To enable parallelized structure generation, we developed a distributed, Transformer-based framework built upon the core architecture of GPT-2^[43]. The underlying generative engine employs a decoder-only configuration featuring 12 stacked Transformer blocks, 8 attention heads, and a 512-dimensional embedding space, trained with a batch size of 144. Each block contains causal masked multi-head self-attention, layer normalization, and a position-wise feed-forward network, and the resulting hidden representations are used for autoregressive prediction of the structural token sequence. Surface environments involving lattice parameters, elemental identities, and atomic positions were mapped into discrete tokens via coordinate-level tokenization. Broad structural priors were initially established by pretraining the framework on 2 million entries from the OC20-S2EF dataset, with architectural and tokenization consistency maintained throughout validation against the OC20-S2EF Val-ID split^[46]. Tailored exploration of the reaction space was achieved by fine-tuning the pretrained model on 14,000 *OCH₂CH₃ adsorption structures, split into 90% training and 10% validation subsets, for 14 epochs. This specialized adaptation allowed the network to transition from general geometric representations to focused sampling of intermediate-specific potential energy surfaces. Autoregressive sampling was performed at a temperature of 1.0 on a single NVIDIA H100 GPU. A random seed of 42 was used for both fine-tuning and sampling. This highly optimized execution pipeline generated a target pool of 1 million candidate structures, serving as the foundational dataset for downstream deduplication, clustering, and surrogate-property evaluation.

Electronic structure evaluations of the screened structural motifs were conducted via spin-polarized DFT simulations implemented within the Vienna Ab initio Simulation Package (VASP) package^[48,49]. Exchange-correlation interactions were described using the revised Perdew-Burke-Ernzerhof (RPBE) functional^[50], and core-valence interactions were treated using the projector augmented-wave (PAW) method^[51]. A plane-wave kinetic-energy cutoff of 350 eV was employed, and metallic occupations were treated using first-order Methfessel-Paxton smearing with a width of 0.2 eV. Slab atoms located within 2.0 Å below the uppermost slab atom along the third lattice-vector direction were allowed to relax, whereas deeper slab atoms were fixed; all adsorbate atoms were allowed to relax. Reciprocal-space integration over the Brillouin zone was performed using Γ-centered k₁ × k₂ × 1 meshes, where k_i = max[1, round(40/|a_i|)] and |a_i| is the length of the corresponding in-plane lattice vector in Å. Geometry optimizations were considered converged when the residual force on each relaxed atom was below 0.05 eVÅ^-1 and the electronic self-consistency threshold was set to 1 × 10^-4 eV. The same DFT settings were applied consistently to all 20 representative benchmark systems. The adsorption energies were evaluated according to Equation (1), where the adsorbate reference energies were derived via linear combinations of the standard OC20 atomic reference energies^[46]. Each production DFT relaxation was performed on CPUs using 12 MPI processes. Representative CPU/GPU wall-clock benchmarks for UMA and VASP calculations are provided in Supplementary Table 1.

SGD was employed to identify interpretable elemental descriptor conditions correlated with target labels within the structural candidate pools^[52]. The search for subgroup rules was executed independently across the binary and ternary compositional spaces, using a feature space constructed from intrinsic properties of the constituent elements [Supplementary Table 2]: atomic radius (R), electron affinity (EA), ionization potential (IP), cohesive energy (EC), the number of d-valence electrons (Nd), the number of group valence electrons (Nv), electronegativity (EN), Mendeleev number (MN), and relative atomic mass (M). Implemented via the beam search algorithm within the pysubgroup framework^[53], the search targeted the positive structural class as a binary objective variable with the quality function set to StandardQF (a = 0.5) and a maximum rule depth of 5. The resulting rules were ranked by their quality function values, and statistical metrics including total sample coverage, positive class coverage, subgroup positive ratio, baseline positive ratio, and enrichment factor were systematically recorded to evaluate the enrichment capabilities of varying elemental descriptor combinations for the positive structures.

Next, we introduced a post hoc Shapley-based condition-attribution method to quantify the contribution of individual conditions within each discovered rule^[54]. For each subset S of the conditions, the StandardQF score of the subgroup defined by S was used as the characteristic-function value v(S). For a rule containing n conditions, all 2ⁿ possible condition subsets were enumerated, and the Shapley value of each condition was calculated as the weighted average of its marginal contribution to the StandardQF score over all subsets not containing that condition. Additional methodological details for SGD rule search and Shapley attribution can be found in the Supplementary Materials.

