Extended Nonlocal Energy-Optimized Kernels for Accurate Optical Spectra of Strained and Unstrained Solids

We present an extended version of the nonlocal energy-optimized (NEO) exchange-correlation kernel within time-dependent density functional theory (TDDFT) to compute optical absorption spectra of medium- to wide-gap bulk solids. Building on the short-range NEO kernel, we introduce a long-range correction using local density-based ingredients from GGA and meta-GGA functionals. The screening parameters are optimized to reproduce the excitonic features observed in GW-BSE calculations and experimental spectra. Our model accurately captures strain-induced changes in optical response, outperforming traditional kernels such as LRC and JGM-G, especially under compressive strain. We demonstrate that the NEO kernel, with properly tuned parameters, provides a robust and computationally efficient alternative for describing excitonic effects in both pristine and strained materials. Limitations in wide-gap insulators are discussed, along with future directions for incorporating frequency dependence and ultranonlocality.