Nonlinear Optical Properties of Thiolate-Protected Gold Clusters: A Theoretical Survey of the First Hyperpolarizabilities

A series of thiolate-protected gold clusters has been successfully crystallized in recent years, and on the basis of these crystal structures, we investigate the static first hyperpolarizabilities β0 of eight model clusters [Aum(SH)n]z (m = 18–38) by means of density-functional theory. We used simplified ligands −SH, which may lead to higher symmetries than in actual systems (e.g., with −SCH2CH2Ph or −SPh ligands). A dependence of the obtained values on the exchange-correlation functional during geometry optimization was found. No correlation between cluster size and β0 was identified. Instead, the symmetry of the clusters seems to dominate the NLO properties. Our survey predicts strong NLO responses in the chiral Au38(SR)24 cluster, whereas centrosymmetric structures such as the [Au25(SR)18)]− yield hyperpolarizabilities close to zero. This is in line with recent experimental results obtained by second-harmonic generation. The centrosymmetry of the Au25 cluster is efficiently destroyed by ligand exchange, as demonstrated by the inclusion of chiral, bidentate ligands (1,1′-binaphthyl-2,2′-dithiol, 1,1′-biphenyl-2,2′-dithiol) and two thiophenolate ligands. This induces significant hyperpolarizabilities, surpassing those of intrinsically chiral clusters (e.g., Au38(SH)24). Our results are of significance for the use of monolayer-protected noble metal clusters as contrast agents in NLO imaging applications.