Theoretical understanding on the v₁-SO₄^2- band perturbed by the formation of magnesium sulfate ion pairs

The factors determining the spectroscopic characteristics of the v ₁-SO₄^2- band of the MgSO₄ ion pairs are discussed via ab initio calculation, including coupling effect, hydrogen bonding effect, and direct contact effect of Mg²⁺ widi SO ₄^2-. With the calculation of the heavy water hydrated contact ion pairs (CIP), the overlap between the librations of water and the v₁-SO₄^2- band can be separated, and thus the coupling effect is abstracted, and this coupling effect leads to a blue shift for the v₁-SO₄^2- band of 5.6 cm^-1 in the monodentate CIP and 3.6 cm^-1 in the bidentate CIP. The hydrogen bonding between each water molecule without relation to Mg²⁺ and the sulfate ion makes the v₁-SO₄^2- band blue shift of 3.7 cm^-1. When the outer-sphere water around Mg²⁺ are hydrogen bonded between. SO₄^2- and Mg²⁺, it will make the largest disturbance to the v₁-SO₄ ^2- band. Moreover, the inner-sphere water can affect the v ₁-SO₄^2- band conjunct with the direct contact of Mg²⁺ with SO₄^2-, showing a blue shift of 14.4 cm^-1 in the solvent-shared ion pair, 22.6 cm^-1 in the monodentate CIP, 4.3 cm^-1 in the bidentate CIP, and 2.1,4 cm ^-1 in the tridentate CIP. At last, the Raman spectral evolution in the efflorescence production process is tried to be rationalized. The shoulder at 995 cm^-1 is attributed, to the monodentate CIP with 2-3 outer-sphere water molecules, whereas the new peak at 1021 cm^-1 at high concentration is assigned to the formation of aqueous triple ion.