Influence of Nitrogen Doping on Vacancy-Engineered T-Graphene Fragments: Insights into Electronic and Optical Properties

This study investigates the influence of vacancy engineering and nitrogen doping on the structural, electronic, and optical properties of T-graphene fragments (TFs) using density functional theory (DFT) and time-dependent DFT (TD-DFT). A central vacancy and five pyridinic nitrogen doping configurations are explored to modulate the optoelectronic behavior. All systems are thermodynamically stable, exhibiting tunable HOMO–LUMO gaps, orbital distributions, and charge transfer characteristics. Optical absorption spectra show redshifts and enhanced oscillator strengths in doped variants, notably v-NTF2 and v-NTF4. Nonlinear optical (NLO) analysis reveals significant enhancement in both static and frequency-dependent responses. v-NTF2 displays an exceptionally high first-order hyperpolarizability (⟨β⟩ = 1228.05 au), along with a strong electro-optic Pockels effect (β (−ω; ω, 0)) and second harmonic generation (β (−2ω; ω, ω)). Its third-order response, γ (−2ω; ω, ω, 0), also exceeds 1.2 × 105 au under visible excitation. Conceptual DFT descriptors and energy decomposition analysis further supports the observed trends in reactivity, charge delocalization, and stability. These findings demonstrate that strategic nitrogen doping in vacancy-engineered TFs is a powerful route to tailor electronic excitation, optical absorption, and nonlinear susceptibility. The results offer valuable insight into the rational design of next-generation carbon-based materials for optoelectronic, photonic, and NLO device applications.