Third-order nonlinear optical properties of π-stacked donor–acceptor cyclophanes: a DFT investigation

Abstract

The electronic and nonlinear optical (NLO) properties of cyclophane-based complexes were modulated by introducing various donor groups and acceptor groups. The donor groups comprise carbazole (KZ), benzo[1,2-b:4,5-b′]dithiophene (BDT), and dihydroindolo[3,2-b]indole (DN), while the acceptor groups comprise 1,4,5,8-naphthalenetetracarboxylic diimide (NDI) and 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene (BOD). Reduced density gradient analysis confirmed the characteristic weak π–π stacking interactions between the donor and acceptor units. Significantly, these complexes exhibit remarkably large second hyperpolarizabilities of 3.43 × 10⁵–5.62 × 10⁵ a.u., with NDI-based systems showing consistently superior NLO responses compared to their BOD-based counterparts. A comprehensive analysis of electronic transitions, hyperpolarizability tensors, and hyperpolarizability densities provides a deep understanding of the nature of optical properties. In NDI/BOD-based systems, the excitation transitions exhibit significant charge transfer character from the donor moieties (KZ/BDT/DN) to the NDI/BOD unit, along with local excitation (LE) components. However, BOD-based systems additionally demonstrate reverse charge transfer from the BOD unit back to the KZ/BDT moieties. The decomposition of the hyperpolarizability contribution analysis reveals that stronger electron-donating groups enhance positive contributions. Notably, BOD acceptors exhibit anomalous negative effects compared to NDI analogues. This research offers a basis for understanding the structure–property relationships of cyclophanes.