Another look at structure of gold clusters Au n from perspective of phenomenological shell model Pham Vu Nhat a,b , Nguyen Thanh Si c , Jerzy Leszczynski d , Minh Tho Nguyen a,b,e,⇑ a Computational Chemistry Research Group, Ton Duc Thang University, Ho Chi Minh City, Viet Nam b Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Viet Nam c Department of Chemistry, Can Tho University, Can Tho, Viet Nam d Interdisciplinary Center for Nanotoxicity, Jackson State University, Jackson, MS 39217, USA e Department of Chemistry, KU Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium article info Article history: Received 1 May 2017 In final form 21 June 2017 Available online 29 June 2017 Keywords: Gold clusters Au 20 Phenomenological shell model Frank-Kasper structure DFT computations abstract Geometric, energetic and electronic properties of Aun clusters, n = 2–20 are determined using DFT calcu- lations (BB95/cc-pVTZ-PP). Global equilibrium structures were confirmed or found, and the growth mechanism was established. Au-clusters prefer 2D-geometries up to Au 11 and are generated from the lowest-lying isomer of the smaller size by adding an extra gold atom. Transition from an oblate form to a pyramid is observed at Au 17 . Au n containing 17–20 atoms favor tetrahedral evolution by adding atoms to the Frank-Kasper 16-vertex. Binding energy per atom, second-order difference of energy, and one-step fragmentation energy show that Au 6 and Au 20 have high thermodynamic stability. Their valence electrons of generate magic numbers that can be understood using the phenomenological shell model. Due to Jahn-Teller effect, Au 16 is characterized by oblate structure whereas the anion Au 16 -exhibits Frank-Kasper form. Ó 2017 Elsevier B.V. All rights reserved. 1. Introduction The studies of metal clusters have grown exponentially in recent time as a deep knowledge on their molecular and electronic structures constitutes an initial step in any attempt of understand- ing and interpreting experimental observations on thermal, opti- cal, magnetic, and catalytic properties of nano-particles [1,2]. Experimental results on clusters become more and more available, owing to the use of modern spectrometric techniques, and thereby theoretical steps can be taken for understanding and interpretation of the observed findings. However, relatively little is known about their complex and subtle relationships between structure (both geometric and electronic) with thermodynamic stability and reac- tivity. Generally, one may only expect that the physical and chem- ical properties of small and medium-sized clusters, containing no more than a few hundred atoms (diameters of 1–3 nm) [3], strongly depend on either their size and/or shape, and differ con- siderably from both individual atoms or molecules and bulk. Up to the early 1980s, the most carefully studied clusters were indeed small, containing utmost about a dozen atoms, as much lar- ger particles were primarily believed to be essentially bulk-like, and the surface was thought to scatter electrons randomly [1]. Such a bias was however changed since Knight et al. [4] produced and detected clusters of alkali metals containing up to 100 atoms, and certain (magic) sizes were found to be much more abundant than the others. For the sodium clusters produced, large peaks on the mass spectra correspond to systems containing 2, 8, 20, 40, 58 and 92 atoms. A widely accepted explanation for such a phe- nomenon was based on a strong delocalization of the external s electrons [5,6]. Thus they can be treated as particles moving around a spherical pseudo-potential composed of the inner elec- trons along with the nuclei. This highly delocalized behavior of valence electrons brings about the main characteristics of simple metal clusters: formation of electronic shells, and the occurrence of shell closing effect are somewhat similar to those in free atoms. Consequently, a cluster in which the number of valence electrons matches the shell closure, namely 1S/1P/1D/2S/1F/2P/..., is pro- duced more abundantly as compared to the immediately following ones, and is called a ‘‘magic” cluster. This approach, currently known as the ‘‘phenomenological shell model” (PSM), has been proven to be a simple but effective model to interpret the stability pattern and electronic structure of small-size metal clusters [7]. In http://dx.doi.org/10.1016/j.chemphys.2017.06.009 0301-0104/Ó 2017 Elsevier B.V. All rights reserved. ⇑ Corresponding author at: Department of Chemistry, KU Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium. E-mail addresses: nhat@ctu.edu.vn (P.V. Nhat), nguyenminhtho@tdt.edu.vn, minh.nguyen@kuleuven.be (M.T. Nguyen). Chemical Physics 493 (2017) 140–148 Contents lists available at ScienceDirect Chemical Physics journal homepage: www.elsevier.com/locate/chemphys