The thermodynamics of ion pair formation between Ca²⁺ and SO₄^2– has been studied using a rigid ion force field, the polarizable AMOEBA force field, and ab initio molecular dynamics simulation. The results obtained from the three methods are remarkably similar and consistent with the available experimental data and show that the ion association is driven by an increase in entropy, which can be related to the release of water molecules as previously found for Ca²⁺ and CO₃^2–. Two new rigid ion force fields targeting different solvation free energies for sulfate have been developed. The comparison between static and dynamic properties of the solvated anion, as well as the pairing free energy with Ca²⁺, suggest that the model with the strongest solvation is more realistic, which may help to resolve the inconsistency in the current literature.

中文翻译：

---

钙-硫酸盐离子对形成的计算洞察力

使用刚性离子力场，可极化的AMOEBA力场和从头算分子动力学模拟研究了Ca ²⁺和SO ₄ ^2–之间离子对形成的热力学。从这三种方法获得的结果非常相似，并且与可用的实验数据一致，表明离子缔合是由熵的增加驱动的，这可能与先前发现的Ca ²⁺和CO的水分子的释放有关。₃ ^2–。已经开发了针对硫酸盐的不同溶剂化自由能的两个新的刚性离子力场。溶剂化阴离子的静态和动态性质以及与Ca ²⁺配对的自由能之间的比较表明，具有最强溶剂化的模型更为实际，这可能有助于解决当前文献中的不一致问题。