Planar and cagelike structures of gold clusters: Density-functional pseudopotential calculations

Abstract

We study why gold forms planar and cage-like clusters while copper and silver do not. We use density functional theory and norm-conserving pseudo-potentials with and without a scalar relativistic component. For the exchange-correlation (xc) functional we use both the generalized gradient (GGA) and the local density (LDA) approximations. We find that planar Aun structures, with up to n = 11, have lower energy than the three-dimensional isomers only with scalar-relativistic pseudopotentials and the GGA. In all other calculations, with more than 6 or 7 noble metal atoms, we obtain three dimensional structures. However, as a general trend we find that planar structures are more favorable with GGA than with LDA. In the total energy balance, kinetic energy favors planar and cage structures, while xc-energy favors 3D structures. As a second step, we construct cluster structures having only surface atoms with O h , T d , and I h symmetry. Then, assuming one valence electron per atom, we select those with 2(l + 1) 2 electrons (with l integer), which correspond to the filling of a spherical electronic shell formed by node-less one electron wave functions. Using scalar relativistic GGA molecular dynamics at T = 600K, we show that the cage-like structures of neutral Au32, Au50, and Au162 are meta-stable. Finally, we calculate the static polarizability of the two lowest energy isomers of Aun clusters as a means to discriminate isomers with planar (or cagelike) geometry from those with compact structures. We also fit our data to a semi-empirical relation for the size dependent polarizability which involves the effective valence and the kinetic energy components for the homogeneous and inhomogeneous electron density. Analyzing that fit, we find that the dipole polarizability of gold clusters with planar and cage-like structures corresponds to the linear response of 1.56 delocalized valence electrons, suggesting a strong screening of the valence interactions due to the d-electrons.

Magnetic Anisotropies of Late Transition Metal Atomic Clusters

“…We have found here that the MAE further enhances the consistency of LDA and GGA in Pd, Pt and Ir MACs. In contrast, we confirm that the choice of functional is important for Au n clusters [5,21], even after including the SOI. We have borrowed the atomic configuration for the pseudopotentials from Quantum ESPRESSO package's web page [16].…”

“…Among all these devices, metallic atomic clusters (MACs) [3] stand out since, on the one hand they represent the natural bridge between atomic and materials physics and, in the other, they can be grown, deposited on surfaces or embedded in diverse matrices, and characterized with relatively well-established techniques. Further, the magnetic properties of MACs show promise for a wide spectrum of applications, ranging from medicine to spintronics.Magnetism in small MACs has been extensively studied both experimentally and theoretically along the past decade [4,5]. It is therefore somewhat surprising that, even though spin-orbit effects are also expected to be enhanced in MACs, there are very few published theoretical papers that include the spin-orbit interaction (SOI) in their simulations [6,7,8,9].…”

“…Magnetism in small MACs has been extensively studied both experimentally and theoretically along the past decade [4,5]. It is therefore somewhat surprising that, even though spin-orbit effects are also expected to be enhanced in MACs, there are very few published theoretical papers that include the spin-orbit interaction (SOI) in their simulations [6,7,8,9].…”

Theoretical study of isoelectronicSinMclusters (M=Sc−,TiTorres1, Fernández2, Balbás3 2007Phys. Rev. B1095631View full textAdd to dashboardCite

“…36,37 In that model, the orbital angular moment is a good quantum number, that is, the single particle states belong to the irreducible representations of the rotation group O + ͑3͒. For an empty cage, these states have predominantly zero radial nodes, 48 and are labeled as 1s ,1p ,1d ,1f ,1g ,1h ,.... The predominant covalent bonding in Si 16 M, as suggested by our Mulliken population analysis, is the result of hybridization of the empty-cage states and the endohedral atom valence states having the same orbital angular moment character.…”

Revealing the Mechanism of the Low-Energy Electron Yield Enhancement from Sensitizing Nanoparticles

“…The delocalization comes from a partial hybridization of the 6s and 5d atomic shells. The integration of the oscillator strength up to 11.2 eV (energy at which the first dip after the resonance peak is observed in the TDDFT spectrum) reveals that about 1.5 electrons from each atom contribute to the collective plasmon-type excitation, indicating delocalization of some fraction of d electrons [27]. Thus, the total photoabsorption spectrum of a gold NP in the energy region up to 60 eV approximately is equal to the sum of the plasmon contribution and that of the 5d electron excitations in individual atoms, σ γ ≈ σ pl + σ 5d .…”