The Kohn-Sham equations underlie many important applications such as the discovery of new catalysts.

The Kohn-Sham equations underlie many important applications such as the discovery of new catalysts. Recent machine learning work on catalyst modeling has focused on prediction of the energy, but has so far not yet demonstrated significant out-of-distribution generalization. Here we investigate another approach based on the pointwise learning of the Kohn-Sham charge-density. On a new dataset of bulk catalysts with charge densities, we show density models can generalize to new structures with combinations of elements not seen at train time, a form of combinatorial generalization. We show that over 80% of binary and ternary test cases achieve faster convergence than standard baselines in Density Functional Theory, amounting to an average reduction of 13% in the number of iterations required to reach convergence, which may be of independent interest. Our results suggest that density learning is a viable alternative, trading greater inference costs for a step towards combinatorial generalization, a key property for applications.

Chemical reaction mechanisms provide crucial insight into synthesizability, yet current Computer-Assisted Synthesis Planning (CASP) systems lack mechanistic grounding. We introduce a computational framework for teaching language models to predict chemical reaction mechanisms through arrow pushing formalism, a century-old notation that tracks electron flow while respecting conservation laws. We developed MechSMILES, a compact textual format encoding molecular structure and electron flow, and trained language models on four mechanism prediction tasks of increasing complexity using mechanistic reaction datasets, such as mech-USPTO-31k and FlowER. Our models achieve more than 95\% top-3 accuracy on elementary step prediction and scores that surpass 73\% on mech-USPTO-31k, and 93\% on FlowER dataset for the retrieval of complete reaction mechanisms on our hardest task. This mechanistic understanding enables three key applications. First, our models serve as post-hoc validators for CASP systems, filtering chemically implausible transformations. Second, they enable holistic atom-to-atom mapping that tracks all atoms, including hydrogens. Third, they extract catalyst-aware reaction templates that distinguish recycled catalysts from spectator species. By grounding predictions in physically meaningful electron moves that ensure conservation of mass and charge, this work provides a pathway toward more explainable and chemically valid computational synthesis planning, while providing an architecture-agnostic framework for the benchmarking of mechanism prediction.

Specifically, we extend the Catalyst approach originally designed for deterministic objectives to the stochastic setting.

We thank the reviewers for their insightful comments and respond to their concerns and questions below. We thank the reviewers for noting a few problems with Figure 1. Note that the norms are indeed Euclidean. All algorithms are implemented in C++ in the file utils/svm.h Addressing non-convex problems would be very interesting, but beyond the scope of our paper.

We thank reviewers for useful comments. LCPP is different from proximal point as it uses proximal point in the objective and convexification in constraint. It is unclear whether these subsets will be algorithmically well behaved, i.e., the optimal Lagrange multiplier for such constraints will be small. Figure 1: (a)-(e) SCAD constrained optimization. We can always improve the language as pointed out by the reviewer.

We got a sneak peek inside Found Energy's lab, just as it gears up to supply heat and hydrogen to its first customer. The crushed-up soda can disappears in a cloud of steam and--though it's not visible--hydrogen gas. "I can just keep this reaction going by adding more water," says Peter Godart, squirting some into the steaming beaker. "This is room-temperature water, and it's immediately boiling. Doing this on your stove would be slower than this." Godart is the founder and CEO of Found Energy, a startup in Boston that aims to harness the energy in scraps of aluminum metal to power industrial processes without fossil fuels.

The conversion of $\mathrm{CO_2}$ into useful products such as methanol is a key strategy for abating climate change and our dependence on fossil fuels. Developing new catalysts for this process is costly and time-consuming and can thus benefit from computational exploration of possible active sites. However, this is complicated by the complexity of the materials and reaction networks. Here, we present a workflow for exploring transition states of elementary reaction steps at inverse catalysts, which is based on the training of a neural network-based machine learning interatomic potential. We focus on the crucial formate intermediate and its formation over nanoclusters of indium oxide supported on Cu(111). The speedup compared to an approach purely based on density functional theory allows us to probe a wide variety of active sites found at nanoclusters of different sizes and stoichiometries. Analysis of the obtained set of transition state geometries reveals different structure--activity trends at the edge or interior of the nanoclusters. Furthermore, the identified geometries allow for the breaking of linear scaling relations, which could be a key underlying reason for the excellent catalytic performance of inverse catalysts observed in experiments.

Efficient and inexpensive energy storage is essential for accelerating the adoption of renewable energy and ensuring a stable supply, despite fluctuations in sources such as wind and solar. Electrocatalysts play a key role in hydrogen energy storage (HES), allowing the energy to be stored as hydrogen. However, the development of affordable and high-performance catalysts for this process remains a significant challenge. We introduce Catalyst GFlowNet, a generative model that leverages machine learning-based predictors of formation and adsorption energy to design crystal surfaces that act as efficient catalysts. We demonstrate the performance of the model through a proof-of-concept application to the hydrogen evolution reaction, a key reaction in HES, for which we successfully identified platinum as the most efficient known catalyst. In future work, we aim to extend this approach to the oxygen evolution reaction, where current optimal catalysts are expensive metal oxides, and open the search space to discover new materials. This generative modeling framework offers a promising pathway for accelerating the search for novel and efficient catalysts.