Hydrated proton clusters: Ab initio molecular dynamics simulation and simulated annealing

An ab initio molecular dynamics simulation technique is developed employing the Born–Oppenheimer (BO) approach in the framework of a Gaussian implementation of Kohn–Sham density functional theory (DFT). Simulation results for ${\mathrm{H}}_{\mathrm{5}}{\mathrm{O}}_{\mathrm{2}}^{\mathrm{+}}$ at 200 K are reported. The density profiles, autocorrelation functions and power spectra are presented. The anharmonic frequencies at 200 K are found to be close to the harmonic frequencies calculated directly from quantum methods at 0 K. Structures of large hydrated proton clusters are optimized. Simulated annealing techniques were employed to search for low energy structures and found to be very useful for clusters with 7–8 water molecules. A few very different structures with ground state energy 1–2 kcal/mol apart are shown. ${\mathrm{H}}_{\mathrm{3}}{\mathrm{O}}^{\mathrm{+}}$ is found to be the central unit of a few structures optimized. The ionic hydrogen bond was responsible for the stability of the ${\mathrm{H}}_{\mathrm{9}}{\mathrm{O}}_{\mathrm{4}}^{\mathrm{+}}$ unit in the large hydrated proton clusters. We also find structures with nascent ${\mathrm{H}}_{\mathrm{5}}{\mathrm{O}}_{\mathrm{2}}^{\mathrm{+}}$ units at the center whose energy is close to, sometimes even lower than that of the ${\mathrm{H}}_{\mathrm{3}}{\mathrm{O}}^{\mathrm{+}}$ centered structures. This can be used to explain the solvation facilitated proton transfer in clusters and in solution. The vibrational frequencies of the structures we optimized are tabulated and compared with the experimental results of Price et al. Questions are raised regarding their prediction of a new feature due to water molecules in the third solvation shell. Some new features have been observed for large clusters with heretofore unpredicted structures.