Origin of second harmonic generation in noncentrosymmetric crystal structures containing lone pair electrons

Material systems with lone-pair electrons have long been a treasure trove in the search for large second harmonic generation effects. Revealing the origin of second harmonic generation in nonlinear optical materials can provide theoretical guidance for the design of new materials. In this work, the origin of second harmonic generation in non-centrosymmetric materials containing lone pair electrons is revealed by analyzing the orbital interactions on the sublattice. Stereochemically inactive Pb 6\textit{s} orbitals with high symmetry in CsPbCO3F contribute less to the second harmonic generation. In contrast, the contribution of stereochemically active Pb 6s orbital in PbB5O7F3 and PbB2O3F2 is more obvious. Significantly, the orbitals of the interaction between lead and oxygen make a very significant contribution because these orbitals are located at the band edge and in non-centrosymmetric sublattices.