Electrolysis of water to produce hydrogen (H) can solve the current energy crisis and environmental problems. However, efficient hydrogen evolution reaction (HER) catalysts are still limited to a few noble metals, thus prohibiting their broad applications. Herein, first-principles calculations were carried out to investigate the theoretical HER performances of a series of N-doped graphenes containing inexpensive single- and dual-metal atoms. Among them, MN₄-gra (M = Fe, Co, Ni), homonuclear MMN₆-gra, and heteronuclear M1M2N₆-gra mostly exhibit low HER activities due to the weak H adsorption, and only CoN₄-gra, NiNiN₆-gra, and CoNiN₆-gra show better ΔG_*H values of 0.19, 0.15 and 0.27 eV, respectively. In contrast, low-coordinated MMN₅-gra and M1M2N₅-gra both have rather high HER activities. In particular, the ΔG_*H values of FeNiN₅-gra and CoNiN₅-gra are as low as -0.04 and -0.06 eV, respectively, very close to the ideal 0 eV. Detailed analyses reveal that such high activity mainly stems from the reduced metal coordination and the synergistic effect between the two metals, which greatly enhance the adsorption ability of the active center. More interestingly, the strong H adsorption of MMN₅-gra/M1M2N₅-gra could enable them to further adsorb a second H atom and generate a stable HMH intermediate to yield the final product H₂. Under this novel mechanism, the two-step |ΔG_*H| values of FeNiN₅-gra and CoNiN₅-gra are all no more than 0.10 eV. Our work not only discloses the important effect of coordination regulation and site synergy on enhancing the catalytic activity but also finds a new HER path on the metal-embedded N-doped graphenes.

While crystal structure prediction (CSP) remains a longstanding challenge, we introduce ParetoCSP, a novel algorithm for CSP, which combines a multi-objective genetic algorithm (GA) with a neural network inter-atomic potential model to find energetically optimal crystal structures given chemical compositions. We enhance the updated multi-objective GA (NSGA-III) by incorporating the genotypic age as an independent optimization criterion and employ the M3GNet universal inter-atomic potential to guide the GA search. Compared to GN-OA, a state-of-the-art neural potential-based CSP algorithm, ParetoCSP demonstrated significantly better predictive capabilities, outperforming by a factor of 2.562 across 55 diverse benchmark structures, as evaluated by seven performance metrics. Trajectory analysis of the traversed structures of all algorithms shows that ParetoCSP generated more valid structures than other algorithms, which helped guide the GA to search more effectively for the optimal structures. Our implementation code is available at https://github.com/sadmanomee/ParetoCSP.

In order to efficiently explore the chemical space of all possible small molecules, a common approach is to compress the dimension of the system to facilitate downstream machine learning tasks. Towards this end, we present a data-driven approach for clustering potential energy landscapes of molecular structures by applying recently developed Network Embedding techniques to obtain latent variables defined through the embedding function. To scale up the method, we also incorporate an entropy sensitive adaptive scheme for hierarchical sampling of the energy landscape, based on Metadynamics and Transition Path Theory. Taking into account the kinetic information implied by the energy landscape of a system, we can interpret dynamical node-node relationships in reduced dimensions. We demonstrate the framework through Lennard-Jones clusters and a human DNA sequence.

Machine learning (ML) models in materials science are mainly developed for predicting global properties, such as formation energy, band gap, and elastic modulus. Thus, these models usually fall short in describing local characteristics, such as molecular adsorption on surfaces. Here, we introduce a local environment interaction-based ML framework that contains a modified graph-based Voronoi tessellation geometrical representation, improved fingerprint feature engineering, and traditional ML and advanced deep learning (DL) algorithms. The precise characterization can be extracted using this framework for representing local information of adsorption of molecules on a surface. Using both traditional ML and advanced DL algorithms, we demonstrate remarkable prediction accuracy and robustness on 0D, two-dimensional (2D), and three-dimensional (3D) catalysts. Furthermore, it is found that the employment of this approach reduces data requirements and augments computational speed, specifically for DL algorithms. This work provides an effective and universal ML framework for various applications of molecular adsorption from catalysis, sensors, carbon capture, and energy storage to drug delivery, signifying a novel and promising avenue in the field of materials informatics. The implementation code in this work is available at https://github.com/mpeshel/LEI-framework_LERN.