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.