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 (${\ensuremath{\chi}}_ijk⁽²⁾)$ exhibit strong bandgap (${E}_g$) dependence, fundamentally distorting their correlation with actual conversion efficiency (\ensuremath{\eta}). 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 ${\ensuremath{\varphi}}_ijk={\ensuremath{\delta}}_ijk\ifmmode\cdot\else\textperiodcentered\fi{}{{\ensuremath{\chi}}_ii}⁽¹⁾$, incorporating a static Miller dispersion correction (${\ensuremath{\delta}}_ijk$) that enables cross-${E}_g$ evaluations and reveals structural limits of achievable \ensuremath{\eta} through fundamental parameter optimization. Our first-principles calculations, performed using our in-house NLOtools, demonstrate the advantage of ${\ensuremath{\varphi}}_ijk$ over ${\ensuremath{\chi}}_ijk⁽²⁾$ in decoupling ${E}_g$ effects while establishing a robust framework for rational design. This framework is demonstrated through the rational design of ${\mathrm{KCuMoS}}₄$, where targeted skeletal reconstruction and elemental substitution yielded a superior intrinsic NLO potential, confirmed by its concurrently high ${\ensuremath{\varphi}}_ijk$ and normalized ${\mathrm{\ensuremath{\Phi}}}_ijk$ values. The favorable performance of ${\mathrm{KCuMoS}}₄$ illustrates a route to mitigating the classic trade-off between ${\ensuremath{\chi}}_ijk⁽²⁾$ and ${E}_g$, providing a practical methodology for the rational design of high-performance NLO materials.