Unified Topological Framework for Representation and Construction of Generalized Carbon Nanobelts

The expanding structural and topological diversity of macrocyclic polycyclic aromatic hydrocarbons, including carbon nanobelts (CNBs), cycloarenes, and their twisted analogs, demands a unified framework to overcome fragmented nomenclature schemes. Here, we present a topology-driven framework that unifies these systems as generalized CNBs by conceptualizing them as segments excised from generalized carbon nanocones with varying opening angles, spanning tubular, conical, and flat geometries within a single descriptive space. Central to this approach is the introduction of bijective path codes that provide a mathematically rigorous, machine-tractable representation of annulation patterns. We further establish a simple topological parity rule, whereby the parity of positive path segments serves as a robust invariant distinguishing Hückel and Möbius topologies. Building on this representation, we develop an automated construction protocol, implemented in the open-source beltopkit package, that converts path codes directly into three-dimensional geometries. To this end, a novel topology-constrained optimization algorithm is devised, allowing reliable generation of highly strained and multiply twisted macrocycles. As a representative demonstration of our approach, exhaustive enumeration of 12-ring generalized CNB topoisomers reveals a rich isomeric landscape and identifies multiple previously unrecognized low-energy structures competitive with experimentally synthesized infinitene. This framework provides a computationally tractable foundation for integrating complex macrocyclic nanocarbons into cheminformatics and machine learning workflows, enabling large-scale, data-driven exploration of new structures and synthetic targets.