Key Factors Controlling the Large Second Harmonic Generation in Nonlinear Optical Materials

The second harmonic generation (SHG) responses of nonisostructural nonlinear optical (NLO) compounds, β-BaB2O4, LiB3O5, CsB3O5, CsLiB6O10, KBe2BO3F2, and LiCs2PO4, were examined by density functional theory (DFT) calculations, and the contributions of their individual cations and anions were determined by performing atomic response theory analyses. In all of these compounds, the contribution of all metal cations lies in the range of ∼9.3 to ∼29.7% of the total SHG responses, and that of all anions lies between ∼57.4 and ∼72.3%. However, in terms of individual atom contribution, a large metal cation can contribute more than does an anion to the total SHG response. Our work shows that the SHG contribution of an individual anion (e.g., O2–) is weakened when it forms covalent bonds with its surrounding cations (e.g., O–B). The contribution of an individual cation is further affected by the homogeneity of its surrounding anion distribution and also by how strongly the polarizabilities of its surrounding anions are weakened by covalent bonding with other cations. The SHG response increases with αsum/(NEg), an important parameter useful in searching for new NLO materials, where αsum is the sum of the polarizabilities of all of the ions in the primitive unit cell, N is the total number of atoms per primitive cell, and Eg is the band gap.