2 Nanoscience & Nanotechnology-Asia, 2012, 2, 2-10 2210-6820/12 $58.00+.00 © 2012 Bentham Science Publishers Structures and Stabilities: Quantum-Chemical Study of Au n (n = 2-2016) Nanoclusters by Extended Huckel and DFT Approaches Bakhtiyor Rasulev 1, * , Marquita Watkins 1 , Melissa Theodore 2 , Joany Jackman 2 and Jerzy Leszczynski 1 1 Interdisciplinary Center for Nanotoxicity, Department of Chemistry, Jackson State University, 1400 J. R. Lynch Street, P. O. Box 17910, Jackson, MS 39217, USA; 2 Applied Physics Laboratory, The Johns Hopkins University, Laurel, Maryland Abstract: A fundamental understanding of the physical and chemical properties of gold clusters, namely, the size dependence of these properties, is necessary for developing wide range of gold clusters’ applications. Having this purpose in mind, the structural and energetic properties, such as binding energies, relative stability and band gaps ∆E HL (HOMO- LUMO gaps) are evaluated. The gold clusters in a wide range of sizes, Au n (n=2 - 2016), were constructed and studied by Density Functional Theory and Extended Hückel Theory approaches. It was shown that the high values of ∆E HL for the clusters with n= 2, 6, 8, 20 correlate with the highest stability. This finding explains the existence of magic numbers for gold clusters. The 20 atom tetrahedral cluster stands out as particularly stable, comparing to the other small clusters. The binding energy E B is found to increase with the cluster size. The second difference in energy - ∆ 2 E(n) value is used as the criterion of stability, in addition to ∆E HL and also shows a tendency to increase with the cluster size. This behavior suggests a transition of larger clusters towards bulk metallic properties. Both curves - ∆ 2 E(n) and ∆E HL show sharp transformation from high values to close to 0 eV at n=252-504 cluster sizes (it relates to ca 2 nm cluster size). Keywords: Gold, Clusters, ab initio, Hückel, DFT, Nanoparticle, Modeling. 1. INTRODUCTION Nanoparticles and particularly, gold clusters, have received significant attention because of their potential applications in many areas of industry and medicine [1-5]. The considerable interest in gold clusters in recent years is motivated in part by the catalytic activity of small clusters [2,6,7]. Development of fundamental understanding of the physical and chemical properties of gold clusters, namely, the size dependence of these properties, is main focus of research devoted to advancement of wide range of their applications. However, direct and comprehensive experimental studies on small gold clusters are difficult to carry out. Therefore, smaller gold clusters have been extensively investigated by application of quantum-chemical computational methods over the past several years [6-21]. Systematic structural studies of gold clusters over wide size ranges play an important role as the molecular structure provides the critical information for understanding all other cluster properties and therefore this molecular characteristic may be a determining factor in their physical and chemical behavior. Though the gold clusters have attracted an attention of computational chemists for the last ten years, however mainly small size clusters with n = 2-20 have been investigated [6,9-14,17-19,22-24]. Starting from semi- empirical and extended Hückel calculations, with increased computer power also ab initio methods were used for such *Address correspondence to this author at the Interdisciplinary Center for Nanotoxicity, Department of Chemistry, Jackson State University, 1400 J. R. Lynch Street, P. O. Box 17910, Jackson, MS 39217, USA; Fax: +1 601 979 7823; E-mail: rasulev@icnanotox.org studies [12,13]. A DFT investigation was performed for low- energy electronic structures of small gold clusters with n= 2- 12 where authors discussed various energy trends related to the cluster size [17]. In the other study [15] the molecular dynamics method was used for investigation of structural stability of gold clusters with n=3-555. The author used FCC generated geometries for the spherical structures of gold clusters with n 13-555 atoms. Xing [11] studied medium sized gold clusters with n=11-24 atoms, using electron diffraction data, DFT and molecular dynamics simulations, confirming the prevalence of planar structures for ground states of gold clusters up to Au 16 size. In the following study [25] the stability of neutral gold clusters with n=15-19 were investigated using DFT method for calculations. Recently, Tsunoyama and coworkers [26] experimentally determined magic numbers for the gold clusters stabilized by poly-vinylpyrrolidone (PVP). Using the mass-spectra and statistical analysis they showed that the magic numbers are approximately as follows: 35±1, 43±1, 58±1, 70±3, 107±4, 130±1 and 150±2. Unfortunately, they did not reveal the magic numbers for the clusters larger than 150 atoms. Moreover, the authors noticed that larger magic numbers 107±4, 130±1, and 150±2 obviously deviate from those of the electronic shell model. They hypothesized that, upon protection by PVP, the electronic and geometric structures of the Au n cores (n≈107, 130, and 150) are substantially modified, and the cores become more stable than their neighbors. Although, it is established that the magic numbers of free Au clusters are 8, 18, 20, 34, 40, 58, 92, 138,…, which is explained in terms of closure of the electronic shells created by spherical potentials. The authors of the current study for the last few years have performed a systematic analysis of various