Mechanical Tuning of Singlet–Triplet Resonance for Efficient Triplet–Triplet Annihilation Upconversion

Triplet–triplet annihilation upconversion depends on a near-resonant energetic balance between the relevant singlet and triplet excited states. Here we introduce a computational framework for mechanically tuning this balance by applying an external force that permits to locate the molecular geometry reaching the singlet–triplet resonance condition, i.e., ES1 – ES0 = 2(ET1 – ES0). Our approach formulates this problem as a constrained optimization in which the force magnitude is minimized while enforcing the target energetic resonance condition. Using a local quadratic model for the triplet-state potential energy surface together with a linearized description of the relevant energy gaps, we derive a minimum-force update procedure to obtain the optimal displacement and the associated external force. The resulting algorithm provides the mechanically controlled geometry and the optimal force vector required to reach it. The method offers a practical computational route to identify mechanically accessible structures with improved upconversion characteristics, paving the way for the design of mechanoresponsive chromophores and materials with stress-tunable optical behavior.