In both the TD-ADGA calculation and the reference calculation, the initial TDH state is prepared as the VSCF ground state on the PES for the A ′ state. The TDH time-evolution is then subsequently carried out on the PES for the A state. Since we change the PES, the TDH initial state is no longer a stationary state and the TDH wave function will start to move on the A state PES. We have chosen to use the A ′ → A transition, since the transition from the ground state to either the A or A ′ state dissociates the bromine dimer.