Physical Mechanisms of Linear and Nonlinear Optical Responses in Ferrocene-Embedded Cycloparaphenylenes

This study employs molecular orbital (MO) analysis, density of states (DOS) analysis, and advanced techniques such as charge density difference (CDD), transition density matrix (TDM), transition electric dipole moment density (TEDM), and transition magnetic dipole moment density (TMDM) to systematically investigate the electronic structure characteristics of Fc-[8]CPP and Fc-[11]CPP. Using density functional theory (DFT) and time-dependent DFT (TD-DFT), the π-electron delocalization properties and optical behaviors of these molecules were analyzed. Furthermore, their responses to external electromagnetic fields were explored through electronic circular dichroism (ECD) and Raman spectroscopy, comparing chiral optical responses and electron–vibration coupling effects to elucidate their photophysical properties. The results reveal that the HOMO-LUMO energy gaps of Fc-[8]CPP and Fc-[11]CPP are 5.81 eV and 5.95 eV, respectively, with a slight increase as ring size grows; Fc-[8]CPP exhibits a stronger chiral response, while Fc-[11]CPP shows reduced chirality due to enhanced symmetry. Finally, TD-DFT calculations demonstrate that their optical absorption is dominated by localized excitations with partial charge transfer contributions. These findings provide a theoretical foundation for designing conjugated macrocyclic materials with superior optoelectronic performance.