🔬 materials science

OxiGen: Oxidation-State-Aware Crystal Generation

OxiGen is a novel oxidation-state-aware crystal diffusion model that explicitly incorporates oxidation states and enforces global charge neutrality through a structured output layer, thereby significantly improving the generation of stable, unique, and experimentally realizable inorganic materials compared to existing methods.

Original authors: Dylan John, Kim E. Jelfs, Alex M. Ganose, Eleonora Giunchiglia

Published 2026-10-07

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CC BY 4.0

Original authors: Dylan John, Kim E. Jelfs, Alex M. Ganose, Eleonora Giunchiglia

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The search for new materials is a fundamental engine of modern technology, driving the development of better batteries, more efficient solar panels, and powerful catalysts. For decades, scientists have relied on trial and error or the slow sifting of existing databases to find these substances. Recently, artificial intelligence has offered a faster path: instead of searching through what already exists, generative models can imagine entirely new crystal structures from scratch, a process known as inverse design. However, there is a catch. While these computer programs are excellent at creating shapes that look like crystals, they often fail to create ones that could actually exist in a laboratory. The problem lies in the invisible rules of chemistry that govern how atoms stick together. Specifically, every atom in a crystal carries a specific electrical charge, known as an oxidation state. For a crystal to be stable and real, the sum of all these charges must balance out perfectly to zero. If the charges do not cancel each other out, the material is chemically impossible, no matter how beautiful its structure looks on a screen.

A team of researchers at Imperial College London has developed a new artificial intelligence system called OxiGen to solve this specific problem. Previous AI models for crystal generation treated atoms merely as types of elements, like carbon or oxygen, and only checked if the final result balanced its charges as an afterthought. This approach often led the AI to invent materials that required extremely rare or impossible charge combinations to work, rendering them useless for real-world use. OxiGen changes this by teaching the AI to think about the charge of every single atom while it is building the crystal. Instead of guessing the element first and fixing the charge later, the model generates a specific "species" for each spot in the crystal, which includes both the element and its exact electrical charge. This ensures that the AI is always aware of the electrical balance it needs to maintain.

To make sure the charges always add up to zero, the researchers built a special mathematical filter into the AI's decision-making process. Imagine the AI is filling a long row of slots with different atoms. As it places each one, it keeps a running total of the electrical charge. The new system uses a structured method to check every possible combination of atoms it could choose next, ensuring that the final total will always be zero before it even commits to a choice. This is not a random guess; it is a precise calculation that guarantees the final result is chemically valid. The researchers tested this system against several other leading AI models using a large database of known crystal structures. They found that OxiGen was far superior at creating crystals that matched the real-world patterns of how charges are distributed. While other models often produced materials that required rare, unlikely charge states to balance, OxiGen consistently generated crystals with the common, stable charge combinations found in nature.

The results showed that OxiGen did not just produce chemically valid materials; it produced better ones overall. When the team asked the AI to generate thousands of new crystals, OxiGen created a higher percentage of structures that were stable, unique, and truly novel compared to any other method tested. Even when the researchers asked the AI to design crystals with specific properties, such as a particular ability to conduct electricity or a specific color, OxiGen maintained its high level of chemical validity. Other models tended to break the rules of chemistry when pushed to meet these specific targets, creating impossible materials. OxiGen, however, stayed grounded in chemical reality. The study suggests that by explicitly teaching artificial intelligence the fundamental rules of electrical balance, researchers can guide these powerful tools to discover materials that are not just mathematically interesting, but actually realizable in a lab. This approach offers a promising path forward for accelerating the discovery of the next generation of sustainable technologies.

=== SUMMARY ===

Technical Summary: OxiGen – Oxidation-State-Aware Crystal Generation

Problem Statement

Generative models offer a pathway to accelerate inorganic materials discovery through inverse design, yet generating experimentally realizable crystals remains a significant challenge. While existing crystal generative models can produce charge-neutral structures, they often fail to reproduce the distributions of oxidation states observed in synthesised materials. Many generated crystals rely on rare or chemically improbable oxidation states to satisfy charge neutrality, a limitation not always captured by standard stability metrics like energy above the convex hull. Consequently, these models may generate structures that are theoretically stable but chemically implausible or difficult to synthesize. The core problem is the lack of explicit representation and enforcement of oxidation-state frequencies and global charge neutrality within the generative process.

Methodology

The authors propose OxiGen, a crystal diffusion model that explicitly represents oxidation states during generation and enforces charge neutrality by construction.

