Exploring the frequency-dependent nonlinear optical response of push-pull configured thianthrene-based chromophores: DFT/TD-DFT approach

The current study aimed to investigate the frequency-dependent nonlinear optical (NLO) properties of thianthrene-based derivatives ( PTMR1 – PTMD7 ). These derivatives feature a donor– π –acceptor (D– π –A) architecture, developed via structural modifications of the reference compound ( PTMR1 ) by substituting various acceptor groups. The optoelectronic properties of the designed compounds were evaluated using density functional theory (DFT) and time-dependent density functional theory (TD-DFT) at the M06/6-311G(d,p) level of theory. The structural geometries of PTMR1 and its derivatives were optimized at the same level of theory. These optimized geometries were subsequently employed to analyze the UV–Visible (UV-Vis) absorption spectra, density of states (DOS), natural bond orbitals (NBO), frontier molecular orbitals (FMOs), and transition density matrix (TDM) to understand their NLO behavior. The FMO analysis indicated that PTMD6 exhibited the smallest energy gap (2.629 eV ) among all the compounds. Consistently, the DOS plots and TDM heat maps confirmed efficient charge transfer from the highest occupied molecular orbital (HOMO) to the lowest occupied molecular orbital (LUMO) in PTMD2 – PTMD7 . NBO analysis confirmed hyperconjugation and intramolecular charge transfer (ICT), validating the D–π–A framework and effective push–pull character of PTMD2 – PTMD7 . The global reactivity parameters (GRPs) values were also computed, corresponding to the energy gap of HOMOs and LUMOs. Again, PTMD6 with the smallest energy gap showed the lowest hardness (1.315 eV ) and the highest softness (0.380 eV ) among the tailored derivatives. The absorption maxima ( λ max ) values of the derivatives (433.329 – 549.186 nm ) were found to be higher than that of the PTMR1 (430.995 nm ). Notably, the NLO responses were significantly enhanced in the derivatives compared to PTMR1 . PTMD6 exhibited the highest values of linear hyperpolarizability < α > = (1.53×10⁻ 22 esu ), first hyperpolarizability β total = (5.36×10⁻ 28 esu ), and second hyperpolarizability γ total = (3.91×10⁻ 33 esu ). Furthermore, the frequency-dependent NLO results showed substantial enhancement at operational wavelengths (1064–532 nm ) for all compounds. This study provides valuable insights for designing NLO materials through strategic substitution with suitable organic linking species. The findings highlight the potential of thianthrene-based D–π–A systems as promising candidates for advanced photonic and optoelectronic applications.