Infrared vibronic absorption spectrum and spin–orbit calculations of the upper spin–orbit component of the Au3 ground state

On the ligand-core interaction in ligand-protected gold superatoms. Insights from Au25(XR)18 (X = S, Se, Te) via relativistic DFT calculations

The stabilization of gold nanoparticles by using thiolate-based ligands is a relevant issue in the design of functional nanostructures. Superatomic clusters, through the prominent Au₂₅(SR)₁₈ aggregate, offer a prototypical template to deepen the understanding of the different behaviors gained by the inclusion of different chalcogen atoms at the ligand layer. Through the study of [Au₂₅(XMe)₁₈]^- (X = S, Se and Te), our results revealed that the bonding between the formally [Au₁₃]⁵⁺ core and the protecting layer (PL), further involves the unoccupied 1D-, 1F- and 2S-[Au₁₃] superatomic shells, acting as a charge acceptor in the PL → Au₁₃ charge transfer upon formation of the cluster. In addition, the optical properties showed an increase in the Stokes shift between the S₀→ S₁ excitation, and S₀← S₁ emission, going from -SMe to -TeMe, owing to a more distorted core in the excited state for the heavier counterpart. The approach here employed expands the bonding picture between the [Au₁₃]⁵⁺ and the protecting layer between different anchor atoms, in addition to the formal ionic description of an isolated core. These findings seek to enhance our understanding of bonding, and the optical characteristic resulting from the use of heavier chalcogen atoms in the protecting layer, which can be employed as design guidelines to incorporate or modify the molecular properties towards the synthesis of ligand-protected gold clusters.

Spin–orbit effects in optical spectra of gold–silver trimers

Photodissociation spectra of cationic gold–silver trimers are analysed using relativistic electronic structure theories paying special attention to the importance of spin–orbit and charge transfer effects.

The Peculiar Role of the Au3 Unit in Aum Clusters: σ-Aromaticity of the Au5Zn+ Ion

The stability of small Au_m (m = 4-7) clusters is investigated by analyzing their energetic, geometric, vibrational, magnetic, and electron density properties. Gold clusters can be constructed from stable cyclic 3-center-2-electron (3c-2e) Au₃⁺ units (3-rings) with σ-aromaticity. The stabilization requires a flow of negative charge from internal 3-rings with electron-deficient bonding to peripheral 3-ring units with stronger Au-Au bonds. The valence-isoelectronic clusters Au₆ and Au₅Zn⁺ have similar electronic properties: Au₅Zn⁺ is a strongly σ-aromatic molecule. An understanding of the structure of Au_m clusters is obtained by deriving a Clar's Rule equivalent for polycyclic gold clusters: The structure with the larger number of rings with dominant 3c-2e character and a smaller degree of 3c-3e character occupies the global minimum of the Au_m potential energy surface.

Aun (n = 1,11) Clusters Interacting With Lone-Pair Ligands

We analyze the pattern of binding energies (BEs) of small Aun clusters (n = 1-7, 11) with lone-pair ligands (L = H2O, SH2, NH3, PH3, PF3, PCl3, and PMe3) employing the density functional theory. We use PBE0 functional with the dispersion correction and scalar relativistic effective core potential. This approach provides correct BEs when compared with benchmark CCSD(T) calculations for Au-L and Au2-L complexes. The pattern of BEs of Aun-L complexes is irregular with BE for Au3 ≈ Au4 > Au2 > Au7 > Au5 > Au11 > Au6 > Au1. Electron affinities (EAs) of Aun clusters exhibit oscillatory pattern with the cluster size. Binding energies of Aun-L complexes are oscillatory as well following EAs of Aun clusters. BEs of odd and even Aun-L complexes were analyzed separately. The bonding mechanism in odd Aun-L complexes is dominated by the lone pair → metal electron donation to the singly occupied valence Aun orbital accompanied by the back-donation. Even Aun clusters create covalent Aun-L bonds with BEs higher than those in odd Aun-L complexes. The BEs pattern and optimized geometries of Aun-L complexes correspond to the picture of creating the gold-ligand bond through the lone pair of a ligand interacting with the singly occupied molecular orbital in odd clusters or lowest unoccupied molecular orbital in even clusters of Aun. Ligands in both odd and even Aun-L complexes form three groups with binding energies that correlate with their ionization energies. The lowest BE is calculated for H2O as a ligand, followed by SH2 and NH3. PX3 ligands exhibit highest BEs.

Vibrational anharmonicity of small gold and silver clusters using the VSCF method

We study the vibrational spectra of small neutral gold (Au₂–Au₁₀) and silver (Ag₂–Au₅) clusters using the vibrational self-consistent field method (VSCF) in order to account for anharmonicity.

The shape of Au8: gold leaf or gold nugget?

The size at which nonplanar isomers of neutral, pristine gold nanoclusters become energetically favored over planar ones is still debated amongst theoreticians and experimentalists. Spectroscopy confirms planarity is preferred at sizes up to Au7, however, starting with Au8, the uncertainty remains for larger nanoclusters. Au8 computational studies have had different outcomes: the planar D4h "cloverleaf" isomer competes with the nonplanar Td, C2v and D2d "nugget" isomers for greatest energetic stability. We here examine the 2D vs. 3D preference in Au8 by presenting our own B2PLYP, MP2 and CCSD(T) calculations on these isomers: these methods afford a better treatment of long-range correlation, which is at the root of gold's characteristic aurophilicity. We then use findings from these high-accuracy computations to evaluate two less expensive DFT approaches, applicable to much larger nanoclusters: alongside the standard functional PBE, we consider M06-L (highly parametrized to incorporate long-range dispersive interactions). We find that increasing basis set size within the B2PLYP framework has a greater destabilizing effect on the nuggets than it has on the Au8 cloverleaf. Our CCSD(T) and B2PLYP predictions, replicated by DFT-PBE, all identify the cloverleaf as the most stable isomer; MP2 and DFT-M06-L show overestimation of aurophilicity, and favor, respectively, the nonplanar D2d and Td nuggets in its stead. We conclude that PBE, which more closely reproduces CCSD(T) findings, may be a better candidate density functional for the simulation of gold nanoclusters in this context.

Theory and simulation in heterogeneous gold catalysis

This critical review covers the application of quantum chemistry to the burgeoning area of the heterogeneous oxidation by Au. We focus on the most established reaction, the oxidation of CO at low temperature. The review begins with an overview of the methods available comparing the treatment of the electron-electron interaction and relativistic effects. The structure of Au particles and their interaction with oxide reviews is then discussed in detail. Calculations of the adsorption and reaction of CO and O2 are then considered and results from isolated and supported Au clusters compared (155 references).

Density Functional Theory Study of the Jahn−Teller Effect and Spin−Orbit Coupling for Copper and Gold Trimers

The Born-Oppenheimer potential energy hypersurfaces of copper and gold trimers were calculated using density functional theory with an analytic potential. The calculated Jahn-Teller distortion energies, pseudorotation barriers, dissociation, and isomerization energies for the two trimers are discussed. Global minima from the surfaces were optimized using the density functional theory method as well as the coupled cluster-singles-doubles-with-triples energies technique. The agreement of the optimized structures with the analytic potential was very good. The Mulliken population analysis compared favorably with the experimental electron spin resonance results. Spin-orbit coupling was subsequently included and the effect was significant for gold, but negligible for copper. The spin-orbit effect suppressed the Jahn-Teller distortion of the gold trimer, and the potential surface with the spin-orbit effect included was also obtained. The spin-orbit splitting for the D(3h) geometry of the gold trimer was in excellent agreement with the most recent infrared spectroscopic results.