Grouper: symmetry-aware functional-group graph representations for generative exploration of chemical space

The vastness of chemical space holds immense potential for discovery, yet its systematic exploration remains computationally daunting. We mitigate this complexity by focusing on chemically meaningful differences captured by functional-group motifs and collapsing symmetry-equivalent configurations. We operationalize this principle with a symmetry-aware, hierarchical representation of molecules composed of functional groups. Combined with combinatorial and algebraic methods, this enables efficient generation and analysis of chemical spaces. By exploiting graph and group symmetry, we cut isomorphism checks by nearly 99% compared with naïve enumeration near the exhaustive limit. The resulting computational savings, together with scalable, parallel code, give access to previously untenable strategies such as exhaustive design, verified via Pólya theory. This framework ensures interoperability across simulation formats and data-driven models, enabling end-to-end molecular design (generation, characterization, and analysis). We demonstrate its utility in solubility optimization and polymer functionalization, opening pathways to synthetically meaningful, computationally tractable discovery pipelines.