A DFT/TD-DFT Study of Self-Assembled Carborane Metallacycles as Tunable Third-Order Nonlinear Optical Platforms: Synergistic Evolution of Dimensionality and Topology in Structure–Property Relationships

Abstract Coordination-driven self-assembly provides a modular route to functional supramolecular materials, yet the relationship between architectural parameters and third-order nonlinear optical (NLO) response remains largely unexplored. Here, DFT/TD-DFT investigations are performed on carborane-based assemblies spanning a 0D building block 1, 1D linear scaffolds 2–3, and 2D metallacycles 4–7 with rectangle (C2), triangle (C3), and square (C4) topologies. Dimensionality and topology emerge as independent but synergistic variables governing the second hyperpolarizability (γ). Progression from 0D/1D to 2D enhances γave by up to 13.8-fold, from 87.1 × 10–36 esu (1) to 1199.1 × 10–36 esu (7), through cyclic conjugation and multidirectional charge transfer. Within the 2D series, high-symmetry C3 and C4 topologies yield near-isotropic in-plane γ tensors (γxxxx ≈ γyyyy), whereas the C2 rectangle confines the response along its long axis despite the largest longitudinal component. The γave order 7 > 5 > 6 > 4 therefore reflects the synergy of framework symmetry and corner-unit conjugation rather than molecular size. Frequency-dependent calculations confirm that these trends persist under dynamic optical conditions. These findings establish design principles for 2D metallacyclic NLO platforms and higher-symmetry architectures, providing predictive guidelines for the rational construction of next-generation (3D polyhedral frameworks) NLO materials via coordination-driven self-assembly.