Physical Mechanisms of Linear and Nonlinear Spectra of All-Benzene Catenane and Trefoil Knots Based on the First Principle

Abstract

In this study, we investigate the physical mechanisms underlying the linear and nonlinear optical spectra of all-benzene catenane and trefoil knot structures using first-principles calculations based on density functional theory (DFT). Our results reveal significant variations in electrostatic potential, electronic structures, and photon absorption characteristics across the three topological molecules. The energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the molecules is different, which affects the ability of electron transitions. One-photon absorption (OPA) and two-photon absorption (TPA) spectra were analyzed through transition density matrix (TDM) and electron-hole density diagrams, demonstrating distinct electronic transitions and charge transfer characteristics. Additionally, Raman and resonance Raman spectroscopies, coupled with vibrational mode analysis, provide insight into the nonlinear optical properties of these molecules. Magnetically induced current density analyses further reveal substantial electronic delocalization, emphasizing the role of π-conjugation in their optical responses. This work provides a theoretical foundation for advancing the use of topological carbon nanomaterials in optoelectronics and nonlinear optics.