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Molecular search is important in chemistry, biology, and informatics for identifying molecular structures within large data sets, improving knowledge discovery and innovation, and making chemical data FAIR (findable, accessible, interoperable, reusable). Search algorithms for polymers are significantly less developed than those for small molecules because polymer search relies on searching by polymer name, which can be challenging because polymer naming is overly broad (i.e., polyethylene), complicated for complex chemical structures, and often does not correspond to official IUPAC conventions. Chemical structure search in polymers is limited to substructures, such as monomers, without awareness of connectivity or topology. This work introduces a novel query language and graph traversal search algorithm for polymers that provides the first search method able to fully capture all of the chemical structures present in polymers. The BigSMARTS query language, an extension of the small-molecule SMARTS language, allows users to write queries that localize monomer and functional group searches to different parts of the polymer, like the middle block of a triblock, the side chain of a graft, and the backbone of a repeat unit. The substructure search algorithm is based on the traversal of graph representations of the generating functions for the stochastic graphs of polymers. Operationally, the algorithm first identifies cycles representing the monomers and then the end groups and finally performs a depth-first search to match entire subgraphs. To validate the algorithm, hundreds of queries were searched against hundreds of target chemistries and topologies from the literature, with approximately 440,000 query–target pairs. This tool provides a detailed algorithm that can be implemented in search engines to provide search results with full matching of the monomer connectivity and polymer topology. 

Defining the similarity between chemical entities is an essential task in polymer informatics, enabling ranking, clustering, and classification. Despite its importance, the pairwise chemical similarity of polymers remains an open problem. Here, a similarity function for polymers with well-defined backbones is designed based on polymers’ stochastic graph representations generated from canonical BigSMILES, a structurally based line notation for describing macromolecules. The stochastic graph representations are separated into three parts: repeat units, end groups, and polymer topology. The earth mover’s distance is utilized to calculate the similarity of the repeat units and end groups, while the graph edit distance is used to calculate the similarity of the topology. These three values can be linearly or nonlinearly combined to yield an overall pairwise chemical similarity score for polymers that is largely consistent with the chemical intuition of expert users and is adjustable based on the relative importance of different chemical features for a given similarity problem. This method gives a reliable solution to quantitatively calculate the pairwise chemical similarity score for polymers and represents a vital step toward building search engines and quantitative design tools for polymer data. 

As a machine-recognizable representation of polymer connectivity, BigSMILES line notation extends SMILES from deterministic to stochastic structures. The same framework that allows BigSMILES to accommodate stochastic covalent connectivity can be extended to non-covalent bonds, enhancing its value for polymers, supramolecular materials, and colloidal chemistry. Non-covalent bonds are captured through the inclusion of annotations to pseudo atoms serving as complementary binding pairs, minimal key/value pairs to elaborate other relevant attributes, and indexes to specify the pairing among potential donors and acceptors or bond delocalization. Incorporating these annotations into BigSMILES line notation enables the representation of four common classes of non-covalent bonds in polymer science: electrostatic interactions, hydrogen bonding, metal–ligand complexation, and π–π stacking. The principal advantage of non-covalent BigSMILES is the ability to accommodate a broad variety of non-covalent chemistry with a simple user-orientated, semi-flexible annotation formalism. This goal is achieved by encoding a universal but non-exhaustive representation of non-covalent or stochastic bonding patterns through syntax for (de)protonated and delocalized state of bonding as well as nested bonds for correlated bonding and multi-component mixture. By allowing user-defined descriptors in the annotation expression, further applications in data-driven research can be envisioned to represent chemical structures in many other fields, including polymer nanocomposite and surface chemistry.