Charged water clusters

Charged Water Clusters

Ab initio techniques are used to explore the quantum character of the shared proton in the hydrogen--bonded complexes, H₅O₂ ⁺ and H₃O₂ ^- at room temperature. These complexes can be considered as prototypes of strong and intermediate strength hydrogen bonds. Experimental and theoretical studies have tended to focus more on H₅O₂ ⁺ than on H₃O₂ ^- Quantum chemical calculations at the Hartree--Fock level predict asymmetric bonding with one covalent OH bond as the most stable configuration for H₅O₂ ⁺, suggesting that the proton moves on a potential with a double well structure. This corresponds schematically to [H₂O--H^*...OH₂] ⁺ and [H₂O^... H^*--OH₂]⁺ where H^* denotes the shared proton in the hydrogen bond. Using more accurate (correlated) calculations, however, one predict a minimum energy structure [H₂O ^... H^*...OH ₂]⁺ with a centrosymmetric shared proton (approximately 1.2 angstroms from each oxygen atom) in a nearly linear O^... H^* ^...O arrangement. At this O--O distance, the proton moves on a steep potential with a single minimum, suggesting an essentially classical nature for the H₅O₂ ⁺, complex at room temperature. We have previously studied the solvation of a hydronium ion in bulk water, the results of which support the classical picture of a single--minimum potential. When the hydronium--water O^...O distance decreased to less than 2.5 angstroms, the proton migrated to the center of the hydrogen bond, thus forming the H₅O₂ ⁺, complex in about half of all configurations sampled.

There have been considerably fewer studies of the H₃O₂ ^- complex. Accurate quantum chemical calculations suggest that the minimum geometry is not centrosymmetric, as for H₅O₂ ⁺ but rather that the shared proton has one covalent OH bond forming an asymmetric [HO--H^... OH]^- complex. At zero temperature, it appears that the bond symmetrization barrier is extremely small, <= 1 kcal/mol. The O--O distance is approximately 2.5 angstroms, and thus the existence of a small barrier in the bare potential correlates well with the notion that such a low--barrier hydrogen bond can be characterized as being of intermediate strength. It has been speculated that the lowest vibrational state might lie above the barrier.

The above discussion makes clear the necessity of using an accurate electronic structure theory to ensure a reliably accurate representation of the hydrogen bonded complexes. In order to sample both thermal and quantum fluctuations of many coupled degrees of freedom simultaneously in a non--perturbative manner, numerical simulations based on Feynman's path integral formulation of quantum statistical mechanics are carried out. This method is combined with the Car-Parrinello density functional based ab initio molecular dynamics scheme, thus eliminating the need for an empirical potential function. This approach includes full internuclear anharmonicity as well as ro--vibrational excitations and coupling. Each path integral simulation is accompanied by an equivalent calculation in which the nuclei are treated as classical point particles, allowing pure thermal fluctuations to be studied independent of quantum fluctuations.

The spatial distribution function is a property of key interesting in understanding the nature of the shared proton. In order to represent this multidimensional quantity, configurations taken from the simulations are superimposed on one another. The following two images represent classical (left) and path integral (right) Car-Parrinello simulations of the H₅O₂ ⁺ at T=300K.

The following two images represent classical (left) and path integral (right) Car-Parrinello simulations of the H₃O₂ ^- at T=300K.

There is a striking similarity between the classical (top left) and quantum (top right) H₅O₂ ⁺ simulations at room temperature. In both cases, the shared proton resides preferentially midway between the two oxygen atoms, the quantum proton being only slightly more delocalized.

Unlike H₅O₂ ⁺ the classical picture of the H₃O₂ ^- complex changes even on a qualitative level once nuclear quantum effects are included. Classically, the configurations (bottom left and bottom right) show a clustering of the shared proton at positions that are within a covalent OH bond distance from the two oxygen atoms, leading to a reduction in density near the midpoint (bottom left) This is indicative of an effective potential with a double well nature at room temperature. The quantum simulation (bottom right), on the other hand, shows a clustering in the center along the O--O bond, similar to the H₅O₂ ⁺.

The figures above can be quantified by plotting the distribution functions of the O--O distance and the asymmetric stretch coordinate corresponding to each.

One is thus lead to speculate that the importance of nuclear quantum effects in many proton transfer problems can be predicted qualitatively once the distribution of the distances between the donor and acceptor atoms that share the proton is known. In particular, our results suggest that OH^- should prove to be the more promising species from the point of view of quantum phenomena.

References

Quantum nuclear ab initio molecular dynamics study of water wires .
H.S. Mei, M.E. Tuckerman, D.E. Sagnella and M.L. Klein J. Phys. Chem. B 102, 10446 (1998).

On the quantum nature of the shared proton in hydrogen bonds.
M.E. Tuckerman, D. Marx, M.L. Klein and M. Parrinello, Science 275, 817 (1997).