Hybrid Functionals with Spatially Resolved Screening for Excited-State Calculations

Accurately predicting excited-state properties of heterogeneous systems remains a central challenge in computational chemistry and materials science. Dielectric-dependent hybrid functionals have achieved notable success for bulk semiconductors and insulators, but their reliance on a scalar macroscopic dielectric constant hampers their applicability to systems with spatially inhomogeneous screening environments. Here, we use hybrid functionals with spatially dependent screened exchange within linear-response time-dependent density functional theory (TDDFT), and we evaluate analytical excited-state forces, enabling geometry relaxation on excited-state potential-energy surfaces and the computation of adiabatic excitation energies. We first consider point defects in three-dimensional bulk hosts, including diamond, silicon carbide, and magnesium oxide, and we show that our approach preserves the accuracy of conventional dielectric-dependent hybrid functionals. For systems with strongly heterogeneous dielectric environments, including the Cr(o-tolyl)4 molecular qubit embedded in a Sn(o-tolyl)4 host matrix and the CBCN defect in monolayer h-BN, hybrid functionals with spatially dependent screened exchange yield substantially improved agreement with experiment and high-level many-body benchmarks, compared to conventional dielectric-dependent hybrid functionals. Our results establish hybrid-functional TDDFT with spatially dependent screened exchange as a broadly applicable and physically motivated strategy for excited-state simulations of complex, inhomogeneous environments.