Density functional theory studies on the solvent effects in Al(H2O)63+ water-exchange reactions: the number and arrangement of outer-sphere water molecules

Abstract

Density functional theory (DFT) calculations combined with cluster models are performed at the B3LYP/6-311+G(d,p) level for investigating the solvent effects in Al(H₂O)₆³⁺ water-exchange reactions. A “One-by-one” method is proposed to obtain the most representative number and arrangement of explicit H₂Os in the second hydration sphere. First, all the possible ways to locate one explicit H₂O in second sphere (N_m′ = 1) based on the gas phase structure (N_m′ = 0) are examined, and the optimal pathway (with the lowest energy barrier) for N_m′ = 1 is determined. Next, more explicit H₂Os are added one by one until the inner-sphere is fully hydrogen bonded. Finally, the optimal pathways with N_m′ = 0–7 are obtained. The structural and energetic parameters as well as the lifetimes of the transition states are compared with the results obtained with the “Independent-minimum” method and the “Independent-average” method, and all three methods show that the pathway with N_m′ = 6 may be representative. Our results give a new idea for finding the representative pathway for water-exchange reactions in other hydrated metal ion systems.