Having access to accurate electron densities in chemical systems, especially for dynamical systems involving chemical reactions, ion transport, and other charge transfer processes, is crucial for numerous applications in materials chemistry. Traditional methods for computationally predicting electron density data for such systems include quantum mechanical (QM) techniques, such as density functional theory. However, poor scaling of these QM methods restricts their use to relatively small system sizes and short dynamic time scales. To overcome this limitation, we have developed a deep neural network machine learning formalism, which we call deep charge density prediction (DeepCDP), for predicting charge densities by only using atomic positions for molecules and condensed phase (periodic) systems. Our method uses the weighted smooth overlap of atomic positions to fingerprint environments on a grid-point basis and map it to electron density data generated from QM simulations. We trained models for bulk systems of copper, LiF, and silicon; for a molecular system, water; and for two-dimensional charged and uncharged systems, hydroxyl-functionalized graphane, with and without an added proton. We showed that DeepCDP achieves prediction $R^2$ values greater than 0.99 and mean squared error values on the order of ${10}^{-5}$$e^2$ Å${}^{-6}$ for most systems. DeepCDP scales linearly with system size, is highly parallelizable, and is capable of accurately predicting the excess charge in protonated hydroxyl-functionalized graphane. We demonstrate how DeepCDP can be used to accurately track the location of charges (protons) by computing electron densities at a few selected grid points in the materials, thus significantly reducing the computational cost. We also show that our models can be transferable, allowing prediction of electron densities for systems on which it has not been trained but that contain a subset of atomic species on which it has been trained. Our approach can be used to develop models that span different chemical systems and train them for the study of large-scale charge transport and chemical reactions.

Discovering chemical reaction pathways using quantum mechanics is impractical for many systems of practical interest because of unfavorable scaling and computational cost. While machine learning interatomic potentials (MLIPs) trained on quantum mechanical data offer a promising alternative, they face challenges for reactive systems due to the need for extensive sampling of the potential energy surface in regions that are far from equilibrium geometries. Unfortunately, traditional MLIP training protocols are not designed for comprehensive reaction exploration. We present a reactive active learning (RAL) framework that is designed to efficiently train MLIPs to achieve near-quantum mechanical accuracy for reactive systems for situations where one may not have prior knowledge of the possible transition states, reaction pathways, or even the potential products. Our method combines automated reaction exploration, uncertainty-driven active learning, and transition state sampling to build accurate potentials. We demonstrate RAL's effectiveness across three different systems: uncatalyzed ammonia synthesis (gas-phase), methanimine hydrolysis (solution phase), and methane activation on titanium carbide surfaces (heterogeneous). The resulting MLIPs accurately predict reaction barriers and transition states. For catalysis, we show that RAL-trained MLIPs identify Ti₂C as the most active methane activation surface (90% decomposition at 1000 K) through C-vacancy mediated mechanisms. The framework's ability to simulate large systems (∼900 atoms) over nanosecond time scales provides previously inaccessible insights into surface poisoning and reaction networks. We show that reactive exploration is essential for adequately capturing the potential energy surface, with chemical and configurational sampling working synergistically to improve model accuracy. Our results establish general guidelines for training robust reactive potentials and open new possibilities for computational discovery of catalysts and reaction mechanisms.

Development of new materials capable of conducting protons in the absence of water is crucial for improving the performance, reducing the cost, and extending the operating conditions for proton exchange membrane fuel cells. We present detailed atomistic simulations showing that graphanol (hydroxylated graphane) will conduct protons anhydrously with very low diffusion barriers. We developed a deep learning potential (DP) for graphanol that has near-density functional theory accuracy but requires a very small fraction of the computational cost. We used our DP to calculate proton self-diffusion coefficients as a function of temperature, to estimate the overall barrier to proton diffusion, and to characterize the impact of thermal fluctuations as a function of system size. We propose and test a detailed mechanism for proton conduction on the surface of graphanol. We show that protons can rapidly hop along Grotthuss chains containing several hydroxyl groups aligned such that hydrogen bonds allow for conduction of protons forward and backward along the chain without hydroxyl group rotation. Long-range proton transport only takes place as new Grotthuss chains are formed by rotation of one or more hydroxyl groups in the chain. Thus, the overall diffusion barrier consists of a convolution of the intrinsic proton hopping barrier and the intrinsic hydroxyl rotation barrier. Our results provide a set of design rules for developing new anhydrous proton conducting membranes with even lower diffusion barriers.