Reflection-Equivariant Diffusion for 3D Structure Determination from Isotopologue Rotational Spectra in Natural Abundance

Structure determination is necessary to identify unknown organic molecules, such as those in natural products, forensic samples, the interstellar medium, and laboratory syntheses. Rotational spectroscopy enables structure determination by providing accurate 3D information about small organic molecules via their moments of inertia. Using these moments, Kraitchman analysis determines isotopic substitution coordinates, which are the unsigned $|x|,|y|,|z|$ coordinates of all atoms with natural isotopic abundance, including carbon, nitrogen, and oxygen. While unsigned substitution coordinates can verify guesses of structures, the missing $+/-$ signs make it challenging to determine the actual structure from the substitution coordinates alone. To tackle this inverse problem, we develop KREED (Kraitchman REflection-Equivariant Diffusion), a generative diffusion model that infers a molecule's complete 3D structure from its molecular formula, moments of inertia, and unsigned substitution coordinates of heavy atoms. KREED's top-1 predictions identify the correct 3D structure with >98% accuracy on the QM9 and GEOM datasets when provided with substitution coordinates of all heavy atoms with natural isotopic abundance. When substitution coordinates are restricted to only a subset of carbons, accuracy is retained at 91% on QM9 and 32% on GEOM. On a test set of experimentally measured substitution coordinates gathered from the literature, KREED predicts the correct all-atom 3D structure in 25 of 33 cases, demonstrating experimental applicability for context-free 3D structure determination with rotational spectroscopy.

Group SELFIES: A Robust Fragment-Based Molecular String Representation

We introduce Group SELFIES, a molecular string representation that leverages group tokens to represent functional groups or entire substructures while maintaining chemical robustness guarantees. Molecular string representations, such as SMILES and SELFIES, serve as the basis for molecular generation and optimization in chemical language models, deep generative models, and evolutionary methods. While SMILES and SELFIES leverage atomic representations, Group SELFIES builds on top of the chemical robustness guarantees of SELFIES by enabling group tokens, thereby creating additional flexibility to the representation. Moreover, the group tokens in Group SELFIES can take advantage of inductive biases of molecular fragments that capture meaningful chemical motifs. The advantages of capturing chemical motifs and flexibility are demonstrated in our experiments, which show that Group SELFIES improves distribution learning of common molecular datasets. Further experiments also show that random sampling of Group SELFIES strings improves the quality of generated molecules compared to regular SELFIES strings. Our open-source implementation of Group SELFIES is available online, which we hope will aid future research in molecular generation and optimization.