Energy Gap Law for Exciton Dynamics in Gold Cluster Molecules

The energy gap law relates the nonradiative decay rate to the energy gap separating the ground and excited states. Here we report that the energy gap law can be applied to exciton dynamics in gold cluster molecules. Size-dependent electrochemical and optical properties were investigated for a series of n-hexanethiolate-protected gold clusters ranging from Au25 to Au333. Voltammetric studies reveal that the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO–LUMO) gaps of these clusters decrease with increasing cluster size. Combined femtosecond and nanosecond time-resolved transient absorption measurements show that the exciton lifetimes decrease with increasing cluster size. Comparison of the size-dependent exciton lifetimes with the HOMO–LUMO gaps shows that they are linearly correlated, demonstrating the energy gap law for excitons in these gold cluster molecules.