At the Douglas-Kroll-Hess level, the B3PW91 hybrid functional along with relativistic all-electron basis sets are used to evaluate geometric parameters, binding energies, vertical ionization potentials and electron affinities, and HOMO-LUMO (highest occupied molecular orbital-lowest unoccupied molecular orbital) energy gaps of the small golden clusters (Au n , n ≤ 8).The so expected odd-even oscillations of the experimental ionization potentials and electron affinities are confirmed in this work and the Au 7 cluster is predicted to be the most reactive cluster. Using the optimized geometries, DKH2 static mean dipole polarizability and polarizability anisotropy are also computed. From n ≥ 2, the mean dipole polarizabilities per atom present an odd-even oscillatory characteristic, whereas the polarizability anisotropies increase with the cluster size. At the non-relativistic level, the second hyperpolarizabilities are calculated. It is the first time that hyperpolarizabilities of gold clusters are reported. Comparisons with theoretical results obtained previously for the copper and silver clusters at the same level of theory are made.Keywords: B3PW91 functional, all-electron basis sets, DKH2 calculations, gold clusters, (hyper)polarizabilities
IntroductionAtomic cluster is formed by an assembling of a few or hundreds of atoms. It is necessary to understand how the cluster properties vary with the size, to clarify how they evolve in the direction of the bulk properties. Metal clusters have received special attention in the literature due to their unusual characteristics, properties, and applications to build new electronic devices.1 Theoretical 2-11 and experimental [12][13][14][15][16][17][18][19] studies about metal clusters have been carried out for about thirty three years. Among the metal clusters, there is an increasing interest [20][21][22][23][24][25][26][27][28][29][30][31][32] in the noble metals (Cu, Ag, and Au) because they can be considered as a connection between the alkali metals and the transition metals. We recall that their electronic configurations are nd 10 (n + 1)s 1 , with n = 3, 4, and 5, respectively to Cu, Ag and Au. It has been verified that in general the gold clusters and compounds present large relativistic effects when compared to those of the copper and silver ones. 33,34 We would like to cite the experiments about vertical ionization potentials and electron affinities performed by some research groups, 28,[35][36][37][38][39] where the results of all studied gold clusters surpass those of the copper and silver ones (see Figure 2 of Wesendrup et al.). 29 As a consequence of this finding, the properties and surfaces of the gold clusters will be differently affected. Thus, a study about the variation of such properties with the cluster size will be interesting. In this article, the vertical ionization potentials and electron affinities of gold clusters with up to 8 atoms as well as binding energies, highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) energ...