CatRetriever: Contrastive Representation Learning for Slab-to-Bulk Retrieval in Generative Catalyst Discovery

Technical Summary: CatRetriever for Slab-to-Bulk Retrieval in Generative Catalyst Discovery

Problem Statement
The field of heterogeneous catalyst discovery is increasingly utilizing generative AI models to propose novel surface-adsorbate structures. However, a critical bottleneck exists: these models operate at the "slab" level (surface representation) and do not provide the corresponding parent "bulk" crystal structure. This omission prevents the rigorous assessment of bulk-dependent properties essential for practical deployment, including formation energy, surface energy, crystallographic symmetry, and synthesizability. While slab-to-bulk inference is necessary to evaluate thermodynamic plausibility and phase stability, existing methods rely on inefficient database lookups or fail to address the non-unique nature of the mapping, where a single surface motif may correspond to multiple chemically or structurally similar bulk candidates.

Methodology
To address this, the authors introduce CatRetriever, a contrastive representation learning model designed to align slab and bulk crystal representations within a shared latent space.

• Data Construction: A retrieval search space was constructed using the Materials Project database, filtered for binary and ternary bulk structures with formation energies below 0 eV/atom and energy above the hull ($E_{hull}$) below 0.1 eV/atom, resulting in 38,901 bulk candidates. From these, 1,384,140 slab structures were generated for low-index Miller surfaces.
• Model Architecture: CatRetriever utilizes the pretrained Universal Model for Atoms (UMA; uma-s-1p1) as a frozen backbone to extract structural embeddings for both bulk and slab inputs. These embeddings are pooled to fixed-length vectors and passed through separate projection heads to map them into a shared latent space ($Z_s$ for slabs, $Z_b$ for bulks).
• Training Strategy: The model is trained using a contrastive learning formulation. For a given query slab, the true parent bulk is defined as a positive pair, while all other bulk candidates in the pool serve as implicit negative pairs. The objective is to maximize the similarity score ($r(s, b) = Z_s^T Z_b$, equivalent to cosine similarity) for matched pairs while minimizing it for unmatched pairs.
• Discovery Pipeline: The authors propose an end-to-end workflow that integrates:
  1. Target-Conditioned Generation: Using CatGPT to generate slab-adsorbate structures guided by specific adsorption energy targets (e.g., N* adsorption energy of −0.90 eV for ammonia decomposition).
  2. Retrieval: Using CatRetriever to rank parent bulk candidates from the Materials Project (MP) database.
  3. Search Space Expansion: For queries where MP retrieval scores are insufficient, the generative model MatterGen is employed to create new bulk candidates within the same chemical system, which are then re-ranked by CatRetriever.
  4. Validation: Final candidates undergo adsorption energy distribution analysis using UMA to verify if the parent bulk exposes surface sites with the desired binding strength.

Key Results

• Retrieval Performance: CatRetriever demonstrates high accuracy in retrieving the correct parent bulk from a slab query. On an in-distribution test set, it achieves a Recall@1 (R@1) of 91.9% and Recall@3 (R@3) of 98.8%. Crucially, it maintains robust generalization on a holdout set (containing bulk structures entirely excluded from training), achieving R@1 of 91.5% and R@3 of 98.9%.
• Representation Quality: The learned embedding space effectively separates matched slab-bulk pairs from non-matching candidates, with positive similarity scores ($s_{pos}$) clearly shifted higher than negative scores ($s_{neg}$).
• Pipeline Efficacy: In a case study targeting thermal ammonia decomposition, the pipeline successfully identified plausible bulk candidates. For queries where the MP database yielded low retrieval scores, MatterGen successfully expanded the search space, generating candidates that exceeded the retrieval score threshold in 65% of previously unmatched cases.
• Thermodynamic and Functional Validation: The workflow successfully connected generated slabs to bulk structures (e.g., MP-retrieved NbS and MatterGen-generated Ca$_3$Cd) that were both thermodynamically stable (low $E_{hull}$) and capable of exposing surface sites with adsorption energies within the target window (−1.00 to −0.80 eV).

Significance and Claims
The paper claims that CatRetriever provides a scalable, modular solution to the "missing slab-to-bulk connection" in generative catalyst discovery. By framing the problem as a retrieval task rather than a strict classification, the model accommodates the inherent non-uniqueness of slab-to-bulk inference. The authors assert that this approach enables the transition from purely generative surface models to physically grounded discovery workflows. Specifically, the framework allows researchers to:

1. Rapidly shortlist plausible parent bulk candidates for generated surface motifs.
2. Evaluate bulk-dependent thermodynamic properties (stability, synthesizability) that cannot be inferred from isolated slabs.
3. Systematically validate whether a candidate bulk can reproduce the target catalytic activity across diverse surface environments.

The work concludes that while current generative models excel at surface design, the integration of CatRetriever and generative search-space expansion is essential for bridging the gap between generated surface structures and viable, bulk-verified catalyst candidates. The authors acknowledge limitations, noting that the current workflow is a post-generation retrieval framework rather than a joint generator, and that generalization to chemical spaces entirely absent from the training distribution remains an open challenge.