Lars Ojamäe

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.

Spectroscopic probing of local hydrogen-bonding structures in liquid water

We have studied the electronic structure of liquid water using x-ray absorption spectroscopy at the oxygen K edge. Since the x-ray absorption process takes less than a femtosecond, it allows probing of the molecular orbital structure of frozen, local geometries of water molecules at a timescale that has not previously been accessible. Our results indicate that the electronic structure of liquid water is significantly different from that of the solid and gaseous forms, resulting in a pronounced pre-edge feature below the main absorption edge in the spectrum. Theoretical calculations of these spectra suggest that this feature originates from specific configurations of water, for which the H-bond is broken on the H-donating site of the water molecule. This study provides a fingerprint for identifying broken donating H-bonds in the liquid and shows that an unsaturated H-bonding environment exists for a dominating fraction of the water molecules.

Potential models for simulations of the solvated proton in water

Analytical potential models are designed for simulations of water with excess protons. The potentials describe both intramolecular and intermolecular interactions, and allow dissociation and formation of the species (H2O)nH+. The potentials are parametrized in the form of interactions between H+ and O2− ions, with additional three-body (H–O–H) interaction terms and self-consistent treatment of the polarizability of the oxygen ions. The screening of electrostatic interactions caused by the overlap of the electron clouds in the real molecules is modeled by functions modifying the electric field at short distances. The model was derived by fitting to the potential surface of the H5O2+ ion and other species, as obtained from ab initio MP2 calculations employing an extensive basis set. Emphasis was put on modeling the potential-energy surface for the proton-transfer reaction. Potential-surface profiles, geometry-optimized structures and formation energies of H5O2+, protonated water clusters [H+(H2O)n, n=2–4] a...

On the use of graph invariants for efficiently generating hydrogen bond topologies and predicting physical properties of water clusters and ice

Water clusters and some phases of ice are characterized by many isomers with similar oxygen positions, but which differ in direction of hydrogen bonds. A relationship between physical properties, like energy or magnitude of the dipole moment, and hydrogen bond arrangements has long been conjectured. The topology of the hydrogen bond network can be summarized by oriented graphs. Since scalar physical properties like the energy are invariant to symmetry operations, graphical invariants are the proper features of the hydrogen bond network which can be used to discover the correlation with physical properties. We demonstrate how graph invariants are generated and illustrate some of their formal properties. It is shown that invariants can be used to change the enumeration of symmetry-distinct hydrogen bond topologies, nominally a task whose computational cost scales like N2, where N is the number of configurations, into an N ln N process. The utility of graph invariants is confirmed by considering two water clusters, the (H2O)6 cage and (H2O)20 dodecahedron, which, respectively, possess 27 and 30 026 symmetry-distinct hydrogen bond topologies associated with roughly the same oxygen atom arrangements. Physical properties of these clusters are successfully fit to a handful of graph invariants. Using a small number of isomers as a training set, the energy of other isomers of the (H2O)20 dodecahedron can even be estimated well enough to locate phase transitions. Some preliminary results for unit cells of ice-Ih are given to illustrate the application of our results to periodic systems.

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.

Short H-bonds and spontaneous self-dissociation in (H2O)20: Effects of H-bond topology

There are 30026 symmetry-distinct ways to arrange 20 water molecules in a dodecahedral cage with nearly optimum hydrogen bond lengths and angles, analogous to the arrangements that give rise to the zero-point entropy in ice-Ih. The energy of hydrogen bond isomers in (H2O)20, assumed to be similar in the past, differs by up to 70 kcal/mol. The isomers differ widely in their hydrogen bond lengths, some exhibiting bond lengths as short as ∼2.4 A. The differences among the isomers extends to their chemical properties: In some arrangements one or more water molecules spontaneously self-dissociate, giving rise to spatially separated excess proton and hydroxyl ion units in the cluster. Isomers that exhibit these unusual properties can be identified by features of their hydrogen bond topology.

A theoretical study of water clusters: the relation between hydrogen-bond topology and interaction energy from quantum-chemical computations for clusters with up to 22 molecules

Quantum-chemical calculations of a variety of water clusters with eight, ten and twelve molecules were performed, as well as for selected clusters with up to 22 water molecules. Geometry optimizations were carried out at the B3LYP/cc-pVDZ level and single-point energies were calculated at the B3LYP/aug-cc-pVDZ level for selected clusters. The electronic energies were studied with respect to the geometry of the oxygen arrangement and six different characteristics of the hydrogen-bond arrangement in the cluster. Especially the effect of the placement of the non-hydrogen bonding hydrogens on the interaction energy was studied. Models for the interaction energy with respect to different characteristics of the hydrogen-bond arrangement were derived through least-square fits. The results from the study of the clusters with eight, ten and twelve molecules are used to predict possible low-energy structures for various shapes of clusters with up to 22 molecules.

