Theoretical Study of the Cage Water Hexamer Structure

Instanton theory of tunneling in molecules with asymmetric isotopic substitutions

We consider quantum tunneling in asymmetric double-well systems for which the local minima in the two wells have the same energy, but the frequencies differ slightly. In a molecular context, this situation can arise if the symmetry is broken by isotopic substitutions. We derive a generalization of instanton theory for these asymmetric systems, leading to a semiclassical expression for the tunneling matrix element and hence the energy-level splitting. We benchmark the method using a set of one- and two-dimensional models, for which the results compare favorably with numerically exact quantum calculations. Using the ring-polymer instanton approach, we apply the method to compute the level splittings in various isotopomers of malonaldehyde in full dimensionality and analyze the relative contributions from the zero-point energy difference and tunneling effects.

Ring-Stacking Water Clusters: Morphology and Stabilities

The structures and interaction energies of water clusters with ring stacking motifs are studied by using ab initio calculations. The structures of the water clusters are constructed by stacking either single rings or multi-rings of tetramer, pentamer, and hexamer. We found that, in the single-ring-stacking motif, the most stable isomers exhibit an alternative clockwise-anticlockwise stacking pattern. We also show that four-layer single-ring-stacking isomers are not energetically favorable in comparison with those of two-layer multi-ring-stacking isomers. The relative stability of the isomers is also analyzed in terms of H-bond strength and elastic distortions of the water molecules.

Terahertz VRT Spectroscopy of the Water Hexamer-h12 Cage: Dramatic Libration-Induced Enhancement of Hydrogen Bond Tunneling Dynamics

We report the assignment and analysis of 176 transitions belonging to a librational band of the (H₂O)₆ cage isomer near 525 cm^-1(15 THz). From a fit of the transitions to an asymmetric top model, we observe both dramatic changes in the rotational constants relative to the ground state, indicating significant nonrigidity, and striking enhancement in the tunneling motions that break and reform the hydrogen bonds in the cluster. This is the fifth water cluster system to display such an enhancement in the 15 THz librational region, the details of which may help to elucidate the hydrogen bond dynamics occurring in bulk liquid water.

Concerted hydrogen-bond breaking by quantum tunneling in the water hexamer prism

The nature of the intermolecular forces between water molecules is the same in small hydrogen-bonded clusters as in the bulk. The rotational spectra of the clusters therefore give insight into the intermolecular forces present in liquid water and ice. The water hexamer is the smallest water cluster to support low-energy structures with branched three-dimensional hydrogen-bond networks, rather than cyclic two-dimensional topologies. Here we report measurements of splitting patterns in rotational transitions of the water hexamer prism, and we used quantum simulations to show that they result from geared and antigeared rotations of a pair of water molecules. Unlike previously reported tunneling motions in water clusters, the geared motion involves the concerted breaking of two hydrogen bonds. Similar types of motion may be feasible in interfacial and confined water.

How Many Water Molecules Does it Take to Dissociate HCl?

The potential energy surfaces of the HCl(H2O)n (n is the number of water molecules) clusters are systematically explored using density functional theory and high-level ab initio computations. On the basis of electronic energies, the number of water molecules needed for HCl dissociation is four as reported by some experimental groups. However, this number is five owing to the inclusion of entropic factors. Wiberg bond indices are calculated and analyzed, and the results provide a quadratic correlation and classification of clusters according to the nondissociated, partially dissociated, and fully dissociated character of the H-Cl bond. Our computations show that if temperature is not controlled during the experiment, the values obtained for the dipole moment (or for any measurable property) are susceptible to change, providing a different picture of the number of water molecules needed for HCl dissociation in a nanoscopic droplet.

