

Research conducted by J.D. Smith, C.D. Cappa, B.M. Messer, R.C. Cohen, and R.J. Saykally (University of California, Berkeley, and Berkeley Lab) and K.R. Wilson (Berkeley Lab).

Research funding: U.S. Department of Energy, Office of Basic Energy Sciences (BES). Operation of the ALS is supported by BES.

Publication about this research: J.D. Smith, C.D. Cappa, K.R. Wilson, B.M. Messer, R.C. Cohen, and R.J. Saykally, “Energetics of hydrogen bond network rearrangements in liquid water,” Science 306, 851 (2004).