A Theoretical Investigation of the Linear and Nonlinear Optical Responses of Scandium- and Yttrium-Doped (sub-nm) Ag and Au Clusters

We investigate the linear and nonlinear optical properties of (sub-nm) Ag6 and Au6 clusters doped with Sc and Y using time-dependent density functional theory. Both parent clusters have D3h ground-state geometries but exhibit noticeably different electronic structures; scalar-relativistic corrections in Au6 induce significant s-d hybridization, resulting in larger HOMO-LUMO gaps and reduced one-photon absorption (OPA) cross-sections compared to Ag6. Two-photon absorption (TPA) peaks in the UV region show resonance enhancement via coupling with OPA-active states, with Ag6 having larger cross-sections than Au6. Doping with Sc and Y modifies the optical responses by breaking configurational symmetry and lifting HOMO degeneracies. ScAg5 and YAg5 energetically prefer planar configurations with higher dopant orbital contributions, while ScAu5 and YAu5 prefer non-planar configurations. This leads to blue-shifted, intensified OPA transitions and larger TPA cross-sections in doped clusters than in parent clusters. Doped Ag clusters exhibit a significantly stronger TPA response in the biologically relevant 1.8–2.0 eV (620–690 nm) spectral region for in vivo imaging. Furthermore, a higher degree of Sc(Y)-Au hybridization generates additional TPA pathways and also facilitates electronic transitions at 1064 nm, enhancing the first hyperpolarizability (β (−2ω; ω, ω)) for YAu5. Overall, the results show that these (sub-nm) Sc/Y-doped noble metal clusters are promising candidates for photonic and biomedical imaging applications.