Mikael Leetmaa

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.

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.

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.

Are recent water models obtained by fitting diffraction data consistent with infrared/Raman and x-ray absorption spectra?

X-ray absorption (XA) spectra have been computed based on water structures obtained from a recent fit to x-ray and neutron diffraction data using models ranging from symmetrical to asymmetrical local coordination of the water molecules [A. K. Soper, J. Phys.: Condens. Matter 17, S3273 (2005)]. It is found that both the obtained symmetric and asymmetric structural models of water give similar looking XA spectra, which do not match the experiment. The fitted models both contain unphysical structures that are allowed by the diffraction data, where, e.g., hydrogen-hydrogen interactions may occur. A modification to the asymmetric model, in which the non-hydrogen-bonded OH intramolecular distance is allowed to become shorter while the bonded OH distance becomes longer, improves the situation somewhat, but the overall agreement is still unsatisfactory. The electric field (E-field) distributions and infrared (IR) spectra are also calculated using two established theoretical approaches, which, however, show significant discrepancies in their predictions for the asymmetric structural models. Both approaches predict the Raman spectrum of the symmetric model fitted to the diffraction data to be significantly blueshifted compared to experiment. At the moment no water model exists that can equally well describe IR/Raman, x-ray absorption spectroscopy, and diffraction data.

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.

Oxygen-oxygen correlations in liquid water: Addressing the discrepancy between diffraction and extended x-ray absorption fine-structure using a novel multiple-data set fitting technique

The first peak of the oxygen-oxygen pair-correlation function (O-O PCF) is a critical measure of the first coordination-shell distances in liquid water. Recently, a discrepancy has been uncovered between diffraction and extended x-ray absorption fine-structure (EXAFS) regarding the height and position of this peak, where EXAFS gives a considerably more well-defined peak at a shorter distance compared to the diffraction results. This discrepancy is here investigated through a novel multiple-data set structure modeling technique, SpecSwap-RMC, based on the reverse Monte Carlo (RMC) method. Fitting simultaneously to both EXAFS and a diffraction-based O-O PCF shows that even though the reported EXAFS results disagree with diffraction, the two techniques can be reconciled by taking into account a strong contribution from the photoelectron scattering focusing effect in EXAFS originating from nearly linear hydrogen bonds. This many-body contribution, which is usually neglected in RMC modeling of EXAFS data, is included in the fits by precomputing and storing EXAFS signals from real-space multiple-scattering calculations on a large number of unique water clusters. On the other hand, fitting also the O-O PCF from diffraction is seen to enhance the amount of structural disorder in the joint fit. Thus, both structures containing nearly linear hydrogen bonds and local structural disorder are important to reproduce diffraction and EXAFS simultaneously. This work also illustrates a few of many possible uses of the SpecSwap-RMC method in modeling disordered materials, particularly for fitting computationally demanding techniques and combining multiple data sets.

SpecSwap-RMC : A novel reverse Monte Carlo approach using a discrete set of local configurations and pre-computed properties

We present a novel approach to reverse Monte Carlo (RMC) modeling, SpecSwap-RMC, specifically applicable to structure modeling based on properties that require significant computer time to evaluate. In this approach pre-computed property data from a discrete set of local configurations are used and the configuration space is expressed in this basis. Atomistic moves are replaced with swap moves of contributions to a sample set representing the state of the simulated system. We demonstrate the approach by fitting jointly and separately the EXAFS signal and x-ray absorption spectrum (XAS) of ice Ih using a SpecSwap sample set of 80 configurations from a library of 1382 local structures with associated pre-computed spectra. As an additional demonstration we compare SpecSwap and FEFFIT fits of EXAFS data on crystalline copper, finding excellent agreement. SpecSwap-RMC thus extends RMC structure modeling to any property that can be computed from a structure irrespective of computational expense, but at the cost of a reduced configuration space. The method is general enough that it can be applied to any sets of computed properties, not necessarily limited to structure determination.

Temporal coarse graining of CO2 and N2 diffusion in zeolite NaKA: from the quantum scale to the macroscopic.

The kinetic CO2-over-N2 sieving capabilities in narrow pore zeolites are dependent on the free-energy barriers of diffusion between the zeolite pores, which can be fine-tuned by altering the framework composition. An ab initio level of theory is necessary to accurately compute the energy barriers, whereas it is desirable to predict the macroscopic scale diffusion for industrial applications. Using ab initio molecular dynamics on the picosecond time scale, the free-energy barriers of diffusion can be predicted for different local pore properties in order to identify those that are rate-determining for the pore-to-pore diffusion. Specifically, we investigate the effects of the Na(+)-to-K(+) exchange at the different cation sites and the CO2 loading in Zeolite NaKA. These computed energy barriers are then used as input for the Kinetic Monte Carlo method, coarse graining the dynamic simulation steps to the pore-to-pore diffusion. With this approach, we simulate how the identified rate-determining properties as well as the application of skin-layer surface defects affect the diffusion driven uptake in a realistic Zeolite NaKA powder particle model on a macroscopic time scale. Lastly, we suggest a model by combining these effects, which provides an excellent agreement with the experimental CO2 and N2 uptake behaviors presented by Liu et al. (Chem. Commun. 2010, 46, 4502-4504).