Reaction Networks\nResemble Low-Dimensional Regular\nLattices

The computational exploration, manipulation, and design\nof complex\nchemical reactions face fundamental challenges related to the high-dimensional\nnature of potential energy surfaces (PESs) that govern reactivity.\nAccurately modeling complex reactions is crucial for understanding\nthe chemical processes involved in, for example, organocatalysis,\nautocatalytic cycles, and one-pot molecular assembly. Our prior research\ndemonstrated that discretizing PESs using heuristics based on bond\nbreaking and bond formation produces a reaction network representation\nwith a low-dimensional structure (metric space). We now find that\nthese stoichiometry-preserving reaction networks possess additional,\nthough approximate, structure and resemble low-dimensional regular\nlattices with a small amount of random edge rewiring. The heuristics-based\ndiscretization thus generates a nonlinear dimensionality reduction\nby a factor of 10 with an <i>a posteriori</i> error measure\n(probability of random rewiring). The structure becomes evident through\na comparative analysis of CHNO reaction networks of varying stoichiometries\nagainst a panel of size-matched generative network models, taking\ninto account their local, metric, and global properties. The generative\nmodels include random networks (Erdős−Rényi and\nbipartite random networks), regular lattices (periodic and nonperiodic),\nand network models with a tunable level of “randomness”\n(Watts–Strogatz graphs and regular lattices with random rewiring).\nThe CHNO networks are simultaneously closely matched in all these\nproperties by 3–4-dimensional regular lattices with 10% or\nless of edges randomly rewired. The effective dimensionality reduction\nis found to be independent of the system size, stoichiometry, and\nruleset, suggesting that search and sampling algorithms for PESs of\ncomplex chemical reactions can be effectively leveraged.