Revealing and exploiting hierarchical material structure through complex atomic networks

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, gamma-B-28.

现代科学的重大挑战之一是在广泛的尺度上忠实地对物质进行建模和理解。从原子开始，可能的构型空间的浩瀚对任何复杂原子和分子系统的模拟都构成了巨大的挑战。我们引入一种计算方法，通过系统地识别原子结构的层次级别并确定各个组分来降低原子构型空间的复杂性。给定一组原子坐标，会根据原子之间的距离生成一个网络。利用模块性优化技术，该网络被分解为模块。这个过程可以在不同的分辨率水平下进行，从而导致系统在不同尺度上的分解，从中可以识别出层次结构。通过考虑表示给定模块分解所需的信息量，我们还可以找到给定原子集合的最简洁描述。我们这种简单、自动且通用的方法被应用于复杂的晶体结构。我们表明，这些结构的模块分解极大地简化了构型空间，这反过来又可用于发现新的晶体结构，并为加速复杂原子集合的分子动力学开辟了一条途径。这种方法的威力通过识别出在原始晶胞中含有56个原子的一种可能的硼同素异形体得以证明，我们是基于对已知的硼密相γ - B - 28进行模块分解，利用加速结构搜索发现它的。