The 6s2 lone-pair electrons (Pb2+, Bi3+) and 5s2 lone-pair electrons (Sn2+, Sb3+) show different responses to birefringence than they do to second harmonic generation (SHG). In the current work, different mechanisms of birefringence and SHG responses induced by Pb2+/Sn2+ cations were investigated using the first-principles method on AB2O3F2 (A = Ba, Sn, Pb). The obtained birefringence and SHG coefficients were in good agreement with the experimental values. The anisotropic lone-pair electron distribution was found at the states near the Fermi level containing cation sp-oxygen p states. Our analyses showed the birefringences of the AB2O3F2 (A = Ba, Sn, Pb) compounds to be directly affected by the anisotropic lone-pair electron distribution, however, the SHG responses of these three compounds have a more complicated relationship with the hybrid cation-oxygen states. The expanded hybrid cation-oxygen states including the lone-pair states were concluded to endow the PbB2O3F2 compound with a stronger SHG response than those displayed by the other compounds.

中文翻译：

---

ns2 阳离子周围不对称孤对电子对双折射和二次谐波产生的不同响应机制

6s2 孤对电子（Pb2+、Bi3+）和 5s2 孤对电子（Sn2+、Sb3+）对双折射的响应与对二次谐波产生 (SHG) 的响应不同。在目前的工作中，使用第一性原理方法对 AB2O3F2 (A = Ba, Sn, Pb) 研究了由 Pb2+/Sn2+ 阳离子引起的双折射和 SHG 响应的不同机制。获得的双折射和倍频系数与实验值非常吻合。在包含阳离子 sp-氧 p 态的费米能级附近的状态处发现了各向异性孤对电子分布。我们的分析表明 AB2O3F2 (A = Ba, Sn, Pb) 化合物的双折射直接受各向异性孤对电子分布的影响，然而，这三种化合物的 SHG 响应与杂化阳离子 - 氧状态有更复杂的关系。包括孤对态在内的扩展的混合阳离子-氧态被认为赋予 PbB2O3F2 化合物比其他化合物显示出的更强的 SHG 响应。