(479d) Hamiltonian Graph Representation of Zeolite Frameworks

Machine learning (ML) has emerged as a critical driver for materials design for drug discovery, energy storage, manufacturing, and emission reduction, among others. The selection, accuracy and efficiency of ML approaches largely depend on the type of molecular representation used for model generation. Zeolites are ultra-large crystalline materials with hundreds of atoms that form closed three-dimensional complex framework topologies with complex internal pore structures with portals, channels, and cages [1]. Describing the structure of a zeolite framework has always been a challenging task. Certesian coordinates-based representation of atomic positions in three dimensions is not the most suitable for ML in the context of large and nanoporous structures like zeolites and metal organic frameworks. To this end, we use a Hamiltonian graph-based representation of complex nanoporous structures, such as zeolites with extended frameworks [2], which provides a new graph-theoretic approach to reduce the computational complexity posed by the vast chemical design space. Unlike Hamiltonian operators, Hamiltonian graphs are graphs where one can traverse all nodes exactly once before reaching the starting node at the end [3]. The Hamiltonian graph-based representation is both invertible and scalable in a sense that it only uses the topologically distinctive T-nodes that must be used to construct the building blocks of a zeolite framework, thereby significantly reducing the computation needed for characterization. For example, the structure of Chabazite zeolite can be represented using a Hamiltonian graph that needs only 12 unique T-nodes and their connectivity matrix. Furthermore, the representation allows to embed all plausible design solutions in a single maximal structure. This enables a deep reinforcement learning (DRL)-based policy-gradient approach to efficiently generate successive designs, with ultimate goal of performing inverse design [4] of periodic nanostructures.

References:

[1] First, E. L.; Gounaris, C. E.; Wei, J.; Floudas, C. A. Computational characterization of zeolite porous networks: an automated approach. Physical Chemistry Chemical Physics 2011, 13, 17339-17358.

[2] Sato, M. Hamiltonian graph representation of zeolite frameworks and Si, Al ordering in the framework. Journal of Mathematical Chemistry 1991, 7, 341-352.

[3] Gross, J. L.; Yellen, J.: Graph theory and its applications; CRC press, 2005.

[4] Sanchez-Lengeling, B.; Aspuru-Guzik, A. Inverse molecular design using machine learning: Generative models for matter engineering. Science 2018, 361, 360-365.