Theoretical Study\non Second-Order Nonlinear Optical\nResponses of Pyrazine-carbazole Derivatives in Gas, Solution, and\nCrystal States

The packing fashion of an organic molecule in the crystal\nplays\na critical role in the global nonlinear optical (NLO) responses under\nambient conditions. To better understand how the crystal packing affects\nthe first hyperpolarizability (β) and achieve efficient NLO\nmaterial, herein, the three positional isomers (regioisomers) through\nchanging the substituted position of 3-carbazole-pyrazine-based isomers\nwere 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\nstates by using the polarizable continuum model and the combined quantum\nmechanics and molecular mechanics method, respectively. These two\nregioisomers (<b>23-B3C</b> and <b>25-B3C</b>) exhibit\ntotally different aggregation behaviors. Through density functional\ntheory (DFT) and time-dependent DFT (TDDFT) calculations, it has been\nconcluded that the geometric changes of <b>23-B3C</b> and <b>25-B3C</b> are mainly contributed by the bond length and dihedral\nangle from gas to the solid phase. Herein, a lower HOMO–LUMO\nenergy gap and a better intramolecular charge-transfer absorption\nare found for <b>25-B3C</b> owing to a more sizable π-conjugation\neffect with smaller bond length alternation. Importantly, the β\nvalue of <b>25-B3C</b> in the crystal with the π–π\nstacking with the same CT direction between the whole backbones (H-aggregate)\nand the end-groups (J-aggregate) commonly can substantially increase\ncompared to that of the monomer. However, the obtained reduction of\nβ value for <b>23-B3C</b> is mainly because of V-aggregate\n(α > 90°) and reverse J-aggregate in crystal. Thus,\nour\nwork showcases a profound understanding of the relationship between\nsolid-state packing and macroscopic second-order NLO properties and\nprovides a feasible molecule strategy for the development of high-efficiency\nNLO materials.