Tensor-Reduced Atomic Density Representations.

Density-based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modeling, and the visualization and analysis of material datasets. The standard mechanism used to incorporate chemical element information is to create separate densities for each element and form tensor products between them. This leads to a steep scaling in the size of the representation as the number of elements increases. Graph neural networks, which do not explicitly use density representations, escape this scaling by mapping the chemical element information into a fixed dimensional space in a learnable way. By exploiting symmetry, we recast this approach as tensor factorization of the standard neighbour-density-based descriptors and, using a new notation, identify connections to existing compression algorithms. In doing so, we form compact tensor-reduced representation of the local atomic environment whose size does not depend on the number of chemical elements, is systematically convergable, and therefore remains applicable to a wide range of data analysis and regression tasks.

Validation of the CoGEF Method as a Predictive Tool for Polymer Mechanochemistry.

The development of force-responsive molecules called mechanophores is a central component of the field of polymer mechanochemistry. Mechanophores enable the design and fabrication of polymers for a variety of applications ranging from sensing to molecular release and self-healing materials. Nevertheless, an insufficient understanding of structure-activity relationships limits experimental development, and thus computation is necessary to guide the structural design of mechanophores. The constrained geometries simulate external force (CoGEF) method is a highly accessible and straightforward computational technique that simulates the effect of mechanical force on a molecule and enables the prediction of mechanochemical reactivity. Here, we use the CoGEF method to systematically evaluate every covalent mechanophore reported to date and compare the predicted mechanochemical reactivity to experimental results. Molecules that are mechanochemically inactive are also studied as negative controls. In general, mechanochemical reactions predicted with the CoGEF method at the common B3LYP/6-31G* level of density functional theory are in excellent agreement with reactivity determined experimentally. Moreover, bond rupture forces obtained from CoGEF calculations are compared to experimentally measured forces and demonstrated to be reliable indicators of mechanochemical activity. This investigation validates the CoGEF method as a powerful tool for predicting mechanochemical reactivity, enabling its widespread adoption to support the developing field of polymer mechanochemistry. Secondarily, this study provides a contemporary catalog of over 100 mechanophores developed to date.