The Bi(III) cations associated with lone pair electrons can help to enhance the linear (birefringence) and nonlinear optical (second harmonic generation, SHG) performances. In this work, the influence of bismuth cations on birefringence or SHG in α, β, γ, δ, and ε-BiB₃O₆, BiB₂O₄F and BiB₂O₄(OH) is investigated via first-principles, real-space atom-cutting and lone pair electron analysis methods. It is revealed that the intensity of lone pair stereochemical activity, induced by the interaction between bismuth and oxygen atoms, influences the birefringence and nonlinear optical responses of different phases of BIBO. For birefringence, a coplanar arrangement of BO₃ groups is conducive to the realization of large birefringence; meanwhile, if the density of BO₃ in the unit cell is high, BO₃ plays a decisive role in large birefringence in BIBO; if the density of BO₃ is low, the effect of the bismuth oxygen polyhedra with lone pairs of electrons will lead to large birefringence in BIBO. Regarding the SHG response, bismuth oxygen polyhedra are responsible for large SHG responses, boron–oxygen groups made a small contribution. Moreover, by comparing the optical properties of BiB₂O₄F and BiB₂O₄(OH), it is also found that the lone pair stereochemical activity can be influenced by other ions such as fluorine in addition to oxygen. A comprehensive understanding is important to elucidate the structure–property relationship and provide a general strategy for searching for new NLO materials.

中文翻译：

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孤对电子效应引起硼酸铋的线性和非线性光学性质的差异†

与孤对电子关联的Bi（III）阳离子可以帮助增强线性（双折射）和非线性光学（二次谐波生成，SHG）性能。在这项工作中，在α，β，γ，δ，和双折射或SHG铋阳离子的影响ε-围兜₃ ö ₆，围兜₂ ö ₄ F和围兜₂ ö ₄（OH）进行了研究通过第一性原理，实空间原子切割和孤对电子分析方法。揭示了铋和氧原子相互作用引起的孤对立体化学活性的强度影响了BIBO不同相的双折射和非线性光学响应。对于双折射，BO ₃基团的共面排列有利于实现大的双折射。同时，如果晶胞中BO ₃的密度高，则BO ₃在BIBO的大双折射中起决定性作用。如果BO ₃的密度当铋氧多面体为低时，孤氧电子对的作用将导致BIBO中的大双折射。关于SHG反应，铋氧多面体负责大量的SHG反应，硼-氧基团贡献很小。此外，通过比较BiB ₂ O ₄ F和BiB ₂ O ₄（OH）的光学性质，还发现孤对立体化学活性除受氧影响外还可受其他离子如氟的影响。全面的理解对于阐明结构与属性的关系并为寻找新的NLO材料提供一般策略非常重要。