To bypass the combinatorial limitation of brute-force site enumeration on multicomponent surfaces, we established a reaction-anchored generative materials informatics framework organized into four integrated stages [Figure 1]. In the first stage, the search space is chemically oriented by defining ethoxy (*OCH₂CH₃) as a late-stage oxygenated C₂ reaction anchor for CO₂RR-to-ethanol pathways. Rather than serving as a complete descriptor of ethanol selectivity, *OCH₂CH₃ is employed to bias the generated structures toward local surface environments intrinsically capable of stabilizing oxygenated C₂ intermediates. These surface environments are subsequently evaluated following adsorbate replacement with *CO and *H, establishing a tri-adsorbate constraint framework that simultaneously considers oxygenated C₂ binding, CO binding, and H adsorption as screening-level descriptors.

In the second stage, this reaction anchor is mapped into a generative structure space via a Transformer-based generative model. The model was pretrained on the OC20 dataset and fine-tuned on *OCH₂CH₃ adsorption configurations, enabling the direct generation of 1,000,000 candidate adsorption structures. In the third stage, oxygen-centered local node embeddings extracted from a pretrained UMA model are used to represent the local microenvironment around the ethoxy O atom. These embeddings are grouped via spherical k-means clustering based on cosine similarity to guide representative sampling and visualized within a Uniform Manifold Approximation and Projection (UMAP) latent space^[55] to identify high-hit clusters under the joint *OCH₂CH₃/*CO/*H adsorption-energy windows.

High-hit clusters identified from the local environment space were subjected to spatial neighborhood expansion and cascade thermodynamic filtering, yielding 1,122 structure-level positive candidates, which were further reduced to 1,098 after elemental safety filtering and consolidated into 75 distinct material-level systems. These 75 systems should therefore be regarded as candidates satisfying the imposed late-stage adsorption constraints, while the energetic accessibility of preceding elementary steps requires further pathway-level evaluation. Representative DFT calculations for *OCH₂CH₃, *CO, and *H adsorption benchmarked the screening-level reliability of UMA-predicted binding energies, while SGD identified interpretable elemental rules governing positive-candidate enrichment. Overall, this workflow effectively translates a million-scale generative surface space into a reaction-constrained, physics-informed candidate pool for ethanol-oriented CO₂RR catalyst discovery.

To construct a reaction-anchored surface library for ethanol-oriented CO₂RR discovery, the fine-tuned Transformer model was deployed to generate *OCH₂CH₃ adsorption configurations at the million scale. Among 1,000,000 generated configurations, 999,996 were successfully decoded into atomic structures. After filtering out unphysical geometries with interatomic distances shorter than 0.7 Å or incorrect adsorbate stoichiometry, 839,237 valid *OCH₂CH₃ adsorption systems were retained for downstream analysis [Figure 2A]. The resulting structural library spans 55 elements across the main-group and transition-metal regions, indicating broad compositional coverage of the generated surface space [Figure 2B]. Compared with the elemental distribution of the fine-tuning dataset [Supplementary Figure 1], the generated set largely preserves the learned chemical domain while exhibiting moderate shifts in relative elemental abundance. UMA-derived substrate embeddings further show that the generated structures substantially overlap with the fine-tuning domain while forming a denser, more continuous coverage within the UMAP space [Figure 2C]. This confirms that the generator preserves the learned adsorption-structure domain while enhancing both sampling density and structural diversity.

To organize this million-scale structural space into locally coherent adsorption environments, the oxygen-centered UMA embeddings were partitioned into 2,000 clusters. The resulting clusters generally exhibited high intra-cluster cosine similarity across varying cluster sizes [Supplementary Figure 2]. Five representative structures were then selected from each cluster according to the 0th, 25th, 50th, 75th, and 95th percentiles of cosine similarity, yielding 10,000 representative candidates for downstream UMA evaluations. For each representative *OCH₂CH₃ structure, the corresponding *CO and *H adsorption configurations were constructed at the identical local site and relaxed. Pairwise Spearman correlation analysis revealed that the three adsorption descriptors are only partially coupled, supporting the necessity of joint multi-adsorbate (*OCH₂CH₃/CO/H) screening rather than relying on a single adsorption descriptor [Supplementary Figure 3].

