Size-dependent linear and nonlinear optical responses of silicon clusters

Owing to strong quantum confinement effects and no periodic constraints, the geometric and electronic structures of silicon clusters differ from those of crystalline silicon. Although previous studies have elucidated the optical properties of silicon clusters, some issues remain unresolved. To address these, this study examined the size-dependent linear and nonlinear optical responses of silicon clusters through first-principles calculations. Silicon clusters exhibited lone-pair-electron-dominated optical response behaviors. With the investigated size range, the orientationally average polarizability (α_ave) and second-order hyperpolarizability (γ_ave) increased with cluster size. However, α_ave and γ_ave per atom exhibited no evident size-dependent trends owing to co-modulation of the lone-pair-number-to-atomic-number ratio and geometry. α_ave and γ_ave were notably sensitive to the nuclear binding strength of lone-pair electrons. Thus, the nonlinear optical effects of silicon clusters are superior to those of phosphorus and sulfur clusters. This investigation offers valuable insights into the optical responses of atomic-precision clusters.