Are Zinc Clusters Really Amorphous? A detailed Protocol for Locat- ing Global Minimum Structures of Clusters † Andr´ es Aguado a,∗ , Andr´ es Vega a , Alexandre Lebon b , and Bernd von Issendorff c Received Xth XXXXXXXXXX 20XX, Accepted Xth XXXXXXXXX 20XX First published on the web Xth XXXXXXXXXX 200X DOI: 10.1039/b000000x We report the results of a conjoint experimental/theoretical effort to assess the structures of free-standing zinc clusters with up to 73 atoms. Experiment provides photoemission spectra for Zn − N cluster anions, to be used as fingerprints in structural assessment, as well as mass spectra for both anion and cation clusters. Theory provides both a detailed description of a novel protocol to locate global minimum structures of clusters in an efficient and reliable way, and its specific application to neutral and charged zinc clusters. Our methodology is based on the well-known hybrid EP-DFT (empirical potential-density functional theory) approach, in which the approximate potential energy surface generated by an empirical Gupta potential is first sampled with unbiased basin hopping simulations, and then a selection of the isomers so identified is re-optimized at a first-principles DFT level. The novelty introduced in our paper is a simple but efficient new recipe to obtain the best possible EP parameters for a given cluster system, with which the first step of the EP-DFT method is to be performed. Our method is able to reproduce experimental measurements at an excellent level for most cluster sizes, implying its ability to locate the true global minimum structures; meanwhile, if exactly the same method is applied based on the existing Gupta potential (fitted to bulk properties), it leads to wrong predicted structures with energies between 1 and 2 eV above the correct ones. Opposite to what was claimed in the past, our work unequivocally demonstrates that Zn clusters are not amorphous, and they rather adopt high symmetry structures for most sizes. We show that Zn clusters have a number of exotic, unprecedented structural and electronic properties which are not expected for clusters of a metallic element, and describe them in detail. 1 Introduction A key step in predicting and rationalising physico-chemical properties of small clusters and nanoparticles is their structural characterization. This is so because the interesting electronic, magnetic, optical, catalytic, etc., properties of nanoparticles depend on the geometry of the ionic skeleton. To achieve a complete characterization would require an exhaustive sam- pling of the potential energy surface (PES), whose complex- ity (number of local minima) increases in an exponential way with the number of atoms in the nanoparticle. At low temper- ature, the most stable structure is that of the global minimum (GM) on the PES, and most experiments probably involve the GM structure, and maybe a few isomers with low excitation energies. As the structure of a free-standing cluster is not di- † Electronic Supplementary Information (ESI) available: Atomic coordinates (in xyz format and ˚ A units) and point group symmetries for the Global Min- imum structures reported in this paper; full computational details and bench- mark calculations aimed at assessing the accuracy of the level of theory em- ployed. See DOI: 10.1039/b000000x/ a Departamento de F´ ısica Te´ orica, At´ omica y ´ Optica, University of Val- ladolid, Valladolid 47071, Spain; E-mail: aguado@metodos.fam.cie.uva.es b Laboratoire Chimie ´ Electrochimie Mol´ eculaire et Chimie Analytique, UMR CNRS 6521, 29285 Brest Cedex, France c Physikalisches Institut, Universit¨ at Freiburg, H.-Herder-Str. 3, D-79104 Freiburg, Germany rectly available from experiment, unbiased global optimiza- tion (GO) is essential for the prediction and later assessment of cluster structures. The structural assessment itself is usually achieved by indirect means, i.e. by comparing the theoretical predictions on several physical observables with experimental measurements (photoemission and vibrational spectra, as well as diffraction patterns and other properties, are considered as good structural “fingerprints”). Several computational methods for structure optimization of nanoparticles have been devised in recent years. In so- called biased algorithms, the user employs either previously available information on smaller clusters of the same mate- rial, or the available structures of chemically similar clusters, or more in general any type of “chemical intuition”, to pro- duce several candidate structures that are then optimized to their respective nearest local minima. These methods can not guarantee the consistent location of the absolute global min- imum, as they obviously lack robustness and transferability, although they may be useful in specific cases. Unbiased meth- ods, on the contrary, make no assumptions whatsoever about the structure of the GM, and are the method of choice for a reliable GO search. Most modern unbiased methods integrate an internal local search algorithm as well, which allows the main GO algorithm to operate exclusively with the energies of 1–23 | 1