To establish a chemically meaningful candidate region, reference-calibrated adsorption-energy windows were constructed using established CO₂RR-active surfaces including Cu (100), Cu (110), Cu (211), Al-Cu/Cu₂O, and Cu₂Mg (111) as benchmarks [Figure 2D]^[56,57]. The working ranges thus were set to -4.2 eV ≤ ΔE_OCH2CH3 ≤ -3.3 eV and -1.0 eV ≤ ΔE_CO ≤ -0.35 eV, while ΔE_H > -0.2 eV enforced as a first-order gate to exclude overly strong hydrogen binding. These windows are not intended to fully determine ethanol selectivity, but to define a reaction-relevant local surface region for candidate prioritization. Applying the joint *OCH₂CH₃/*CO/*H windows to the 10,000 representative candidates identified high-hit structures in specific regions of the O-centered UMAP space [Figure 2E]. These localized regions were subsequently utilized to define high-hit clusters for downstream spatial neighborhood expansion.

Having identified localized high-hit regions within the oxygen-centered UMAP space, we next utilized these regions to guide neighborhood expansion. Positive structures were not uniformly distributed across the oxygen-centered embedding space, but instead formed localized, candidate-enriched microenvironments. A proximity-resolved analysis further confirmed this spatial enrichment: within clusters containing at least two positive candidates, the hit rate decreased systematically with distance from the nearest positive seed, from 77.4% for the 1-5 nearest neighbors to 62.2% for the 11-20 nearest neighbors and 29.0% beyond the 200th neighbor [Figure 3A]. This distance-dependent decay indicates that the O-centered UMA embedding captures chemically meaningful local similarity. Guided by this non-uniform enrichment pattern, we adopted a cluster-guided expansion strategy. Specifically, all members of clusters containing at least two positive representative structures were included in the expansion pool. For clusters containing only one positive representative, the positive seed and its 20 nearest cluster members, ranked by cosine similarity in the O-centered embedding space, were retained for subsequent UMA-based property evaluation.

The expanded structures were subjected to UMA-based tri-adsorbate evaluation. For each selected *OCH₂CH₃ configuration, the corresponding *CO and *H configurations were constructed at the same oxygen-anchored local site and relaxed using the unified UMA protocol. After applying the joint adsorption-energy windows for *OCH₂CH₃, *CO, and *H, the cluster-guided expansion yielded 1,122 unique positive structures after geometric deduplication [Figure 3B]. Compared with the representative-sampling baseline, the cluster-guided expansion strategy elevated the discovery hit rate from 1.53% to 23.44%, achieving an approximate 15-fold enrichment in candidate discovery efficiency [Figure 3C]. Representative structures further show that the enriched candidates span diverse local adsorption motifs and multicomponent surface environments rather than collapsing into a single structural prototype [Figure 3D].

The joint *OCH₂CH₃/*CO/*H thermodynamic adsorption-energy windows were applied across the expanded structural pool to define the positive candidate space [Figure 4]. Within the *OCH₂CH₃ vs. *CO adsorption-energy landscape, the screened structures span a broad energetic distribution, reflecting the diverse local environments sampled by the generative model. The reference-calibrated windows delimit a moderate-binding region for *OCH₂CH₃ and *CO, while the color-coded *H adsorption energy introduces an additional constraint to exclude structures with overly strong H binding and potentially enhanced HER competition [Figure 4A]. Overlap analysis further shows that the three adsorption descriptors impose complementary rather than redundant constraints. Although each single descriptor selects a relatively broad subset, including 2,399 structures satisfying the *OCH₂CH₃ window, 2,248 satisfying the *CO window, and 3,698 satisfying the *H window, only 1,122 structures simultaneously satisfy all three thermodynamic constraints [Figure 4B]. The adsorption-energy distributions confirm this contraction of the candidate space: after multi-adsorbate filtering, the originally broad generated landscape is narrowed into a chemically constrained region characterized by moderate *OCH₂CH₃ and *CO binding together with weak *H adsorption [Figure 4C].

The resulting positive structures show clear compositional convergence under the joint adsorption constraints. Element-level enrichment analysis identifies Cu as the most strongly enriched element, followed by Al, Ge, Si, Zn, and Pd, suggesting that Cu-centered and compositionally modulated local environments are preferentially selected for balancing oxygenated C₂ retention, CO availability, and suppressed H adsorption [Figure 4D]. Conversely, elements exhibiting enrichment factors (lift values) near or below unity are depleted following tri-adsorbate screening. Compositional breakdown reveals that binary systems remain predominant, shifting only slightly from 75.49% to 74.33% of the candidate pool, whereas unary systems increase markedly from 5.06% to 13.99% and ternary systems decrease from 19.39% to 11.68%. The minor quaternary fraction, accounting for 0.06% before screening, is absent after screening [Figure 4E]. This shift demonstrates that increasing elemental complexity does not inherently guarantee multi-adsorbate thermodynamic compatibility. After excluding systems containing toxic or radioactive elements, the candidate pool was further refined from 1,122 to 1,098 structure-level positive candidates. Overall, multi-adsorbate screening combined with toxicity filtration does not merely reduce candidate counts, but reorganizes the generative surface space into a realistic, high-confidence candidate region for material-level catalyst discovery.

