Introduction to modeling nanoclusters and nanoparticles

Abstract

Abstract Although each chapter is self-contained, if you are relatively new to the field of modeling nanoclusters and nanoparticles, or would like to recap important ideas, we first provide an extensive introduction. Here we cover the topic of energy landscapes, where we focus on energy definitions based on analytic forms to describe the interaction between atoms or ions (e.g., Lennard Jones potential)—but clearly these expressions can be replaced with a more full treatment of electronic structure. We also introduce various Monte Carlo approaches typically employed to explore these landscapes. We employ analogies to help with the understanding of how the various algorithms work and give a range of concrete published examples based on the modeling of nanoclusters and nanoparticles of inorganic materials (we leave the coverage of other types of nanoparticles such as metallic clusters and their alloys for later chapters). The development of algorithms for exploring energy landscapes is still very active, where the objectives are to improve their computational efficiency, and/or to expand the range of targeted features/properties. For the latter, historically only the athermal lowest energy minima were first targeted. Afterward, transition points or barriers between minima were also targeted. Nowadays, temperature, pressure, chemical potential, probability flows, and lifetimes of metastable states may all be targeted. For the former objective, reduction in the computational cost of completing a search of an energy landscape may be achieved by a number of means such as (i) employing cheaper to evaluate, yet coarser, measures of the energy landscape before using more computationally expensive refined measures; (ii) employing machine learning algorithms to eventually (once a sufficient training set has been obtained) remove the need to compute the chosen expensive to evaluate the measure of the energy landscape; and (iii) ensuring a search does not get stuck in localized regions through the use of evolutionary ideas (e.g., structural mutations, grouping structures into niches) to maintain or increase the structural diversity in a set of candidate nanoparticle structures. Although new approaches to exploring energy landscapes are continually being proposed, the required foundational background for describing energy landscapes and searching them can be found in numerous text books or reviews on this topic. This introduction is largely adapted from one of these sources [S.M. Woodley, Nanoclusters and nanoparticles, in: S.T. Bromley, M.A. Zwijnenburg (Eds.), Computational Modeling of Inorganic Nanomaterials, CRC Press, Taylor and Francis Group, Boca Raton, USA, 2016, pp. 3–46].