Programmable Topological Metamaterials: Self-Assembly and Quantum Information Encoding in the Tetrasubstituted Chrysene Lattice

Abstract

The transition from passive structural nanomaterials to active, information-processing metamaterials requires a cooperative convergence of chemical synthesis, quantum kinematics, and algebraic topology. In this treatise, we introduce the 3,6,9,12-tetrasubstituted chrysene lattice as a novel, programmable topological nanomaterial. By abstracting the classical polycyclic aromatic hydrocarbon into a rigorous mathematical space, we demonstrate that substitutions at the 3, 6, 9, and 12 coordinates represent the absolute thermodynamic minimum required for stable orthogonal assembly. Utilizing ethylene glycol-based (PEGylated) connectors, the architecture natively achieves precise sp2 to sp3 topological isolation, controlled solvation, and highly ordered pi-stacking. Furthermore, the non-commutative orientation of these molecular tensors establishes a base-four topological cipher, creating four unique interstitial reaction vessels capable of transforming the discrete lattice into a secondary, system-wide continuous molecular structure. Combining these integration mechanisms with the innate chromophore absorption, lasing properties, and dual-channel ballistic transport of the chrysene core, we formally define a new class of synthetic crystal capable of natively encoding and transmitting quantum information.