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

Abstract

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.