Figure 7: The rt-TDDFT Ehrenfest dynamics simulations at 50 K for neutral Ag₅₅ (a,b) and Ag₅₅ with the modified electronic structure

(c,d). In these simulations, the electron–phonon interactions are taken into account explicitly. (a) The dipole moment of the neutral Ag₅₅ is similar to the result without electron–phonon effects shown in Fig. 2a. (b) The energies stored in the plasmon mode and single-particle excitations in the neutral Ag₅₅ are also similar to the results without electron–phonon effects. It should be compared with Fig. 4b. (c) The dipole moment of the Ag₅₅ with the modified electronic structure (no resonant single-particle d to s excitations). The dipole moment exhibits the Rabi oscillation, similar to the case without electron–phonon effects shown in Fig. 6a. (d) The energies stored in the plasmon mode and single-particle excitations also exhibit the Rabi oscillations when no resonant single-particle excitations exist. It should be compared with Fig. 6c. All these results show that phonons play a minor role in the plasmon decay.