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Due to the increasing demand for energy, sustainable energy generation and storage are becoming more and more important in society and research. Electrochemical energy storage devices such as electrochemical double-layer capacitors (EDLCs) play an important role in fulfilling this need. To understand, control and design EDLCs at atomic precision, physical insights from atomistic simulation are clearly needed. However, atomistic simulation of EDLCs faces challenges such as the large system size and the complex chemistry involved at electrified solid-liquid interfaces. To address these challenges, machine learning models for charge prediction have been developed to aid the atomistic simulations of EDLCs in this thesis. Here, a divide-and-conquer approach was taken, and the electrolyte and electrode component were investigated separately.

Initially, a neural network approach called PiNet-dipole was developed to model the supercell polarization in liquid water using two constraints. First, the displacement of the atomic charges is proportional to the itinerant polarization. Second, each water molecule has a net charge of zero. In doing so, a molecular dipole moment distribution can be inferred for liquid water that is surprisingly similar to that computed from Wannier centers. More importantly, PiNet-dipole provides a way to predict atomic charge without resorting to any predefined charge partition schemes. This is followed by using a class of machine learning models called PiNet-chi to predict the response charge as the result of an applied electric field for both organic electrolyte molecules and graphene analogues. Both of these models were then upgraded through the addition of equivariant features in PiNet2. This opened up new ways of predicting dipole moment for both small molecules and condensed phase systems, allowing expansion to the PiNet2-dipole family and enabling a more expressive atomic charge prediction model.

Finally, by combining the PiNet(2)-dipole and the PiNet(2)-chi models and integrating them with the semi-classical molecular dynamics code MetalWalls, the PiNNwall interface was developed to model polarizable and heterogeneous electrodes. PiNNwall was then used to study chemically doped graphene and graphene oxide under different electrical boundary conditions, as well as to investigate the influence of the proton charge on aqueous EDLCs.

Electrochemical energy storage and conversion play increasingly important roles in electrification and sustainable development across the globe. A key challenge therein is to understand, control, and design electrochemical energy materials with atomistic precision. This requires inputs from molecular modeling powered by machine learning (ML) techniques. In this work, we have upgraded our pairwise interaction neural network Python package PiNN via introducing equivariant features to the PiNet2 architecture for fitting potential energy surfaces along with PiNet2-dipole for dipole and charge predictions as well as PiNet2-chi for generating atom-condensed charge response kernels. By benchmarking publicly accessible data sets of small molecules, crystalline materials, and liquid electrolytes, we found that the equivariant PiNet2 shows significant improvements over the original PiNet architecture and provides a state-of-the-art overall performance. Furthermore, leveraging on plug-ins such as PiNNAcLe for an adaptive learn-on-the-fly workflow in generating ML potentials and PiNNwall for modeling heterogeneous electrodes under external bias, we expect PiNN to serve as a versatile and high-performing ML-accelerated platform for molecular modeling of electrochemical systems.

Electrochemical energy storage and conversion play increasingly important roles in electrification and sustainable development across the globe. A key challenge therein is to understand, control, and design electrochemical energy materials with atomistic precision. This requires inputs from molecular modeling powered by machine learning (ML) techniques. In this work, we have upgraded our pairwise interaction neural network Python package PiNN via introducing equivariant features to the PiNet2 architecture for fitting potential energy surfaces along with PiNet2-dipole for dipole and charge predictions as well as PiNet2-χ for generating atom-condensed charge response kernels. By benchmarking publicly accessible data sets of small molecules, crystalline materials, and liquid electrolytes, we found that the equivariant PiNet2 shows significant improvements over the original PiNet architecture and provides a state-of-the-art overall performance. Furthermore, leveraging on plug-ins such as PiNNAcLe for an adaptive learn-on-the-fly workflow in generating ML potentials and PiNNwall for modeling heterogeneous electrodes under external bias, we expect PiNN to serve as a versatile and high-performing ML-accelerated platform for molecular modeling of electrochemical systems.

Capacitive storage devices allow for fast charge and discharge cycles, making them the perfect complements to batteries for high power applications. Many materials display interesting capacitive properties when they are put in contact with ionic solutions despite their very different structures and (surface) reactivity. Among them, nanocarbons are the most important for practical applications, but many nanomaterials have recently emerged, such as conductive metal-organic frameworks, 2D materials, and a wide variety of metal oxides. These heterogeneous and complex electrode materials are difficult to model with conventional approaches. However, the development of computational methods, the incorporation of machine learning techniques, and the increasing power in high performance computing now allow us to tackle these types of systems. In this Review, we summarize the current efforts in this direction. We show that depending on the nature of the materials and of the charging mechanisms, different methods, or combinations of them, can provide desirable atomic-scale insight on the interactions at play. We mainly focus on two important aspects: (i) the study of ion adsorption in complex nanoporous materials, which require the extension of constant potential molecular dynamics to multicomponent systems, and (ii) the characterization of Faradaic processes in pseudocapacitors, that involves the use of electronic structure-based methods. We also discuss how recently developed simulation methods will allow bridges to be made between double-layer capacitors and pseudocapacitors for future high power electricity storage devices.