The electronic structure of free water clusters probed by Auger electron spectroscopy

(H2O)(N) clusters generated in a supersonic expansion source with N approximately 1000 were core ionized by synchrotron radiation, giving rise to core-level photoelectron and Auger electron spectra (AES), free from charging effects. The AES is interpreted as being intermediate between the molecular and solid water spectra showing broadened bands as well as a significant shoulder at high kinetic energy. Qualitative considerations as well as ab initio calculations explain this shoulder to be due to delocalized final states in which the two valence holes are mostly located at different water molecules. The ab initio calculations show that valence hole configurations with both valence holes at the core-ionized water molecule are admixed to these final states and give rise to their intensity in the AES. Density-functional investigations of model systems for the doubly ionized final states--the water dimer and a 20-molecule water cluster--were performed to analyze the localization of the two valence holes in the electronic ground states. Whereas these holes are preferentially located at the same water molecule in the dimer, they are delocalized in the cluster showing a preference of the holes for surface molecules. The calculated double-ionization potential of the cluster (22.1 eV) is in reasonable agreement with the low-energy limit of the delocalized hole shoulder in the AES.

Theoretical characterization of divacancies at the surface and in bulk MgO

Two types of divacancy at the (001) surface of MgO are theoretically studied and compared with the corresponding defect in the bulk: the pit, where a surface magnesium and the oxygen ion underneath are removed, and the tub, where both removed ions are at the surface. All calculations have been performed by means of the EMBED program which adopts an embedded-cluster approach in the frame of the Hartree-Fock (HF) approximation [C. Pisani F. Cora, R. Nada, and R. Orlando, Comput. Phys. Commun. 82, 139 (1994); C. Pisani and U. Birkenheuer, ibid. 96, 152 (1996)]; the semi-infinite host crystal for the study of the surface defects has been simulated with a four-layer slab. The energy released on formation of the divacancy from the two charged isolated vacancies is very high, almost 300 kcal/mol. The tub divacancy is the most stable, both as a neutral and as a singly charged defect. For the paramagnetic center (one electron trapped in the cavity), spin density data are provided and discussed with reference to results from electron paramagnetic resonance experiments and molecular cluster calculations [E. Giamello M. C. Paganini, D. Murphy, A. M. Ferrari, and G. Pacchioni, J. Phys. Chem. 101, 971 (1997)]. It is suggested that the tub divacancy is a common defect, if not the most common, at the highly dehydrated MgO surface.

A theoretical study of water equilibria: The cluster distribution versus temperature and pressure for (H2O)n, n=1–60, and ice

The size distribution of water clusters at equilibrium is studied using quantum-chemical calculations in combination with statistical thermodynamics. The necessary energetic data is obtained by quantum-chemical B3LYP computations and through extrapolations from the B3LYP results for the larger clusters. Clusters with up to 60 molecules are included in the equilibrium computations. Populations of different cluster sizes are calculated using both an ideal gas model with noninteracting clusters and a model where a correction for the interaction energy is included analogous to the van der Waals law. In standard vapor the majority of the water molecules are monomers. For the ideal gas model at 1 atm large clusters [56-mer (0-120 K) and 28-mer (100-260 K)] dominate at low temperatures and separate to smaller clusters [21-22-mer (170-280 K) and 4-6-mer (270-320 K) and to monomers (300-350 K)] when the temperature is increased. At lower pressure the transition from clusters to monomers lies at lower temperatures and fewer cluster sizes are formed. The computed size distribution exhibits enhanced peaks for the clusters consisting of 21 and 28 water molecules; these sizes are for protonated water clusters often referred to as magic numbers. If cluster-cluster interactions are included in the model the transition from clusters to monomers is sharper (i.e., occurs over a smaller temperature interval) than when the ideal-gas model is used. Clusters with 20-22 molecules dominate in the liquid region. When a large icelike cluster is included it will dominate for temperatures up to 325 K for the noninteracting clusters model. Thermodynamic properties (C(p), DeltaH) were calculated with in general good agreement with experimental values for the solid and gas phase. A formula for the number of H-bond topologies in a given cluster structure is derived. For the 20-mer it is shown that the number of topologies contributes to making the population of dodecahedron-shaped cluster larger than that of a lower-energy fused prism cluster at high temperatures.