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This work uses the nonrelativistic and scalar-relativistic second-order Douglas-Kroll-Hess (DKH2) Hamiltonians together with the all-electron basis sets to determine the structures, stabilities and electronic properties of the small neutral gold clusters, Aun (n ≤ 6). Several levels of theory including the all-electron scalar-relativistic DKH2-M06HF/TZP-DKH, DKH2-B3LYP/TZP-DKH and DKH2-B3LYP/DZP-DKH along with the nonrelativistic B3LYP/DZP are used to calculate the static polarizabilities, polarizability anisotropies, second difference of the cluster energies, fragmentation energies, binding energies, the highest occupied-lowest unoccupied (HOMO-LUMO) energy gaps, ionization potentials and electron affinities of the small gold clusters. We find that the vertical ionization potentials and adiabatic electron affinities are in good agreement with the experimental data at the DKH2-B3LYP/DZP-DKH level of theory, while the best bond length and geometries are obtained at the DKH2-M06HF/TZP-DKH level.

Herein we report the density functional theory (DFT) calculations of nonlinear optical (NLO) properties of neutral gold clusters Aun (n=2-10) applying long-range corrected LC-M06L functional and Los-Alamos National Laboratory double-ζ polarized basis set. The effects of the incident frequency on the first and second-order hyperpolarizability together with the influence of the external electric field on the frontier orbitals of neutral gold clusters are investigated. It is found that the application of external electric field can increase or decrease the gap energy of neutral gold clusters depending on the direction and magnitude of the applied field. More importantly, by correctly controlling the direction and magnitude of the external electric field, reactive gold clusters having low gap energies can be achieved. Furthermore, the external electric field has more important effect on the virtual orbitals of gold hexamer and decreases the energy of these orbitals along the directions parallel to the molecular plane, resulting in low-energy excitations. The low-energy excitations are expected to play important role in the high second-order hyperpolarizability and better response to the applied field. The third-order nonlinear (NLO) properties of gold hexamer are also strongly affected by the frequency of the incident light and thus can be tuned using the incident frequency for applications. The present work may propose new strategies for enhancing the nonlinear optical response of neutral gold clusters.