Theoretical Study on Second-Order Nonlinear Optical Responses of Pyrazine-carbazole Derivatives in Gas, Solution, and Crystal States

The packing fashion of an organic molecule in the crystal plays a critical role in the global nonlinear optical (NLO) responses under ambient conditions. To better understand how the crystal packing affects the first hyperpolarizability (β) and achieve efficient NLO material, herein, the three positional isomers (regioisomers) through changing the substituted position of 3-carbazole-pyrazine-based isomers were performed. The phenyl groups with different positions (<i>ortho</i>-, <i>meta</i>-, and <i>para</i>-) of pyrazine, named <b>23-B3C</b>, <b>25-B3C</b>, and <b>26-B3C</b>, are theoretically studied in gas, solvent, and solid states by using the polarizable continuum model and the combined quantum mechanics and molecular mechanics method, respectively. These two regioisomers (<b>23-B3C</b> and <b>25-B3C</b>) exhibit totally different aggregation behaviors. Through density functional theory (DFT) and time-dependent DFT (TDDFT) calculations, it has been concluded that the geometric changes of <b>23-B3C</b> and <b>25-B3C</b> are mainly contributed by the bond length and dihedral angle from gas to the solid phase. Herein, a lower HOMO-LUMO energy gap and a better intramolecular charge-transfer absorption are found for <b>25-B3C</b> owing to a more sizable π-conjugation effect with smaller bond length alternation. Importantly, the β value of <b>25-B3C</b> in the crystal with the π-π stacking with the same CT direction between the whole backbones (H-aggregate) and the end-groups (J-aggregate) commonly can substantially increase compared to that of the monomer. However, the obtained reduction of β value for <b>23-B3C</b> is mainly because of V-aggregate (α > 90°) and reverse J-aggregate in crystal. Thus, our work showcases a profound understanding of the relationship between solid-state packing and macroscopic second-order NLO properties and provides a feasible molecule strategy for the development of high-efficiency NLO materials.