Exchange-vibronic coupling, spin frustration, and choice of ground spin state in triangular organic triradicals

Organic and main-group triradicals have potential applications in molecular magnetism and quantum information science, but the factors that determine whether a triangular triradical adopts a high-spin quartet or spin-frustrated doublet ground state remain poorly understood. Here, we present a multireference computational investigation of four triangular triradicals, including two experimentally characterized species and two rationally designed variants. The first experimentally characterized system is a triaza[4]triangulene triradical with a robust quartet ground state. The second is a boron-triptycene triangular triradical with a doublet ground state commonly attributed to Jahn-Teller distortion, although our computations reveal that the spin-frustrated doublet state is already strongly stabilized in the near-symmetric geometry. This provides quantitative evidence that triangular triradicals can remain spin-frustrated even in the absence of Jahn-Teller distortion, with subsequent distortions only amplifying rather than causing the low-spin ground state. The intrinsic electronic spin frustration of the triangular scaffold primarily determines the spin-state ordering, while vibrational modulation of magnetic exchange interactions governs the dynamic stability and thermal susceptibility of the spin manifold. By performing exchange-vibronic coupling analysis for triradical doublet-quartet energy gaps, ΔED-Q, through mode-resolved d(ΔED-Q)/dQi gradients and the resulting total thermal fluctuations, σtot, we identify symmetry-breaking vibrational modes whose thermal population strongly modulates these energy gaps. Mechanistic insights from this framework guide the rational design of the two additional triradicals with dramatically reduced doublet-quartet gaps, further validated for 19 additional systems. Our work establishes a design framework for tuning magnetic properties in triangular organic triradicals.