Reaction Networks Resemble Low-Dimensional Regular Lattices

The computational exploration, manipulation, and design of complex chemical reactions face fundamental challenges related to the high-dimensional nature of potential energy surfaces (PESs) that govern reactivity. Accurately modeling complex reactions is crucial for understanding the chemical processes involved in, for example, organocatalysis, autocatalytic cycles, and one-pot molecular assembly. Our prior research demonstrated that discretizing PESs using heuristics based on bond breaking and bond formation produces a reaction network representation with a low-dimensional structure (metric space). We now find that these reaction networks possess additional, though approximate, structure and resemble low-dimensional regular lattices with a small amount of random edge rewiring. The heuristics-based discretization thus generates a nonlinear dimensionality reduction by a factor of ten with an a posteriori error measure (probability of random rewiring). The structure becomes evident through a comparative analysis of CHNO reaction networks of varying stoichiometries against a panel of size-matched generative network models, taking into account their local, metric, and global properties. The generative models include random networks (Erdős-Rényi and bipartite random networks), regular lattices (periodic and non-periodic), and network models with a tunable level of "randomness" (Watts-Strogatz graphs and regular lattices with random rewiring). The CHNO networks are simultaneously closely matched in all these properties by 3-4-dimensional regular lattices with 10% or less of edges randomly rewired. The effective dimensionality reduction is found to be independent of the system size, stoichiometry, and rule set, suggesting that search and sampling algorithms for PESs of complex chemical reactions can be effectively leveraged.