Polygonal tessellations as predictive models of molecular monolayers

Abstract

Molecular self-assembly plays a very important role in various aspects of technology as well as in biological systems. Governed by covalent, hydrogen or van der Waals interactions–self-assembly of alike molecules results in a large variety of complex patterns even in two dimensions (2D). Prediction of pattern formation for 2D molecular networks is extremely important, though very challenging, and so far, relied on computationally involved approaches such as density functional theory, classical molecular dynamics, Monte Carlo, or machine learning. Such methods, however, do not guarantee that all possible patterns will be considered and often rely on intuition. Here, we introduce a much simpler, though rigorous, hierarchical geometric model founded on the mean-field theory of 2D polygonal tessellations to predict extended network patterns based on molecular-level information. Based on graph theory, this approach yields pattern classification and pattern prediction within well-defined ranges. When applied to existing experimental data, our model provides a different view of self-assembled molecular patterns, leading to interesting predictions on admissible patterns and potential additional phases. While developed for hydrogen-bonded systems, an extension to covalently bonded graphene-derived materials or 3D structures such as fullerenes is possible, significantly opening the range of potential future applications.

Predicting Molecular Self-Assembly on Metal Surfaces Using Graph Neural Networks Based on Experimental Data Sets

“…In comparison with the previous works of applying informatics techniques to predict molecular self-assemblies, ,, our model has a better generality since it is able to predict molecular self-assemblies directly with the chemical models without being optimized. Note that a recent work demonstrated modeling and predicting hydrogen-bonded supramolecular patterns by a mean field theory of space-filling tessellations at different molecular levels, while the ML model is not limited to the type of intermolecular interactions.…”