1. Species Representation

Unlike previous models that generate element identities ( $A$ ) and infer oxidation states implicitly, OxiGen generates species ( $S$ ), defined as element–oxidation-state pairs $(a, z)$ . The crystal is represented as $M = (S, F, L)$ , where $F$ are fractional coordinates and $L$ is the lattice matrix. The vocabulary $S$ consists of species observed in synthesised materials. This explicit representation allows the model to learn oxidation-state frequencies directly from the training data.

2. Structured Inference via Finite-State Automaton

A critical challenge in generating species is ensuring the global constraint that the sum of oxidation states equals zero (charge neutrality). Independent sampling from site-wise distributions often violates this constraint. To address this, OxiGen introduces a structured output layer that performs exact inference over a finite-state automaton (FSA).

FSA Formulation: The charge-neutrality constraint is modeled as an additive process where the state represents the cumulative charge. Valid assignments correspond to paths from an initial state (charge 0) to an accepting state (charge 0) after $N$ sites.
Dynamic Programming: The model employs a forward–backward algorithm (adapted from Hidden Markov Models) to compute exact marginal probabilities and perform Maximum A Posteriori (MAP) decoding under the constraint.
- Forward Pass: Computes the probability mass of all prefixes ending with a specific cumulative charge.
- Backward Pass: Computes the probability mass of suffixes that complete a given cumulative charge to zero.
Sampling: During the reverse diffusion step, OxiGen samples a complete, charge-neutral species assignment $\hat{S}_0$ from the structured distribution $\tilde{p}_\theta(S_0 | M_t, t)$ using the computed backward weights. This ensures that every generated crystal satisfies charge neutrality by construction, without requiring post-hoc filtering.

3. Model Architecture

OxiGen builds upon the MatterGen architecture, an SE(3)-equivariant graph neural network. It retains the continuous diffusion processes for fractional coordinates and lattice matrices but modifies the discrete diffusion process for species. It uses an absorbing-state discrete diffusion process (based on MDLM) where sites are masked and then denoised. The structured output layer is applied during sampling, while the standard factorised masked-diffusion objective is used for training (though a structured training objective was explored in ablation studies).

Key Contributions

Structured Output Layer: The development of a layer that uses dynamic programming over a finite-state automaton to perform exact charge-neutral inference for discrete diffusion models.
OxiGen Model: The introduction of a crystal diffusion model that explicitly generates species (element + oxidation state) and enforces global charge neutrality during the sampling process.
Empirical Validation: Demonstration that OxiGen substantially improves oxidation-state fidelity, generates a higher rate of stable, unique, and novel crystals compared to baselines, and maintains high compositional validity even under property conditioning.

Results

The authors evaluated OxiGen on the MP-20-OS dataset (a subset of the Materials Project with oxidation-state labels) against five strong baselines: DiffCSP, MatterGen, FlowMM, OMatG, and Crystalite.

Oxidation-State Fidelity: OxiGen achieved the highest Oxidation-State Frequency Score ( $f_{OS}$ ) (90.65%) and the lowest Oxidation-State Distribution Distance ( $d_{OS}$ ) (0.0911) among all methods. It closely matched the test-set distributions of common oxidation states, whereas baselines relied more heavily on uncommon states.
Stability and Novelty: OxiGen generated the highest rate of Stable, Unique, and Novel (S.U.N.) crystals (26.38%), outperforming all baselines. It also achieved the lowest relaxation RMSD (0.1679 Å), indicating high structural fidelity.
Conditional Generation: In band-gap conditioned generation experiments, OxiGen maintained consistently high compositional validity across target band gaps (1–7 eV), whereas baselines like MatterGen saw a sharp decline in validity as targets moved away from the training distribution.
Ablation Studies: Removing the structured output layer resulted in a significant drop in charge neutrality (from 100% to ~39%) and oxidation-state fidelity. Using species representation alone provided only modest improvements, highlighting the necessity of the structured inference layer.

Significance and Claims

The paper claims that OxiGen demonstrates how incorporating prior chemical knowledge—specifically through simple heuristics like charge neutrality and observed oxidation-state frequencies—can guide generative models toward more chemically plausible materials. By explicitly representing oxidation states and enforcing constraints via structured inference, the model bridges the gap between theoretical stability and experimental realizability.

The authors note that their approach requires only minimal modification to existing diffusion model architectures, suggesting it could be readily integrated into other crystal generative models. They position OxiGen as a step toward more reliable inverse design, where generated candidates are not only stable but also chemically valid according to established rules of inorganic chemistry.

Limitations Acknowledged:
The authors explicitly state that OxiGen inherits the limitations of formal integer oxidation states, which may be ambiguous or undefined for systems with substantial covalency, charge delocalization, or metallic bonding. Additionally, the model relies on oxidation-state assignments inferred by their predictor, which may contain errors. The method currently enforces charge neutrality but does not yet enforce other constraints like electronegativity balance or local coordination consistency.