Efficient and Accurate Methods for the Geometry Optimization of Water Clusters: Application of Analytic Gradients for the Two-Body:Many-Body QM:QM Fragmentation Method to (H2O)n, n=3-10

The structures of more than 70 low-lying water clusters ranging in size from (H2O)(3) to (H2O)(10) have been fully optimized with several different quantum mechanical electronic structure methods, including second-order Moller-Plesset perturbation theory (MP2) in conjunction with correlation consistent triple-zeta basis sets (aug-cc-pVTZ for O and cc-pVTZ for H, abbreviated haTZ). Optimized structures obtained with less demanding computational procedures were compared to the MP2/haTZ ones using both MP2/haTZ single point energies and the root-mean-square (RMS) deviations of unweighted Cartesian coordinates. Based on these criteria, B3LYP/6-31+G(d,2p) substantially outperforms both HF/haTZ and MP2/6-31G*. B3LYP/6-31+G (d,2p) structures never deviate from the MP2/haTZ geometries by more than 0.44 kcal mol(-1) on the MP2/haTZ potential energy surface, whereas the errors associated with the HF/haTZ and MP2/6-31G* structures grow as large as 12.20 and 2.98 kcal mol(-1), respectively. The most accurate results, however, were obtained with the two-body:many-body QM:QM fragmentation method for weakly bound clusters, in which all one- and two-body interactions are calculated at the high-level, while a low-level calculation is performed on the entire cluster to capture the cooperative effects (nonadditivity). With the haTZ basis set, the MP2: HF two-body:many-body fragmentation method generates structures that deviate from the MP2/haTZ ones by 0.01 kcal mol(-1) on average and not by more than 0.03 kcal mol(-1).