Nonadiabatic derivative couplings through multiple Franck-Condon modes dictate the energy gap law for near and short-wave infrared dye molecules

Near infrared (NIR, 700 - 1,000 nm) and short-wave infrared (SWIR, 1,000 - 2,000 nm) dye molecules exhibit significant nonradiative decay rates from the first singlet excited state to the ground state. While these trends can be empirically explained by a simple energy gap law, detailed mechanisms of the nearly universal behavior have remained unsettled for many cases. Theoretical and experimental results for two representative NIR/SWIR dye molecules reported here clarify an important mechanism of such nature. It is shown that the first derivative nonadiabatic coupling terms serve as major coupling pathways for nonadiabatic decay processes exhibiting the energy gap law behavior and that vibrational modes other than the highest frequency ones also make significant contributions to the rate. This assessment is corroborated by further theoretical comparison with possible alternative mechanisms of intersystem crossing to triplet states and also by comparison with experimental data for deuterated molecules.