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

We report a systematic QTAIM study of hydration clusters Mm+(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 dion-O = dion-BCP + dBCP-O, we define the effective ionic radius as the mean ion-BCP distance, dI-BCP. This topologically defined quantity measures the extent of the cationic electronic basin within its hydration environment. The results show that dI-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 dion-BCP/rShannon 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, ρBCP exhibits an exponential decay with dion-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.