Development of a charge-perturbed particle-in-a-sphere model for nanoparticle electronic structure.

The complex surface structure of gold-thiolate nanoparticles is known to affect the calculated density functional theory (DFT) excitation spectra. However, as the nanoparticle size increases, it becomes impractical to calculate the excitation spectrum using DFT. In this study, a new method is developed to determine the energy levels of the thiolate-protected gold nanoparticles [Au(25)(SR)(18)](-), Au(102)(SR)(44) and Au(144)(SR)(60). A 3 nm thiolate-protected nanoparticle is also modeled. The particle-in-a-sphere model is used to represent the core while the ligands are treated as point charge perturbations. The electronic structures obtained with this model are qualitatively similar to DFT results. The symmetry of the arrangement of the perturbations around the core plays a major role in determining the splitting of the orbitals. The radius chosen to represent the core also affects the orbital splitting. Increasing the number of perturbations around the core shifts the orbitals to higher energies but does not significantly change the band gaps and orbital splitting as long as the symmetrical arrangement of the perturbations is conserved. This model can be applied to any gold nanoparticle with a spherical core, regardless of its size or the nature of the ligands, at very low computational cost.