Intermolecular vibration coupling between libration of water and ν₂-SOH for clusters HSO₄^-(H ₂O)_n

The hydrated bisulfate ion clusters (HSO₄^-(H ₂O)_n, n = 1-10) were optimized at the M06/6-311++G(d,p) level. The factors affecting ν₂-SOH of the clusters involved vibration coupling between ν₂-SOH and the water wagging libration mode (W-H₂O) and hydrogen bonding effect. In order to understand the vibration coupling between W-H₂O and ν₂-SOH for the bisulfate clusters, D₂O instead of H₂O and Se instead of S were used to estimate the uncoupling frequency of ν₂-SOH and W-H₂O, respectively. For HSO₄^- ·H ₂O-I, the uncoupling frequencies of ν₂-SOH and W-H ₂O were obtained at 752.0 and 753.4 cm^-1. After coupling, the frequencies appeared at 782.2 and 732.6 cm^-1. H₂S and NH₄⁺ instead of D₂O in HSO₄ ^-·D₂O-II were compared to analyze the effect of hydrogen bond. The sequence of hydrogen bond strength was found to be HSO ₄^-·H₂S-II < HSO₄ ^-·D₂O-II < HSO₄ ^-·NH₄⁺-II with the respective ν₂-SOH at 736.7, 740.5, and 802.2 cm^-1 increasing in the same order. In HSO₄^-· (H₂O) _n, coupling appeared when n was from 1 to 8. For HSO₄ ^-· (D₂O)_n, no coupling between ν₂-SOH and D₂O librations made it possible to understand the hydrogen bonding effect on the ν₂-SOH. The frequencies of ν₂-SOH for clusters HSO₄ ^-(D₂O)_n almost linearly decreased from 752.0 to 854.6 cm^-1 with n from 1 to 10.