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 the 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 the TPA properties of gold clusters. Our results indicate that the one-and two-photon double-resonance effect is much smaller than previously found, and thus is unlikely to be 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 was 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 non-linear response of the Au25(SR)18- cluster is on the same order as that of bulk gold films.
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