Abstract
One of the great challenges of modern science is to faithfully model, and understand, matter at a wide range of scales. Starting with atoms, the vastness of the space of possible configurations poses a formidable challenge to any simulation of complex atomic and molecular systems. We introduce a computational method to reduce the complexity of atomic configuration space by systematically recognising hierarchical levels of atomic structure, and identifying the individual components. Given a list of atomic coordinates, a network is generated based on the distances between the atoms. Using the technique of modularity optimisation, the network is decomposed into modules. This procedure can be performed at different resolution levels, leading to a decomposition of the system at different scales, from which hierarchical structure can be identified. By considering the amount of information required to represent a given modular decomposition we can furthermore find the most succinct descriptions of a given atomic ensemble. Our straightforward, automatic and general approach is applied to complex crystal structures. We show that modular decomposition of these structures considerably simplifies configuration space, which in turn can be used in discovery of novel crystal structures, and opens up a pathway towards accelerated molecular dynamics of complex atomic ensembles. The power of this approach is demonstrated by the identification of a possible allotrope of boron containing 56 atoms in the primitive unit cell, which we uncover using an accelerated structure search, based on a modular decomposition of a known dense phase of boron, γ-B28.
Highlights
Considerable growth in computational power and its ubiquity has been coupled with the development of efficient algorithms[1, 2] and their implementation in robust[3,4,5] and reliable[6] computer codes
The simplification of the space of possible configurations of complex atomic systems has the potential to vastly accelerate the process of computational materials discovery, among other tasks that can benefit from automatic coarsegraining based on hierarchical decomposition
For atomic structures of a single atomic species we can generate an unweighted network of atoms by imposing a threshold d* on the interatomic distance and connecting atoms that are closer to each other than this threshold distance
Summary
Considerable growth in computational power and its ubiquity has been coupled with the development of efficient algorithms[1, 2] and their implementation in robust[3,4,5] and reliable[6] computer codes. Global measures, calculated across the entire network, such as the average shortest path length,[19] can help us to compare networks as a whole Between these two extremes lies an entire field of research that searches for meaningful descriptions of intermediate structures, such as ‘cliques’,23 ‘communities’[24] and ‘rich clubs’,25 among others. These are sets of nodes or edges which are densely connected, or which share some other defining topological feature. The simplification of the space of possible configurations of complex atomic systems has the potential to vastly accelerate the process of computational materials discovery, among other tasks that can benefit from automatic coarsegraining based on hierarchical decomposition. We illustrate this through the identification of a possible new allotrope of boron
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