cond-mat.mtrl-sciMar 20, 2026
SaveA chemical language model for reticular materials design
Organizations: Department of Chemical Engineering & Biotechnology, University of Cambridge, Cambridge, UK · Department of Chemistry, University of California – Berkeley, Berkeley, CA, USA · Bakar Institute of Digital Materials for the Planet, Berkeley, CA, USA · KACST–UC Berkeley Center of Excellence for Nanomaterials for Clean Energy Applications, King Abdulaziz City for Science and Technology, Riyadh, Saudi Arabia ·
Abstract
Reticular chemistry has enabled the synthesis of tens of thousands of metal-organic frameworks (MOFs), yet the discovery of new materials still relies largely on intuition-driven linker design and iterative experimentation. As a result, researchers explore only a small fraction of the vast chemical space accessible to reticular materials, limiting the systematic discovery of frameworks with targeted properties. Here, we introduce Nexerra-R1, a building-block chemical language model that enables inverse design in reticular chemistry through the targeted generation of organic linkers. Rather than generating complete frameworks directly, Nexerra-R1 operates at the level of molecular building blocks, preserving the modular logic that underpins reticular synthesis. The model supports both unconstrained generation of low-connectivity linkers and scaffold-constrained design of symmetric multidentate motifs compatible with predefined nodes and topologies. We further combine linker generation with flow-guided distributional targeting to steer the generative process toward application-relevant objectives while maintaining chemical validity and assembly feasibility. The generated linkers are subsequently assembled into three-dimensional frameworks and are structurally optimized to produce candidate materials compatible with experimental synthesis. Using Nexerra-R1, we validate this strategy by rediscovering known MOFs and by proposing the experimental synthesis of a previously unreported framework, CU-525, generated entirely in silico. Together, these results establish a general inverse-design paradigm for reticular materials in which controllable chemical language modelling enables the direct translation from computational design to synthesizable frameworks.
Figures & tables
Figure 1: Inverse reticular chemistry with Nexerra R1 . a. MOF structures are represented as nets made of nodes and edges. As a first step, we decouple the design process at the building block level. b. Linkers are encoded as molecular strings (SELFIES) and tokenized into a sequence of symbols. Each token acts as a structural unit that is processed by the model. c. The VAE acts as a bottleneck wherein the encoder defines an approximate posterior over a low-dimensional, continuous latent variable (z), while the decoder reconstructs the original sequence from z. d. Nucleus sampling is used to generate new linkers from the decoder output. e. Subject to the synthetic feasibility of the designed linker, an attempt is made to assemble it into the target net. (A detailed theoretical description of the model is available in Supplementary Information Section B . Supplementary Information Figure B.1 describes the encoder and decoder neural networks. Colour code: Polyhedron - Cu 2 ( - COO) 4 ; Gray - C; Red - O; Blue - N; Yellow - S; White - H; Purple - metal-linker coordination motif).
Figure 2: Linker design. a. Nexerra R1 enables inference in two modes: direct design and scaffold-constrained design. In direct design, Nexerra R1 fully maps the seed to new linkers while in scaffold-constrained design, the scaffold is fixed, and the model generates new arms that are symmetrically grafted to the core. b. Using MOF-5 as a design template, Nexerra R1 generates a library of linkers which are the filtered and scored by a reward function (R). are 6 representative MOFs that were successfully assembled with the Zr 4 O node on the pcu net. c. Using PCN-222 as a design template, are 4 representative MOFs that were assembled with the Zr 6 -oxo node. Since several topologies can be targeted (depending on geometric and topological constraints), we were able to successfully assemble candidates into the 8-connected csq net and the 12-connected ftw net. d. assembled on a ftw net was experimentally synthesized as CU-525. (Colour code: Polyhedron (Purple) – Zn 4 O(COO) 6 ; Polyhedron (Blue) – Zr 6 ( -O) 4 ( -OH) 4 (COO) 8 (OH/H 2 O) 4 ; Gray - C; Red - O; Blue - N; Yellow - S; White - H)
Figure 3: Flow-guided design. a. Nexerra R1 -Flow learns a vector field that transports latent samples from a base distribution to a target distribution under the formulation of optimal-transport conditional flow matching (a detailed theoretical description of the model is available in Supplementary Information Section I.1 ). b. Linker span distributions of molecules sampled from the training dataset (n = 10,000), Nexerra R1 (n = 10,000) and Nexerra R1 -Flow (n = 10,000). The typical generated linker from Nexerra R1 -Flow is 2.4 Å longer compared to the training dataset and 1.7 Å longer compared to Nexerra R1 . c. Using 1,4-benzenedicarboxylic acid as the seed, Nexerra R1 -Flow generates several optimal linkers with a longer span; the best-ranked linker has a span of 10.63 Å which is 1.8 the span of the seed. The corresponding generated structures are presented in Supplementary Information Section I.4 .
