The core electrons are approximate by the Troullier-Martins pseudopotentials 42 with 11, 6 and 1 valence electrons for Au, O and H atoms. Therefore, the Au 20 @H 2 O system has 228 valence electrons and 114 occupied orbitals, and 30 unoccupied states are included in all the calculations. The general gradient approximation exchange-correlation DFT functional Perdew-Burke-Ernzerhof (PBE) with Average-density self-interaction correction 44 is adopted in all DFT/TDDFT calculations. The time-dependent evolution is performed using the approximated enforced time-reversal symmetry algorithm with a time step of 1.5 as. To obtain the optical absorption spectrum, a δ function electric field is used. Nonadiabatic dynamics of Au 20 @H 2 O is treated by TDDFT/Ehrenfest dynamics scheme with temperature fluctuating at around 300 K. The set of equations to be solved for the electron and ion dynamics of Au 20 @H 2 O are