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Abstract
We review the materials science applications of the nested sampling (NS) method, which was originally conceived for calculating the evidence in Bayesian inference. We describe how NS can be adapted to sample the potential energy surface (PES) of atomistic systems, providing a straightforward approximation for the partition function and allowing the evaluation of thermodynamic variables at arbitrary temperatures. After an overview of the basic method, we describe a number of extensions, including using variable cells for constant pressure sampling, the semi-grand-canonical approach for multicomponent systems, parallelizing the algorithm, and visualizing the results. We cover the range of materials applications of NS from the past decade, from exploring the PES of Lennard–Jones clusters to that of multicomponent condensed phase systems. We highlight examples how the information gained via NS promotes the understanding of materials properties through a novel way of visualizing the PES, identifying thermodynamically relevant basins, and calculating the entire pressure–temperature(–composition) phase diagram.Graphic abstract
Highlights
The potential energy surface (PES) describes the interaction energy of a system of particles as a function of the spatial arrangement of atoms and, within the Born–Oppenheimer approximation, contains all structural and mechanical information—both microscopic and macroscopic—about the system. [1] Its global minimum corresponds to the ground-state structure, while the usually numerous local minima are other stable or metastable configurations linked to each other by transition states, which determine the pathways between these different structures, along with the transformation mechanisms
Equilibrium statistical mechanics view of the PES is given by the free energy of various phases, which quantifies the interplay between energetic factors, which favor lower potential energy, and entropic factors, which favor a large configuration space volume accessible to each phase
It is commonly thought that the number of local minima scales exponentially as well [15], which can dramatically increases the computational cost, rendering it impossible to perform an exhaustive search of all potential minima basins of even moderately complex systems
Summary
The potential energy surface (PES) describes the interaction energy of a system of particles as a function of the spatial arrangement of atoms and, within the Born–Oppenheimer approximation, contains all structural and mechanical information—both microscopic and macroscopic—about the system. [1] Its global minimum corresponds to the ground-state structure, while the usually numerous local minima are other stable or metastable configurations linked to each other by transition states, which determine the pathways between these different structures, along with the transformation mechanisms. Equilibrium statistical mechanics view of the PES is given by the free energy of various phases, which quantifies the interplay between energetic factors, which favor lower potential energy, and entropic factors, which favor a large configuration space volume accessible to each phase Those specific regions of the PES where the number of available configurations dramatically decreases as temperature decreases correspond to phase transitions, such as condensation and freezing. Global optimization methods focus on building a database of minima to find the lowest energy structure These include basin hopping [2], genetic algorithms [3,4], minima hopping [5] and simulated annealing [6] with adaptive cooling rates [7], as well as dedicated crystal structure prediction tools, such as AIRSS [8,9], USPEX [10,11], and CALYPSO [12,13]. We review how the nested sampling technique can be adapted to sample the PES of atomic systems, describe its advantages, and illustrate how thermodynamic and structural information can be extracted from the results, with examples from several different applications
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