Figure 4: Flow-guided inverse design of UiO-66 analogues for methane storage. Gravimetric versus volumetric methane uptake at 298 K and 80 bar calculated using GCMC simulations for fcu frameworks assembled from Nexerra R1 -Flow designed linkers (BDC seed). Several candidates simultaneously exceed UiO-66 in both volumetric and gravimetric uptake. The distributional steering achived by Nexerra R1 -Flow enables concurrent improvements in storage performance as shown in the darker shaded region. Insets show representative high-performing optimized structures. (Colour code: Polyhedron – Zr 6 ( -O) 4 ( -OH) 4 (COO) 12 ; Gray - C; Red - O; Blue - N; Yellow - S; White - H)
Supplementary Figure B.1. Nexerra R1 architecture. a. MOF structures are represented as nodes and edges. As a first step, we decouple the design process at the building-block level. b. Linkers are encoded as molecular strings and tokenized into a sequence of symbols. c. The encoder network of the model is composed of a stack of transformer layers that map tokenized vectors in one representation space into a corresponding set of vectors in a new space, and by doing so, learn a rich internal representation. The dataset ( = number of tokens; = number of samples) is first embedded and subsequently undergoes position encoding (PE) to capture sequence order. This embedded tensor is then passed to the transformer stack which applies the self-attention mechanism to capture long-range interactions. d. The VAE acts as a bottleneck wherein the encoder defines an approximate posterior over a low-dimensional continuous latent variable ( ), while the decoder reconstructs the original sequence from . e The decoder is again composed of a stack of transformer layers that projects the latent representation back into high-dimensional data and outputs logits of the vocabulary size (vocab). Here we implement masked self-attention to prevent the decoder from seeing future tokens during training. We condition it on the latent variable using cross-attention. f. Nucleus sampling is used to generate new linkers from the decoder output. g. Subject to chemical validity, an attempt is made to assemble the new linker into the target net (Color code: Polyhedron - Cu 2 ( -COO 4 ); Gray - C; Red - O; Blue - N; Yellow - S; White - H; Purple - [Lr])
Supplementary Figure C.1 List of fragments used to randomly functionalize linkers to expand the training corpus
Algorithm 1 Dataset generation
Supplementary Figure C.2 Distributions of molecular properties – (from left to right) heavy atom count, logP, SCScore, rotatable bond count and molecular weight – for the extended dataset (n = 200,000 sampled randomly from a total 898,677 molecules). Note: The steep cliff observed in the SCScore distribution at large values is because we have filtered values exceeding 4.75 during the functionalization process.
Supplementary Figure C.3 UMAP visualization of the training corpus (n = 50,000, Morgan fingerprints, radius 2, 2048 bits). Colored by (left-right) logP, molecular weight and rotatable bond counts. Note: The colors have been normalized for each property class.
Supplementary Figure C.4 The 50 most commonly observed Murcko scaffolds from the training dataset accounting for 30% of the entire corpus. Ranked in decreasing order of prevalence from left-right, top-bottom.
Supplementary Figure D.1 . The training logs measured over 172 epochs indicate stable training. (First row, left to right): Total loss, reconstruction loss and KL loss. (Second row: left to right): Per-token reconstruction accuracy, internal diversity of sampled molecules and novelty of sampled molecules (n = 5000).
Supplementary Figure D.2 . Distributions for (left to right) logP, fraction Csp 3 and TPSA for generated molecules (n = 10,000) and a non-redundant subset of the test set (n = 10,000). The annotated text represents the KL divergence between the two distributions. A KL divergence of 0.0 would indicate a perfect match (the ideal case).
Supplementary Figure D.3 . UMAP visualization of the latent embeddings of training molecules (gray, n = 50,000) and generated molecules (red, n = 49,950). The generated samples closely overlap the training manifold, although, there is mild clustering of generated molecules in some pockets. Additionally, there are no major pockets outside the training manifold, suggesting that sampling remains within the learned latent space.
Supplementary Figure D.4 . Illustrative examples of molecules sampled freely from the prior of Nexerra R1 . The model is able to generate multi-functional, complex molecules with polyaromatic cores and dense substitution patterns. However, owing to the high expressivity of the CLM, under unconstrained sampling, the ‘hit rate’ for desirable linkers is low. Thus, seed-guided design serves as a more optimal route towards the discovery of exceptional linkers.
Supplementary Figure E.1 . Starting with a generated linker, it is stripped out its ‘[Lr]’ handles, and optimised. Next, we collect a set of candidate attachment sites (described above) and select those sites which maximise the spatial separation between anchor points. We append the required ‘[Lr]’ handles to these selected sites. This workflow is in principle, agnostic to the number of handles.
