Band gap independent intrinsic nonlinear optical response for rational materials design

Nonlinear optical (NLO) phenomena play a pivotal role in materials research and technological advancements, particularly for optoelectronic modulation and advanced photonic devices. Accurate evaluation of intrinsic NLO responses is crucial for targeted material discovery and performance optimization. However, conventional NLO coefficients (Formula presented.) exhibit strong bandgap (Eg) dependence, fundamentally distorting their correlation with actual conversion efficiency (η). This limitation not only impedes fair performance comparisons across materials with different E_g values but also artificially amplifies the NLO capabilities of narrow-E_g systems. To address this critical challenge, we propose an intrinsic NLO metric (p_i¡_k = δ_ijk · χ_ιι⁽¹⁾, incorporating a static Miller dispersion correction (δ_ιjk) that enables cross-E_g evaluations and reveals structural limits of achievable η through fundamental parameter optimization. Our first-principles calculations, performed using our in-house NLOtools, demonstrate the advantage of (φ_ijk over (Formula presented.) in decoupling E_g effects while establishing a robust framework for rational design. This framework is demonstrated through the rational design of KCuMoS4, where targeted skeletal reconstruction and elemental substitution yielded a superior intrinsic NLO potential, confirmed by its concurrently high φ_ijk and normalized Φ_ijk values. The favorable performance of KCuMoS₄ illustrates a route to mitigating the classic trade-offbetween (Formula presented.) and Eg, providing a practical methodology for the rational design of high-performance NLO materials.