Validation of Density Functional Methods for the Calculation of Small Gold Clusters

Xe Adsorption on Noble Metal Clusters: A Density Functional Theory Investigation

The adsorption mechanism of xenon on three noble metal clusters (M = Ag, Au, and Cu) has been investigated in the framework of density functional theory (DFT) within generalized gradient approximation (GGA-PBE). The ab initio calculations were performed with the quantum molecular dynamics (QMD) package ABINIT using the projector augmented (PAW) formalism. The spin-orbit coupling (SOC) and dispersion effects (Van der Waals DFT-D3) have been taken into account. According to these calculations, the M-Xe bonds are partly covalent and electrostatic and their contribution depends on the cluster size and nature. This study underlines the importance of using the SOC and the Van der Waals (VdW) effects. Based on these results, copper nanoparticles have the highest affinity for interaction with xenon compared with silver and gold.

A Global Optimizer for Nanoclusters

We have developed an algorithm to automatically build the global minimum and other low-energy minima of nanoclusters. This method is implemented in PyAR (https://github.com/anooplab/pyar) program. The global optimization in PyAR involves two parts, generation of several trial geometries and gradient-based local optimization of the trial geometries. While generating the trial geometries, a Tabu list is used for storing the information of the already used trial geometries to avoid using the similar trial geometries. In this recursive algorithm, an n-sized cluster is built from the geometries of n−1 clusters. The overall procedure automatically generates many unique minimum energy geometries of clusters with size from 2 up to n using this evolutionary growth strategy. We have used our strategy on some of the well-studied clusters such as Pd, Pt, Au, and Al homometallic clusters, Ru-Pt and Au-Pt binary clusters, and Ag-Au-Pt ternary cluster. We have analyzed some of the popular parameters to characterize the clusters, such as relative energy, singlet-triplet energy difference, binding energy, second-order energy difference, and mixing energy, and compared with the reported properties.

Benchmark Study of Density Functional Theory for Neutral Gold Clusters, Aun (n = 2-8)

Neutral gold clusters, Au_n (n = 2-8), were optimized using coupled cluster singles and doubles with perturbative triples (CCSD(T)) with a triple-ζ-level basis set to develop reliable reference values for their structural and energy parameters in order to assess the performance of density functionals. The performance of 44 density functional theory (DFT) methods for calculating molecular structures and relative energies is assessed with respect to CCSD(T). In addition, their performance when calculating vertical ionization potentials (vIPs) of Au_n (n = 2-8) is also assessed by comparison with experimental values. The revTPSS functional shows good performance for calculating both the structural and energy properties of Au_n (n = 2-8), whereas B3P86 shows a remarkable performance in calculating the vIPs. The quadruple-ζ-level valence basis set is necessary for obtaining accurate energy values in CCSD(T) calculations.

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.

DFT insights into the cycloisomerization of ω-alkynylfuran catalyzed by planar gold clusters: mechanism and selectivity, as compared to Au(i)-catalysis

A detailed reaction mechanism of Au_3–10-catalyzed cycloisomerization of ω-alkynylfuran was systemically investigated at the TPSSh/def2-TZVP levels.

Size evolution and ligand effects on the structures and stability of (AuL)n (L = Cl, SH, SCH3, PH2, P(CH3)2, n = 1–13) clusters

Size evolution on the global minimum structures of (AuCl)_n clusters at n = 1–13.

SCC-DFTB parameters for simulating hybrid gold-thiolates compounds

We present a parametrization of a self-consistent charge density functional-based tight-binding scheme (SCC-DFTB) to describe gold-organic hybrid systems by adding new Au-X (X = Au, H, C, S, N, O) parameters to a previous set designed for organic molecules. With the aim of describing gold-thiolates systems within the DFTB framework, the resulting parameters are successively compared with density functional theory (DFT) data for the description of Au bulk, Aun gold clusters (n = 2, 4, 8, 20), and Aun SCH3 (n = 3 and 25) molecular-sized models. The geometrical, energetic, and electronic parameters obtained at the SCC-DFTB level for the small Au3 SCH3 gold-thiolate compound compare very well with DFT results, and prove that the different binding situations of the sulfur atom on gold are correctly described with the current parameters. For a larger gold-thiolate model, Au25 SCH3 , the electronic density of states and the potential energy surfaces resulting from the chemisorption of the molecule on the gold aggregate obtained with the new SCC-DFTB parameters are also in good agreement with DFT results.

Magic-number gold nanoclusters with diameters from 1 to 3.5 nm: relative stability and catalytic activity for CO oxidation

Relative stability of geometric magic-number gold nanoclusters with high point-group symmetry ((Ih), D(5h), O(h)) and size up to 3.5 nm, as well as structures obtained by global optimization using an empirical potential, is investigated using density functional theory (DFT) calculations. Among high-symmetry nanoclusters, our calculations suggest that from Au(147) to Au(923), the stability follows the order Ih > D(5h) > Oh. However, at the largest size of Au(923), the computed cohesive energy differences among high-symmetry I(h), D(5h) and O(h) isomers are less than 4 meV/atom (at PBE level of theory), suggesting the larger high-symmetry clusters are similar in stability. This conclusion supports a recent experimental demonstration of controlling morphologies of high-symmetry Au(923) clusters ( Plant, S. R.; Cao, L.; Palmer, R. E. J. Am. Chem. Soc. 2014, 136, 7559). Moreover, at and beyond the size of Au(549), the face-centered cubic-(FCC)-based structure appears to be slightly more stable than the Ih structure with comparable size, consistent with experimental observations. Also, for the Au clusters with the size below or near Au(561), reconstructed icosahedral and decahedral clusters with lower symmetry are slightly more stable than the corresponding high-symmetry isomers. Catalytic activities of both high-symmetry and reconstructed I(h)-Au(147) and both Ih-Au(309) clusters are examined. CO adsorption on Au(309) exhibits less sensitivity on the edge and vertex sites compared to Au(147), whereas the CO/O2 coadsorption is still energetically favorable on both gold nanoclusters. Computed activation barriers for CO oxidation are typically around 0.2 eV, suggesting that the gold nanoclusters of ∼ 2 nm in size are highly effective catalysts for CO oxidation.

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.