Supplementary Figure F.1 a .Distribution of the mass-normalized span for molecules from the training set (n = 25,000). Median = 0.02 Å mol g -1 ; p75 = 0.03 Å mol g -1 and p25 = 0.01 Å mol g -1 . The increasing sigmoidal desirability function is centred around p75, with a width of 0.5 (p75 – p25) to favour linkers with favourable mass-normalized spans. b. Distribution of the gravimetric reward score ( ) for molecules from the training set (n = 25,000). Median = 0.52; p75 = 0.58 and p25 = 0.43. Notably, the distribution is not skewed towards either extreme bound – which would have been indicative of collapse. The distribution spans almost the entire range and we also observe a smooth gradient towards higher scores, suggesting that a non-trivial fraction of the training linkers achieve high scores [ .
Supplementary Figure F.2. scores for linkers belong to top-performing MOFs for gravimetric CH 4 storage. The ranking of benchmark linkers is broadly consistent with reported trends. However, for a complete assessment, it is crucial to account for metal-node effects, topology and volumetric packing. As an illustrative example, while MOF-519 and MOF-520 share the same linker, they differ in coordination environments that in-turn have a significant impact on storage capacities.
Supplementary Figure F.3 a . Distribution of the molecular weight of molecules from the training dataset (n = 50,000). The distribution follows an expected trend with a mode around 250 g mol -1 , median of 312 g mol -1 and a long tail that extends past 1250 g mol -1 . Ideal linkers for gas storage should adopt intermediate molecular weights – i.e., not too light to favor low framework densities yet not too heavy to favor high densities. We thus define a Gaussian desirability function (centered around 320 g mol -1 ) with a width of 140 g mol -1 that rewards these intermediate values while penalizing extremes. b. Distribution of the (n = 50,000) and c. scores (n = 25,000) of molecules from the training dataset. has a strong bimodal distribution suggesting the partitioning of the linker space into two classes: linkers with sub-optimal symmetry and linkers with optimal symmetry. Only 1.6% of the linkers attain the maximum . For , the distribution is broad (median = 0.43) with a weak bimodal character. Neither extreme is saturated – confirming that there is no collapse. The weak bimodal character stems from the partitioning of the linker space described above. Here, the smaller class indicates more favorable symmetry and rigidity yet having a reasonable span and molecular weight.
Supplementary Figure F.4 . scores for linkers belong to top-performing MOFs for CH 4 storage. There is a reasonable correlation between the score assigned to the linker and the reported gravimetric and volumetric storage capacities of the MOF. However, for a complete assessment, it is crucial to account for metal-node effects, topology and volumetric packing.
Supplementary Figure F.5. a. Distribution of the scores of linkers from the training set (n = 25,000) of which 93.76% produced valid scores after invalid SMILES cleaning/parsing. The total score distribution remains broad (with median = 0.469), indicating non-collapsed ranking capacity for molecular optimization. b - e. Distributions of individual components scores for b. safety (S); c. performance (P); d. benign-linker score (B) and e. stability (T). Each of these distributions is also non-collapsed to either extreme. We further impose rigid constraints during the design process, such as rejecting molecules with safety scores .
Supplementary Figure G.1 . Direct design mode applied to different classes of bidentate MOF linkers. The seeds are highlighted in yellow.
Supplementary Figure G.2 . Scaffold-constrained design mode applied to the porphyrin-core.
Supplementary Figure H.1 . The porphyrin linker designed using Nexerra R1 (left) and the linker ( L ) used for the synthesis of CU-525
| CU-525 (CCDC: 2514566) | |
|---|---|
| Formula | C 38.67 H 54.67 HfN 7.33 O 5.33 Zn 0.5 |
| F.W. (g mol -1 ) | 918.73 |
| Temperature/K | 100 |
| Wavelength/Å | Synchrotron ( ) |
| Crystal system | Cubic |
| Space group | Pm-3m |
Supplementary Table H.1 . Crystal data and structure refinement for CU-525
Supplementary Figure H.2 . (Top) Optimized structural model of -11 (left) compared to the structure of CU-525 resolved using SCXRD as described above. We note that the MOF assembly algorithm flips the placement of the arm in certain instances leading to conformation deviations from the experimentally resolved structure. (Bottom) Simulated PXRD patterns of -11 (red) and CU-525 (blue). Please note that the patterns have been max-normalized.
Supplementary Figure I.1. (Left to right). rRMSE of predicted and target latent displacement; mean-cosine similarity between the predicted and target latent displacements; median anchor – anchor span for n = 5000 sampled molecules from the model checkpoint. Please note: during training the target is monotonically increased from the 70 th percentile to the 95 th percentile – i.e., the training gets progressively harder as the steps increase, which reflects in the growing rRMSE and dropping cosine.
Supplementary Figure I.2. A subset of linkers generated by Nexerra R1 -Flow using a BDC seed (yellow). These linkers were selected post-filtering for geometric compatibility with the fcu net. The linker highlighted in pink is a rediscovery of the input seed.
Supplementary Figure I.3. A subset of optimized structures assembled on the fcu net from linkers generated from Nexerra R1 -Flow.