Second-Harmonic Generation Response in Nitridophosphates <i>M</i>P₂N₄ (M = Ge, Sn, Pb) and the Role of Stereochemically Active Lone Pairs

The recent synthesis of two noncentrosymmetric (NCS) nitridophosphates, GeP2N4 and Sn6[P12N24], featuring stereochemically active lone pairs (SCALPs), provides an opportunity to explore their role in nonlinear optical (NLO) properties and assess the potential of nitridophosphates for NLO applications. Through high-throughput screening of all nitridophosphate compounds in the Materials Project database and Inorganic Crystal Structure Database, we identify 23 NCS nitridophosphates with nonzero second-harmonic generation (SHG) responses. In comparison, MP2N4 (M = Ge, Sn, Pb) family, in both Pna21 and R3m structures, emerges as the only nitridophosphates that combines significant SHG response and sizable birefringence within a band gap range suitable for infrared NLO applications. First-principles calculations reveal that Pna21 phases of MP2N4 generally exhibit larger SHG responses than the R3m ones and substituting Ge2+ with more polarizable Sn2+ or Pb2+ enhances the SHG response to 4.1 and 7.2 pm/V (∼12 and 22 × KDP), respectively. Our atom response theory analysis indicates that the SHG response is predominantly driven by nonbonding N 2p states, while SCALPs provide a positive but secondary contribution, as the SHG magnitude inversely correlates with SCALP strength. Additionally, we reveal that NaPN2 and HPN2 exhibit impressive SHG response (∼10 × KDP) combined with remarkable band gaps exceeding 6.2 eV, making them promising candidates for ultraviolet (UV) or visible NLO applications. This study sheds light on the mechanisms driving the NLO behavior in MP2N4 and highlights nitridophosphates as a promising platform for developing advanced NLO materials.