Theoretical Investigation of Electron and Nuclear Dynamics in the [Au₂₅(SH)₁₈]^-1 Thiolate-Protected Gold Nanocluster

Clear mechanistic insights into excited state dynamics in thiolate-protected gold nanoclusters are vital for understanding the origin of the photocatalytic enhancement via metal nanoparticles in the visible region. Extensive experimental studies on the [Au₂₅(SR)₁₈]^-1 thiolate-protected gold nanocluster nonradiative relaxation dynamics reported very distinct time constants which span from the femtosecond to nanosecond scale. In this work, the nonradiative excited state relaxations of the [Au₂₅(SH)₁₈]^-1 cluster are investigated theoretically to characterize the electron relaxation dynamics. The core and higher excited states lying in the energy range 0.00-2.20 eV are investigated using time-dependent density functional theory (TD-DFT). The quantum dynamics of these states is studied using a surface hopping method with decoherence correction, augmented with a real-time approach to DFT. Population transfer from the S₁ state to the ground state occurs on the several hundred picoseconds time scale. Relaxation between excited states that arise from core-to-core transitions is found to occur on a much shorter time scale (2-18 ps). No semiring or other states are observed at an energy lower than the core-based S₁ state. This observation suggests that the several picosecond time constants observed by Moran and co-workers could arise from core-to-core transitions rather than from a core-to-semiring transition. A large energy gap between the S₇ and S₆ states is found to be responsible for a relatively slow decay time for S_7. The S₁ state population decrease demonstrates the slowest decay time due to the large energy gap to the ground state. The spectral densities are calculated to understand the electron-phonon interactions that lead to electronic relaxations.