Abstract
Candidate structures for the global minima of adamantane clusters, (C10H16)N, are presented. Based on a rigid model for individual molecules with atom-atom pairwise interactions that include Lennard-Jones and Coulomb contributions, low-energy structures were obtained up to N = 42 using the basin-hopping method. The results indicate that adamantane clusters initially grow accordingly with an icosahedral packing scheme, followed above N = 14 by a structural transition toward face-centered cubic structures. The special stabilities obtained at N = 13, 19, and 38 are consistent with these two structural families, and agree with recent mass spectrometry measurements on cationic adamantane clusters. Coarse-graining the intermolecular potential by averaging over all possible orientations only partially confirm the all-atom results, the magic numbers at 13 and 38 being preserved. However, the details near the structural transition are not captured well, because despite their high symmetry the adamantane molecules are still rather anisotropic.
Highlights
In order to shed some light onto the relative importance of the translational and orientational degrees of freedom and their interplay, and more generally to confirm whether adamantane clusters do correspond to the speculated structures, we have carried out a systematic global optimization investigation in the size range up to 42 molecules, using the basin-hoping method as our main tool
To estimate the relative stability of different cluster sizes, we evaluated the second-energy derivative of the PES, 2E(N) = EN+1 + EN−1 − 2EN, where EN is the energy of the global minimum for (C10H16)N
We have modeled adamantane clusters using a rigid body description and a site-site pairwise force field comprising the traditional Lennard-Jones potential for repulsion-dispersion forces with Coulomb interactions acting between partial charges
Summary
Global optimization is an important topic in the physical and chemical sciences, whether we want to refine a force field, predict the native structure of a protein or the crystal structure of some condensed material, or find a practical solution to machine learning problems (Andricioaei and Straub, 1996; Huber and McCammon, 1997; Doye and Wales, 1998; Wales and Hodges, 1998; Wawak et al, 1998; Klepeis and Floudas, 1999; Liwo et al, 1999; Nigra and Kais, 1999; Wales and Scheraga, 1999; Middleton et al, 2001; Hernández-Rojas and Wales, 2003; James et al, 2005; Fadda and Fadda, 2010; Heiles and Johnston, 2013; Wu et al, 2014; Ballard et al, 2016, 2017; Das and Wales, 2016). Icosahedral-to-cubic transitions are common in atomic and molecular clusters, as they convey the increasing energetic penalty that the highly connected icosahedral structures have to sustain, eventually in favor of less connected and less strained close-packed structures (Doye et al, 1995; Ikeshoji et al, 2001; Calvo and Carré, 2006) Such a transition has been identified as being strongly influenced by the range of the interparticle potential (Doye et al, 1995; Doye and Wales, 1996). In order to shed some light onto the relative importance of the translational and orientational degrees of freedom and their interplay, and more generally to confirm whether adamantane clusters do correspond to the speculated structures, we have carried out a systematic global optimization investigation in the size range up to 42 molecules, using the basin-hoping method as our main tool.
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