The rule of four: anomalous distributions in the stoichiometries of inorganic compounds.

Why are materials with specific characteristics more abundant than others? This is a fundamental question in materials science and one that is traditionally difficult to tackle, given the vastness of compositional and configurational space. We highlight here the anomalous abundance of inorganic compounds whose primitive unit cell contains a number of atoms that is a multiple of four. This occurrence-named here the rule of four-has to our knowledge not previously been reported or studied. Here, we first highlight the rule's existence, especially notable when restricting oneself to experimentally known compounds, and explore its possible relationship with established descriptors of crystal structures, from symmetries to energies. We then investigate this relative abundance by looking at structural descriptors, both of global (packing configurations) and local (the smooth overlap of atomic positions) nature. Contrary to intuition, the overabundance does not correlate with low-energy or high-symmetry structures; in fact, structures which obey the rule of four are characterized by low symmetries and loosely packed arrangements maximizing the free volume. We are able to correlate this abundance with local structural symmetries, and visualize the results using a hybrid supervised-unsupervised machine learning method.

AiiDA 1.0, a scalable computational infrastructure for automated reproducible workflows and data provenance.

The ever-growing availability of computing power and the sustained development of advanced computational methods have contributed much to recent scientific progress. These developments present new challenges driven by the sheer amount of calculations and data to manage. Next-generation exascale supercomputers will harden these challenges, such that automated and scalable solutions become crucial. In recent years, we have been developing AiiDA (aiida.net), a robust open-source high-throughput infrastructure addressing the challenges arising from the needs of automated workflow management and data provenance recording. Here, we introduce developments and capabilities required to reach sustained performance, with AiiDA supporting throughputs of tens of thousands processes/hour, while automatically preserving and storing the full data provenance in a relational database making it queryable and traversable, thus enabling high-performance data analytics. AiiDA's workflow language provides advanced automation, error handling features and a flexible plugin model to allow interfacing with external simulation software. The associated plugin registry enables seamless sharing of extensions, empowering a vibrant user community dedicated to making simulations more robust, user-friendly and reproducible.

Materials Cloud, a platform for open computational science.

Materials Cloud is a platform designed to enable open and seamless sharing of resources for computational science, driven by applications in materials modelling. It hosts (1) archival and dissemination services for raw and curated data, together with their provenance graph, (2) modelling services and virtual machines, (3) tools for data analytics, and pre-/post-processing, and (4) educational materials. Data is citable and archived persistently, providing a comprehensive embodiment of entire simulation pipelines (calculations performed, codes used, data generated) in the form of graphs that allow retracing and reproducing any computed result. When an AiiDA database is shared on Materials Cloud, peers can browse the interconnected record of simulations, download individual files or the full database, and start their research from the results of the original authors. The infrastructure is agnostic to the specific simulation codes used and can support diverse applications in computational science that transcend its initial materials domain.

Analysis of Self-Assembly Pathways with Unsupervised Machine Learning Algorithms.

Colloidal and nanoparticle systems display a rich and exciting phase behavior including the self-assembly of highly complex crystal structures. Nucleation and growth pathways toward crystallization have been studied both computationally and experimentally, but the mechanisms for the formation of the precritical nucleus and consequent crystal growth are yet to be fully understood. Recent advances in the application of machine learning algorithms applied to many-particle systems have led to significant breakthroughs in the ability for high-throughput analysis of phase transitions and the identification of crystal structures. We build upon these techniques to identify and analyze pathways for nucleation and growth in supercooled liquids of colloidal systems modeled with isotropic pair potentials. Our study involves the development of unsupervised machine learning models trained on spherical-harmonics-based descriptors. These models allow us to determine clusters of local environments that are present prior to and during crystallization. We analyze these environments to identify prevalent motifs and local order within the supercooled liquid prior to formation of the critical nucleus.

Inverse design of simple pair potentials for the self-assembly of complex structures.

The synthesis of complex materials through the self-assembly of particles at the nanoscale provides opportunities for the realization of novel material properties. However, the inverse design process to create experimentally feasible interparticle interaction strategies is uniquely challenging. Standard methods for the optimization of isotropic pair potentials tend toward overfitting, resulting in solutions with too many features and length scales that are challenging to map to mechanistic models. Here we introduce a method for the optimization of simple pair potentials that minimizes the relative entropy of the complex target structure while directly considering only those length scales most relevant for self-assembly. Our approach maximizes the relative information of a target pair distribution function with respect to an ansatz distribution function via an iterative update process. During this process, we filter high frequencies from the Fourier spectrum of the pair potential, resulting in interaction potentials that are smoother and simpler in real space and therefore likely easier to make. We show that pair potentials obtained by this method assemble their target structure more robustly with respect to optimization method parameters than potentials optimized without filtering.