A B3LYP study on counterpoise-corrected geometry optimizations for hydrated complexes of [K(H2O)n] and [Na(H2O)n]

We report the basis set dependencies and the basis set superposition errors for the hydrated complexes of K⁺ and Na⁺ ions in relation to the recent studies of the KcsA potassium channel. The basis set superposition errors are estimated by the geometry optimizations at the counterpoise-corrected B3LYP level. The counterpoise optimizations alter the hydration distances by about 0.02–0.03 Å. The enthalpies and free energies for K⁺ + n(H₂O) → K(H₂O)_n]⁺ and Na⁺ + n(H₂O) → Na(H₂O)_n]⁺ (n = 1–6) are compared between the theoretical and experimental values. The results show that the addition of diffuse functions to K, Na, and O species are effective. However, it is also found that the counterpoise corrections using diffuse functions work so as to underestimate the free energies for the complexes with increasing the hydration number. The stabilization energies in aqueous solution are larger for a Na⁺ ion than for a K⁺ ion, suggesting the contributions of their dehydration processes to the ion selectivity of the KcsA potassium channel. The changes in coordination distance between the isolated K(H₂O)₈]⁺ and the K(H₂O)₈]⁺ in the KcsA potassium channel indicate the importance of hydrogen bondings between the first hydration shell and the outer hydration shells.