Layered TiS₂ has been proposed as a versatile host material for various battery chemistries. Nevertheless, its compatibility with aqueous electrolytes has not been thoroughly understood. Herein, we report on a reversible hydration process to account for the electrochemical activity and structural evolution of TiS₂ in a relatively dilute electrolyte for sustainable aqueous Li-ion batteries. Solvated water molecules intercalate in TiS₂ layers together with Li⁺ cations, forming a hydrated phase with a nominal formula unit of Li_0.38(H₂O)_2−δTiS₂ as the end-product. We unambiguously confirm the presence of two layers of intercalated water by complementary electrochemical cycling, operando structural characterization, and computational simulation. Such a process is fast and reversible, delivering 60 mAh g^–1 discharge capacity at a current density of 1250 mA g^–1. Our work provides further design principles for high-rate aqueous Li-ion batteries based on reversible water cointercalation.

Metal-oxide surfaces act as both Brønsted acids and bases, which allows the exchange of protons with the electrolyte solution and generates either positive or negative proton charges depending on the environmental pH. These interfacial proton charges are then compensated by counter-ions from the electrolyte solution, which leads to the formation of the electric double layer (EDL). Because the EDL plays a crucial role in electrochemistry, geochemistry and colloid science, understanding the structure-property relationship of the EDL in metal-oxide systems from both experimental and theoretical approaches is necessary. This article focuses on the physical chemistry of the protonic double layer at the metal-oxide/electrolyte interface. In particular, determinations of the EDL capacitance and the double-layer potential from potentiometric titration experiments, electrochemical methods, surface-sensitive vibrational spectroscopy and X-ray photoelectron spectroscopy are summarized. This is followed by discussions from the atomistic modeling aspect of the EDL, with an emphasis on the density-functional theory-based molecular dynamics simulations. A conclusion and outlook for future works on this topic are also given.

Electrochemical energy storage always involves the capacitive process. The prevailing electrode model used in the molecular simulation of polarizable electrode–electrolyte systems is the Siepmann–Sprik model developed for perfect metal electrodes. This model has been recently extended to study the metallicity in the electrode by including the Thomas–Fermi screening length. Nevertheless, a further extension to heterogeneous electrode models requires introducing chemical specificity, which does not have any analytical recipes. Here, we address this challenge by integrating the atomistic machine learning code (PiNN) for generating the base charge and response kernel and the classical molecular dynamics code (MetalWalls) dedicated to the modeling of electrochemical systems, and this leads to the development of the PiNNwall interface. Apart from the cases of chemically doped graphene and graphene oxide electrodes as shown in this study, the PiNNwall interface also allows us to probe polarized oxide surfaces in which both the proton charge and the electronic charge can coexist. Therefore, this work opens the door for modeling heterogeneous and complex electrode materials often found in energy storage systems.

Response of the electronic density at the electrode–electrolyte interface to the external field (potential) is fundamental in electrochemistry. In density-functional theory, this is captured by the so-called charge response kernel (CRK). Projecting the CRK to its atom-condensed form is an essential step for obtaining the response charge of atoms. In this work, the atom-condensed CRK is learnt from the molecular polarizability using machine learning (ML) models and subsequently used for the response-charge prediction under an external field (potential). As the machine-learnt CRK shows a physical scaling of polarizability over the molecular size and does not (necessarily) require the matrix-inversion operation in practice, this opens up a viable and efficient route for introducing finite-field coupling in the atomistic simulation of electrochemical systems powered by ML models.

Molecular dipole moment in liquid water is an intriguing property, partly due to the fact that there is no unique way to partition the total electron density into individual molecular contributions. The prevailing method to circumvent this problem is to use maximally localized Wannier functions, which perform a unitary transformation of the occupied molecular orbitals by minimizing the spread function of Boys. Here we revisit this problem using a data-driven approach satisfying two physical constraints, namely: (a) The displacement of the atomic charges is proportional to the Berry phase polarization; (b) Each water molecule has a formal charge of zero. It turns out that the distribution of molecular dipole moments in liquid water inferred from latent variables is surprisingly similar to that obtained from maximally localized Wannier functions. Apart from putting a maximum-likelihood footnote to the established method, this work highlights the capability of graph convolution based charge models and the importance of physical constraints on improving the model interpretability.

Batteries and supercapacitors are electrochemical energy storage systems which involve multiple time-scales and length-scales. In terms of the electrolyte which serves as the ionic conductor, a molecular-level understanding of the corresponding transport phenomena, electrochemical (thermal) stability and interfacial properties is crucial for optimizing the device performance and achieving safety requirements. To this end, atomistic machine learning is a promising technology for bridging microscopic models and macroscopic phenomena. Here, we provide a timely snapshot of recent advances in this area. This includes technical considerations that are particularly relevant for modelling electrolytes as well as specific examples of both bulk electrolytes and associated interfaces. A perspective on methodological challenges and new applications is also discussed.