Association patterns in (HF)(m)(H2O)(n) (m + n = 2-8) clusters

In an attempt to understand the phase behavior of aqueous hydrogen fluoride, the clustering in the mixture is investigated at the molecular level. The study is performed at the mPW1B95/6-31+G(d,p) level of theory. Several previous studies attempted to describe the dissociation of HF in water, but in this investigation, the focus is only on the association patterns that are present in this binary mixture. A total of 214 optimized geometries of (HF)n(H2O)m clusters, with m + n as high as 8, were investigated. For each cluster combination, several different conformations are investigated, and the preferred conformations are presented. Using multiple linear regressions, the average strengths of the four possible H-bonding interactions are obtained. The strongest H-bond interaction is reported to be the H2O...H-F interaction. The most probable distributions of mixed clusters as a function of composition are also deduced. It is found that the larger (HF)n(H2O)m clusters are favored both energetically and entropically compared to the ones that are of size m + n < or = 3. Also, the clusters with equimolar contributions of HF and H2O are found to have the strongest interactions.

Can the pH value of water solutions be estimated by quantum chemical calculations of small water clusters?

In the study, various water clusters were explored from the point of view of the proton transfer between H-bonded neighbors. A relatively modest approach--the MP26-31++G(d,p) level--was chosen as acceptable considering the fact that also larger systems have to be included. The tight ion-pair model (with usually three fixed O-O distances) was adopted for the autodissociation process. First, cluster-estimated pH values rapidly decrease as cluster size increases from 2 to 6. For larger clusters in gas phase, the topology of H bonds plays an important role, varying pH from 7 to 13 in hexamers and from 5 to 15 in octamer clusters. The relationship energy/distance was quantified, too. Enhancing our model with the conductorlike screening model (COSMO) approach brought significant improvement in description of the autodissociation reaction with a stable zwitterionic structure. However, when the O-O restrictions were released, the small barrier for backward reaction disappeared, reforming neutral cluster spontaneously. Also Boltzmann weighting procedure was applied, and for the explored clusters in vacuo, the series of pH 25-18-14-13-10 was obtained for cluster sizes n=2, 3, 4, 6, 8. Using the COSMO approach, the analogous series is 15-14-12-10-9. The limit of the series is still about two to three units above the experimentally known pH. In order to reach the size-independent (bulk) value, larger clusters are needed. However, the situation is far from hopeless since (as it was proven in the study) four-coordinated molecules are not involved in the proton transfer process directly; they can only be a part of the surrounding environment.

Improved Density Functionals for Water

The accuracy of existing density functional methods for describing the noncovalent interaction energies in small water clusters is investigated by testing 25 density functionals against a data set of 28 water dimers and 8 water trimers whose structures are taken from the literature and from simulations. The most accurate functionals are found to be PW6B95 with a mean unsigned error of 0.13 kcal/mol and MPWB1K and B98 with mean unsigned errors of 0.15 kcal/mol; the best functional with no Hartree-Fock exchange is mPWLYP, which is a GGA with a mean unsigned error of 0.28 kcal/mol. In comparison, the most popular GGA functionals, PBE and BLYP, have mean unsigned errors of 0.52 and 1.03 kcal/mol, respectively. Since GGAs are very cost efficient for both condensed-phase simulations and electronic structure calculations on large systems, we optimized four new GGAs for water. The best of these, PBE1W and MPWLYP1W, have mean unsigned errors of 0.12 and 0.17 kcal/mol, respectively. These new functionals are well suited for use in condensed-phase simulations of water and ice.

Efficiency considerations in the construction of interpolated potential energy surfaces for the calculation of quantum observables by diffusion Monte Carlo

A modified Shepard interpolation scheme is used to construct global potential energy surfaces (PES) in order to calculate quantum observables--vibrationally averaged internal coordinates, fully anharmonic zero-point energies and nuclear radial distribution functions--for a prototypical loosely bound molecular system, the water dimer. The efficiency of PES construction is examined with respect to (a) the method used to sample configurational space, (b) the method used to choose which points to add to the PES data set, and (c) the use of either a one- or two-part weight function. The most efficient method for constructing the PES is found to require a quantum sampling regime, a combination of both h-weight and rms methods for choosing data points and use of the two-part weight function in the interpolation. Using this regime, the quantum diffusion Monte Carlo zero-point energy converges to the exact result within addition of 50 data points. The vibrationally averaged O-O distance and O-O radial distribution function, however, converge more slowly and require addition of over 500 data points. The methods presented here are expected to be applicable to both other loosely bound complexes as well as tightly bound molecular species. When combined with high quality ab initio calculations, these methods should be able to accurately characterize the PES of such species.