Hydrated proton clusters and solvent effects on the proton transfer barrier: A density functional study

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Abstract
The density functional calculations using the Perdew nonlocal corrections to exchange and correlation have been carried out for a sequence of hydrated proton clusters. The optimized structures were obtained up to H13O+6. It is found that H3O+ is indeed the central unit in all the lowest energy structures we found. Our results support the argument that the structure with a four-coordinate first solvation shell is very unlikely in small hydrated proton clusters. The density functional calculations with the Perdew nonlocal corrections to exchange and correlation give somewhat shorter hydrogen bond lengths, but slightly longer chemical bond lengths as compared with the post-Hartree–Fock calculations. The harmonic vibrational frequencies and IR intensities of various vibrational modes have been generated for all the structures optimized. Results for small clusters are compared with the high resolution experimental spectroscopy studies of Yeh et al. and Begemann et al. Results for larger clusters are used to interpret the low resolution spectra of Schwartz. Very good accord with experimental results is obtained. The solvent effects on proton transfer energy barriers in clusters have been studied by designing a few model systems. The barrier is found to be very sensitive to the solvent configurations. When the solvent water is replaced by the classical partial charge model, a significant change of the barrier is observed, indicating that a quantitative treatment will ultimately require a good pseudopotential to properly account for the quantum nature of the solvent. A combined density functional and molecular dynamics simulation was used to calculate the proton transfer energy and free energy barrier in aqueous solution. The barrier is found to be 3 kcal/mol higher than in gas phase. Very large solvent fluctuation is observed which may have a significant influence on the reaction rate.