Inverse-design of organometallic catalysts with guided equivariant diffusion

Organometallic complexes are ubiquitous in homogenous catalysis, and their optimisation is of particular interest for many technologically relevant reactions. However, due to the large variety of possible metal-ligand and ligand-ligand interactions, finding the best combination of metal and ligands is an immensely challenging task. Here we present an inverse design framework based on a diffusion generative model for \textit{in-silico} design of such complexes. Given the importance of the spatial structure of a catalyst, the model directly operates on all-atom (including explicit \ch{H}) representations in $3$D space. To handle the symmetries inherent to that data representation, it combines an equivariant diffusion model and an equivariant property predictor to drive sampling at inference time. We illustrate the potential of the proposed framework by optimising catalysts for the Suzuki-Miyaura cross-coupling reaction, and validating a selection of novel proposed complexes with \textsc{DFT}.