Comparative theoretical analysis for structural flexibility of carbon nanobelt families.

Understanding the relationship between molecular structure and flexibility in curved π-conjugated macrocycles is essential for the rational design of nanocarbon molecules. Carbon nanobelts and related macrocycles provide well-defined platforms for examining how conjugation topology and bridging motifs influence collective structural motion. Here we present a comparative finite-temperature theoretical analysis of seven π-conjugated macrocycles, including [6]cycloparaphenylene ([6]CPP), methylene- and ethylene-bridged derivatives, fully sp2-fused carbon nanobelts, and a nanobelt containing sp3 interruptions. Finite-temperature atom-centered density matrix propagation (ADMP) trajectories at 300 K were analyzed using covariance principal component analysis together with a geometry-defined elliptic deformation coordinate. Fully sp2-fused nanobelts exhibit the largest apparent stiffness (keff) and the dominant framework-wide elliptic-like deformation among the examined systems, indicating strong circumferential coupling of aromatic units along the fused belt framework. In contrast, nanobelts containing sp3 bridges show reduced stiffness and redistribution of structural fluctuations into localized torsional modes. The calculated flexibility hierarchy agrees with crystallographic atomic displacement parameters (Ueq), providing experimental support for the predicted dynamics. These results establish transferable finite-temperature descriptors linking bridge connectivity and conjugation topology to the mechanical flexibility of curved π-conjugated macrocycles.