The structure-level positive candidates were further consolidated into material-level systems to map their broad distribution across compositional space [Figure 5]. The binary hit-fraction matrix shows localized hotspots rather than uniform enrichment across all element pairs, with Cu-containing combinations forming the major candidate regions [Figure 5A]. Experimentally validated CO₂RR-active systems, including representative Al-Cu, Cu-Ag, Cu-Zn, and Si-Cu compositions, concentrate squarely within these enriched domains, corroborating the chemical validity of our tri-adsorbate screening framework^[57-67]. Meanwhile, additional high-hit binary combinations suggest that the workflow can extend beyond known CO₂RR material families and identify less-explored Cu-centered composition spaces.

The pseudo-ternary composition map shows that ternary candidates are more dispersed, with only a subset satisfying all three adsorption-energy windows or approaching the target region [Figure 5B]. The experimentally reported Al-Cu-Zn ternary composition space is also recovered, indicating that the workflow can capture known composition families beyond binary systems^[68]. Final 75 materials satisfy the joint *OCH₂CH₃/*CO/*H constraints [Supplementary Table 3], including 13 experimentally reported CO₂RR-related systems and 62 less-explored candidates identified in this work. Material-level ranking identifies Cu as the leading unary candidate, with Al-Cu and Cu-Zn dominating the binary space and several ternary systems also retained [Figure 5C]. Representative unary, binary, and ternary materials are further displayed in Figure 5D. Overall, these results show that the joint adsorption constraints reorganize the generated surface space into interpretable composition regions, recovering key experimental CO₂RR families while uncovering additional candidate spaces for further mechanistic and experimental validation.

To convert the screened candidate set into interpretable materials knowledge, SGD was applied to identify descriptor-defined regions associated with positive-candidate enrichment [Figure 6]. Unlike multiparameter predictive models that establish global descriptor-performance relationships, SGD identifies compact combinations of descriptor conditions that define candidate-enriched subspaces. Feature-correlation analysis shows that the selected descriptors retain complementary elemental information despite partial correlations, allowing SGD to identify compact combinations that are not simply driven by descriptor redundancy [Supplementary Figure 4]. The top-rule regions identified for both binary and ternary systems exhibit substantially higher pass rates than their corresponding baseline populations, indicating that positive candidates can be concentrated within simple elemental-property-defined regions [Figure 6A]. To further quantify the relative importance of individual conditions within each rule, we performed a post hoc Shapley-based condition-attribution analysis using the StandardQF score as the characteristic function [Supplementary Figure 5].

For binary candidates, the top rule identifies 309 positives among 559 structures, corresponding to a pass rate of 55.28% compared with a baseline of 23.08%, yielding an enrichment factor of 2.40. Shapley attribution ranks the Mendeleev-number condition of the first element, 64 ≤ MN1 < 69, as the dominant contributor, followed by the atomic-radius condition of the first element, 1.32 ≤ R1 < 1.45, and the d-valence-electron condition of the second element, Nd2 ≥ 10, with respective contributions to Q of 0.0620, 0.0369, and 0.0277 [Supplementary Figure 5A]. Accordingly, Figure 6B visualizes the binary candidate landscape in the two highest-ranked descriptor dimensions, MN1 and R1, with the top-rule boundaries highlighted. These results suggest that favorable binary environments are primarily associated with a specific Mendeleev-number regime and moderate atomic-size range, while the nearly filled d-shell condition further refines the local chemical environment required to jointly balance *OCH₂CH₃, *CO, and *H adsorption. To provide physical support for the SGD-derived binary rule, representative rule-matching and rule-mismatching systems were further compared at the electronic-structure level. Cu-Pd, which satisfies all three SGD conditions (MN1 = 64, Nd2 = 10, R1 = 1.32), exhibits a balanced adsorption profile for *OCH₂CH₃, *CO, and *H, whereas Tc-Ru, lying outside the descriptor-defined region (MN1 = 53, Nd2 = 7, R1 = 1.47), binds *CO and *H substantially more strongly while providing weaker stabilization of *OCH₂CH₃ resulting in an imbalanced multi-adsorbate profile. In Cu-Pd, the Cu 3d and Pd 4d states are concentrated mainly below the Fermi level, with limited H 1s-metal d-state overlap but appreciable overlap with the C 2p and O 2p states of *CO and *OCH₂CH₃. By contrast, Tc-Ru exhibits broader Tc/Ru d-state distributions near the Fermi level and stronger overlap with H 1s and C 2p states, consistent with its adsorption imbalance. The more localized charge redistribution on Cu-Pd further indicates more moderate adsorbate-metal coupling [Supplementary Figures 6 and 7].

