MP2-level QTAIM ionic radii for twenty hydrated mono and divalent cations

We report a systematic QTAIM study of hydration clusters M^m+(H₂O)_n (m = 1, 2; n = 1-8) for twenty mono- and divalent cations at the gas-phase MP2/def2-TZVP level. Global-minimum geometries were verified by harmonic frequency calculations, and QTAIM analysis was performed using AIMAll on the relaxed MP2 electron density. The reliability of the MP2/def2-TZVP + QTAIM approach was assessed against benchmark QTAIM results for Na⁺ and available solution-phase structural data. Calculated ion-O distances at coordination-number saturation reproduce experimental values to within 0-9.7% (mean: 1.6 ± 3.4%) without implicit solvation corrections. By decomposing the ion-O distance as d_ion-O = d_ion-BCP + d_BCP-O, we define the effective ionic radius as the mean ion-BCP distance, d_I-BCP. This topologically defined quantity measures the extent of the cationic electronic basin within its hydration environment. The results show that d_I-BCP converges primarily with coordination number rather than overall cluster size. For Li⁺, Na⁺, and K⁺, exhaustive isomer sampling gives an inter-isomer dispersion below 0.003 Å at fixed coordination number, demonstrating that the BCP position is largely insensitive to second-shell water arrangement. The converged effective ionic radii range from 0.564 Å for Be²⁺ (CN = 4) to 1.755 Å for Cs⁺ (CN = 6), following the Shannon-radius sequence. The d_ion-BCP/r_Shannon ratios fall within 104-109% for alkali metals, 111-125% for alkaline-earth metals, and 122-130% for 3d transition metals, reflecting systematic differences between the QTAIM and crystallographic definitions of ionic size. Across the twenty-cation series, ρ_BCP exhibits an exponential decay with d_ion-BCP, largely independent of charge and electronic configuration. Distinct structural effects are captured, including Jahn-Teller distortion in Cu²⁺, relativistic linear coordination in Hg²⁺, and stereochemically active s² lone pairs in Pb²⁺ and Sn²⁺. These results provide the first systematic series of MP2-level QTAIM effective ionic radii for twenty cations covering groups 1, 2, and the transition metals, serving as a valuable reference for force-field calibration in molecular dynamics and for the modelling of metalloenzyme active sites.