A current challenge in atomistic machine learning is that of efficiently predicting the response of the electron density under electric fields. We address this challenge with symmetry-adapted kernel functions that are specifically derived to account for the rotational symmetry of a three-dimensional vector field. We demonstrate the equivariance of the method on a set of rotated water molecules and show its high efficiency with respect to number of training configurations and features for liquid water and naphthalene crystals. We conclude showcasing applications for relaxed configurations of gold nanoparticles, reproducing the scaling law of the electronic polarizability with size, up to systems with more than 2000 atoms. By deriving a natural extension to equivariant learning models of the electron density, our method provides an accurate and inexpensive strategy to predict the electrostatic response of molecules and materials.

Heterostructuring nanocrystals into a modular metal-semiconductor configuration enables tunable and novel functionalities. Such combinations at the nanoscale equip hybrid structures with unique electronic, optical, and catalytic properties unobserved in single-phase materials. Here, we report the hot-injection synthesis of Pd-Cu3Pd13S6.65Te0.35 nanoheterostructures (NHCs) from PdCu nanoalloy seeds. First, the growth of Pd-rich chalcogenide nanocrystals was initiated over the preformed PdCu surface through simultaneous sulfidation and tellurization, followed by their transformation into Pd-Cu3Pd13S6.65Te0.35 NHCs. By strategically employing moderate-temperature annealing, we achieved the complete migration of Cu+ due to the higher reactivity of Cu in comparison to Pd at that temperature, establishing a novel mechanistic relationship between cation mobility and temperature. This strategy enables controlled semiconductor domain formation and targeted metal migration. The NHCs showed efficient and stable electrocatalytic hydrogen evolution with low Tafel values in acidic media, outperforming conventional nanoelectrocatalysts. Computational analysis identified the active sites responsible for the observed catalytic performance.

In committee of experts strategies, small datasets are extracted from a larger one and utilised for the training of multiple models. These models' predictions are then carefully weighted so as to obtain estimates which are dominated by the model(s) that are most informed in each domain of the data manifold. Here, we show how this divide-and-conquer philosophy provides an avenue in the making of machine learning potentials for atomistic systems, which is general across systems of different natures and efficiently scalable by construction. We benchmark this approach on various datasets and demonstrate that divide-and-conquer linear potentials are more accurate than their single model counterparts, while incurring little to no extra computational cost.