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 (k_eff) 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 (U_eq), 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.