Performance of Density Functionals for the Calculation of Gold Clusters

Abstract

Clusters and nanoparticles of gold have received considerable attention during the past decade. The exceptional catalytic properties of small gold aggregates have motivated research aimed at providing insights into the molecular origins of this unexpected reactivity. The experimental observations have stimulated many theoretical studies of the electronic, structural, and chemical properties of gold clusters. Since it is not practical to calculate gold clusters using high-level ab initio correlation methods, density functional theory (DFT)-based approaches have usually been employed in such calculations, but it is not clear which functionals provide the best performance. Herein we report the results of calculations on the structure and stability of Au2 and Au8, as a model study, using various density functionals. To the best of our knowledge, there has been no previous systematic study for DFT performance on the structure and stability of gold clusters. Although the performance of density functionals is widely known for light element systems, certain functionals successful in light element chemistry may not work effectively in heavy element chemistry. This is due to the strikingly different bonding nature of heavy element systems from their light element analogues. Thus, the results of this work may be useful for future work in choosing the most appropriate density functional for gold clusters when performing DFT calculations. Kohn-Sham DFT calculations were performed with 16 different exchange correlation functionals, namely, the local density approximation (LDA:SVWN), the generalized gradient approximation (GGA:BLYP, BP86, BPW91, PW91, PBE, HCTH, tHCTH, LC-BPW91, LC-PW91 and LCPBE), and the hybrid GGA functionals (B3LYP, B3PW91, mPW1PW91, PBE0 and X3LYP). We used the relativistic effective core potentials derived by Stevens et al. and valence basis sets employed in previous works. All the calculations were carried out using the program package GAUSSIAN 09. Au2 Cluster. We compare the calculated spectroscopic constants, bond length (Re), vibrational frequency (ωe), and dissociation energy (De) with the experimental data 20 in Table 1. Overall, the LDA and several GGA functionals provide good performance for bond length (and vibrational frequency) and dissociation energy, respectively. The use of hybrid GGA functionals, i.e., the inclusion of Hartree-Fock exchange, does not improve the pure GGA results. These observations are in contrast to the known performance of functionals in light element chemistry: in general, LDA < GGA < hybrid GGA. It was reported, for instance, that the performance of the pure BP86 functional is very poor for light element systems, but its performance is observed to be one of the most effective for Au2. It is evident from our calculations that any one functional could not provide reliable spectroscopic constants of Au2. The poor performance of hybrid GGA functionals may be partly ascribed to the functional parameterization optimal to light-element systems only. Intriguingly, the long range correction to the GGA functionals (LC-GGA) improves the performance for bond lengths. Au8 Cluster. There are no experimental data for the structures and energies of Au8. Han 10 reported the relative