Abstract: The structures of ion-associated species between Na⁺, Li⁺, Mg²⁺ and SO₄^2- ions were optimized via ab initio calculations. And the influences of the cations to the ν₁-SO₄^2- frequencies were also investigated. For the ion-associated structures, when there are fewer cations, the repulsion between cations will decrease and thus the bidentate associated structures are easy to form, in which there is shorter distance between metal ion and SO₄^2-. Contrarily, comparing with the increase of the number of cations in the ion clusters, especially for more Mg²⁺ ions which have more positive charge, the repulsions between metal ions would make the clusters instable and more monodentate structures are formed, in which the distances between metal and SO₄^2- ions are longer. The metal ions could influence the ν₁-SO₄^2- frequencies via two ways. The first one is polarization of the cation, which leads the ν₁-SO₄^2- frequency red-shift, while another one is M-O bonding action, which lead the opposite blue-shift. When the number of metal ions ≤2, the first one is dominated. The first metal ion can lead the ν₁-SO₄^2- frequency red-shift, while more metal ions from different directions would decrease the red-shift. When the number of metal ions >2, the M-O bonding action is the main interaction manner. The increase of the monodentate associated structures in the quadruple or quintuple ion clusters, which can lead the more blue-shift than those of the bidentate ones, will make the ν₁-SO₄^2- frequency more blue-shift than those in the triple ion clusters.

Key words: Quantum chemistry calculation, Sulfate, Ion-associated species, ν₁-SO₄^2- frequency