First-principles study of the influence of lone pair electrons and molecular groups on the birefringence of phosphate and fluorophosphate

As a significant nonlinear optical compound, phosphate has been wildly used in all kinds of advanced optical systems. In this work, the electronic structures, and optical properties of a series of XPO3F and X3(PO4)2 (X = Sn, Pb, Sr, Ba) compounds were investigated using the first-principles method in both molecular and crystal levels. The results show that introducing F atoms can lead to enhanced HOMO-LUMO gap and enlarged anisotropy of polarizability. The anionic groups give main contribution to the total birefringence of alkaline earth phosphate and fluorophosphate. As for the post-transition metal phosphate and fluorophosphate, both anionic groups and cation-centric polyhedra play a critical role in determining birefringence. The X-p (X = Sn, and Pb) states nearby the Fermi level are beneficial to get enhanced birefringence, but they do not play a vital role in determining total birefringence.