For ternary candidates, the top rule yields a pass rate of 51.11%, compared with a baseline of 14.12%, corresponding to a 3.62-fold enrichment [Figure 6A]. Shapley analysis identifies the group-valence-electron condition of the first element, Nv1 ∈ [3,4), as the most influential contributor, followed by the Mendeleev-number condition of the third element, MN3 ∈ [69,76), and the d-valence-electron condition of the second element, Nd2 ≥ 10, with respective contributions of 0.033, 0.027, and 0.021 to the StandardQF score. Figure 6C therefore visualizes the candidate distribution using Nv1 and MN3, the two highest-ranked conditions, while Nd2 acts as an additional constraint that further enriches the positive region. The recurrence of Nd2 ≥ 10 in both binary and ternary rules points to the broader relevance of filled-d components, whereas the dominant Nv1 and MN3 conditions in ternary systems indicate that the additional compositional degree of freedom is associated with low-valence and chemically tunable elemental components. Together, the SGD and Shapley analyses reveal that candidate enrichment is governed by a hierarchy of complementary elemental descriptors rather than by any single property, providing an interpretable basis for prioritizing composition spaces beyond direct adsorption-energy filtering.

A subsequent synthesizability assessment identified experimental synthesis precedents for 72 of the 75 final candidate systems, with the remaining three evaluated using Materials Project thermodynamic data [Supplementary Tables 4 and 5]. Sc-Pd-Hf shows a high E_hull of 2.925 eV·atom^-1, indicating limited thermodynamic accessibility. The 20-system UMA-DFT benchmark included four experimentally established CO₂RR-to-ethanol reference systems, together with 16 less-explored screened candidates. Representative unary, binary, and ternary systems with feasible compositional motifs were then subjected to DFT calculations and the results were shown in Supplementary Table 6. The UMA and DFT adsorption energies for the reaction anchor (*OCH₂CH₃) display exceptional agreement, yielding a mean absolute error (MAE) of 0.047 eV and a coefficient of determination (R²) of 0.884 across the candidate region [Figure 6D]. Consistent agreement is also obtained for *CO and *H adsorption, with MAEs of 0.029 and 0.024 eV and R² values of 0.922 and 0.959, respectively [Supplementary Figure 8]. Representative optimized structures further illustrate that the selected candidates cover diverse unary, binary, and ternary local adsorption environments, rather than collapsing into a single structural prototype [Figure 6E and Supplementary Figures 9-11]. Because CO-CO coupling is a key C-C bond-forming step toward C₂ products in CO₂RR^[7], we first evaluated the reaction energy difference between the initial and final states for five representative systems, using Cu as a reference. Cu-Pd-Sn exhibited a substantially higher reaction energy and was therefore excluded from further kinetic analysis [Supplementary Table 7]. Activation barriers were subsequently calculated for Ga-Pt, Sc-Cu-Ga, Al-Cu-Pd, and Cu [Figure 7 and Supplementary Figure 12]. The resulting barriers are 0.613, 1.478, 0.995, and 1.172 eV, respectively. Notably, both Ga-Pt and Al-Cu-Pd exhibit lower barriers than Cu, indicating more favorable CO-CO coupling kinetics. These results provide an additional kinetic criterion for refining the thermodynamically screened candidates. Together, these results demonstrate that the workflow not only identifies candidate surfaces but also extracts interpretable composition rules and provides first-principles validation for representative adsorption environments. The present work establishes a uniform high-throughput thermodynamic screening framework under solvent-free conditions, while solvent, mass-transport, particle-aggregation, and other electrochemical environmental effects will be considered in future validation and refinement under realistic catalyst and electrode conditions.