How relevant is the choice of classical potentials in finding minimal energy cluster conformations? José Rogan a,b , Max Ramírez c , Alejandro Varas d , Miguel Kiwi a,b,⇑ a Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago 7800024, Chile b Centro para el Desarrollo de la Nanociencia y Nanotecnología, CEDENNA, Avenida Ecuador 3493, Santiago 9170124, Chile c Theoretical and Physical Chemistry, University of Saarland, 66123 Saarbrücken, Germany d Nano-Bio Spectroscopy Group and ETSF Scientific Development Centre, Departamento de Física de Materiales, Universidad del País Vasco UPV/EHU, Av. Tolosa 72, E-20018 San Sebastián, Spain article info Article history: Received 16 May 2013 Received in revised form 1 July 2013 Accepted 2 July 2013 Available online 11 July 2013 Keywords: Local and global minima for small clusters Distance between cluster conformations Relevance of the choice of classical potentials Relevance of the diversity of cluster conformations abstract We investigate the relevance of the choice of a particular classical potential in the task of finding global and local energy minima of small cluster conformations, in the context of their use as input for quantum refinement. We contrast results obtained using the many body Gupta and Sutton–Chen potentials for small nickel and copper clusters, with those of a Lennard-Jones pair potential. To obtain quantitative results we introduced a modified version of the concept of distance between configurations and color maps to represent these distances. Our main conclusion is that, for the small clusters we studied, all three potentials lead to practically the same results after quantum refinement is implemented. Ó 2013 Elsevier B.V. All rights reserved. 1. Introduction The search for global and local energy minima of atom cluster conformations has attracted much interest with the availability of increased computational power. On the other hand, since the physical properties of solids, liquids and clusters are mainly determined by structure, the first and crucial step in the descrip- tion and understanding of condensed matter is the precise deter- mination of the geometrical configuration that their constituent atoms do adopt [1]. Several strategies have been developed to tackle the problem, and they can be classified into three main groups: (i) finding the minimal energy structure by means of a phenomenological potential that properly describes the bulk material, and refine the global minimum thus found by quantum relaxation [2–6]; (ii) finding the global minimum plus a set of low lying local minima, followed by their quantum relaxation [7]; and (iii) perform the search quantum mechanically from the start [8,9]. Certainly, the order in which they are mentioned is related to a significant increase in computational cost. In this contribution we address several issues related to these strate- gies; specifically, how relevant is the choice of the phenomeno- logical potentials used in the search for minimal energy conformations; how do the results obtained with different clas- sical potentials compare; and, how do they match the results after quantum refinement is performed [10]. It has repeatedly been shown that the classical global mini- mum conformations do not necessarily correspond to the ones obtained by means of DFT calculations [6,7,10–17]. The implica- tion is that global minima are not transferable from classical to quantum treatments. In this context several improvements have been developed, in particular Hartke [18,19] seem to have been the first to suggest a continuously adapted model potential ap- proach to tackle the problem. This changed the way of approach- ing the implementation of phenomenological potentials, leading to a change of paradigm: rather than focusing on the classical global minimum we realized that the important point was to ob- tain a large set of local minima to be relaxed ab initio in the search of a putative global minimum among the set of resulting structures [10]. Thus, the issue of how accurate the minima gen- erated on the basis of classical potentials have to be becomes a relevant question. In fact, when the objective is to use classically obtained minima for quantum refinement, a valid question 2210-271X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comptc.2013.07.004 ⇑ Corresponding author at: Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago 7800024, Chile. E-mail address: m.kiwi.t@gmail.com (M. Kiwi). Computational and Theoretical Chemistry 1021 (2013) 155–163 Contents lists available at SciVerse ScienceDirect Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc