Effects of Core Distances, Solvent, Ligand, and Level of Theory on the TDDFT Optical Absorption Spectrum of the Thiolate-Protected Au25 Nanoparticle

Density functional theory calculations are employed to calculate geometries (R = H, CH3, CH2CH3, CH2CH2Ph) and excitation energies (R = H, CH3, CH2CH3) for the Au-25(SR)(18)(-) nanoparticle. The splitting between the first two peaks in the optical absorption spectrum is known to arise as a result of ligand-field splitting of superatom D orbitals, and the value of this splitting is found to be a very sensitive probe of gold-gold distances in the Au-25(SH)(18)(-) nanoparticle core. LDA functionals such as X alpha with a triple-zeta basis set are found to predict core geometries in good agreement with experiment, which suggests that this level of theory may be useful in future structural predictions. Asymptotically correct potentials SAOP and LB94 with triple-zeta basis sets yield excitation energies within 0.15-0.20 eV of experimental values; LB94 with a frozen-core basis set is found to be an inexpensive alternative to the preferred SAOP potential. The size of the ligand plays a minor role on the optical absorption spectrum and solvent effects on geometries and excitation energies are negligible, which demonstrates that the core geometric and electronic structure is primarily responsible for the discrete optical absorption exhibited by this nanoparticle.