Importance of Double-Resonance Effects in Two-Photon Absorption Properties of Au25 (SR)18-
The two-photon absorption (TPA) cross sections of small thiolate-protected gold clusters have been shown to be much larger than typical small organic molecules. In comparison with larger nanoparticles, their TPA cross sections per gold atom are also found to be larger. Theoretical simulations have suggested that the large enhancement of these TPA cross sections comes from a one-photon double resonance mechanism. However, it remains difficult to simulate TPA cross sections of thiolate-protected gold clusters due to their large system size and a high density of states. In this work, we report a time-dependent density functional theory (TDDFT) study of the TPA spectra of Au25 (SR)18- cluster based on a damped response theory formalism. Damped response theory enables a consistent treatment of on- and off-resonance molecular properties even for molecules with a high density of states, and thus is well-suited for studying TPA properties for gold clusters. Our results indicate that the one- and two-photon double resonance effect is much smaller than previously found, and thus unlikely the main cause of the large TPA cross sections found experimentally. The effect of symmetry-breaking of the Au25 (SR)18- cluster due to the ligands on the TPA cross sections has been studied and found to only slightly increase the cross section. Furthermore, by comparing with larger nanoparticles we find that the TPA cross section per gold atom scales linearly with the diameter of the particles, and that the Kerr nonlinear response of the Au25 (SR)18- cluster is on the same order as that of bulk gold films.