The particle swarm optimization method in conjunction with density functional calculations is used to search the lower energy structures for the cationic water clusters (H2O)5+. Geometry optimization, vibrational analysis, and infrared spectrum calculation are performed for the most interesting clusters at the MP2/aug-cc-pVDZ level. The relationships between their structural arrangements and their energies are discussed. According to their relative Gibbs free energies, their energy order is determined and four lowest energy isomers are found to have a relative population surpassing 1% below 350 K. Studies reveal that, among these four isomers, one new cluster found here also contributes a lot to the experimental infrared spectrum. Based on topological analysis and reduced density gradient analysis, some meaningful points are found by studying the structural characteristics and the bonding strengths of these cationic water clusters: in the first solvation shell, the central H3O+ motifs may have a stronger interaction with the OH radical than with the water molecules. The interaction in the second solvation shell may also be stronger than that in the first solvation shell, which is opposite to our intuition.

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