Ground-State Structures of Hydrated Calcium Ion Clusters From Comprehensive Genetic Algorithm Search

We searched the lowest-energy structures of hydrated calcium ion clusters Ca²⁺(H₂O)_n (n = 10-18) in the whole potential energy surface by the comprehensive genetic algorithm (CGA). The lowest-energy structures of Ca²⁺(H₂O)_10-12 clusters show that Ca²⁺ is always surrounded by six H₂O molecules in the first shell. The number of first-shell water molecules changes from six to eight at n = 12. In the range of n = 12-18, the number of first-shell water molecules fluctuates between seven and eight, meaning that the cluster could pack the water molecules in the outer shell even though the inner shell is not full. Meanwhile, the number of water molecules in the second shell and the total hydrogen bonds increase with an increase in the cluster size. The distance between Ca²⁺ and the adjacent water molecules increases, while the average adjacent O-O distance decreases as the cluster size increases, indicating that the interaction between Ca²⁺ and the adjacent water molecules becomes weaker and the interaction between water molecules becomes stronger. The interaction energy and natural bond orbital results show that the interaction between Ca²⁺ and the water molecules is mainly derived from the interaction between Ca²⁺ and the adjacent water molecules. The charge transfer from the lone pair electron orbital of adjacent oxygen atoms to the empty orbital of Ca²⁺ plays a leading role in the interaction between Ca²⁺ and water molecules.