In the work of Jia, Zhang, and Cheng, J. Phys. Chem. Lett., 2021, 12: 4616, the authors have developed a differential Helmholtz capacitance model to connect the microscopic information (i.e. the interfacial dipole) and the experimental observable (i.e. the Helmholtz capacitance) using the finite-field based DFTMD simulations. It reveals that the chemisorption of water at the metal-oxide surface is the key contributor to the asymmetric profile of the differential capacitance observed in experiments. This new information could be useful to tailor the interfacial electrochemistry in metal-oxide based super-capacitors for energy storage. This publication serves as a further understanding of aqueous interfaces of metal oxides, which is one of the main objectives of the DeepProton project.
In the work of Knijff and Zhang, Mach. Learn.: Sci. Technol., 2021, 2: 03LT03, the authors have developed a graph convolution-based machine learning (ML) model for describing the supercell polarisation in condensed phase systems using liquid water as a first example. In particular, they revisited a classic problem of molecular dipole moment in liquid water using the state-of-the-art ML technique and found that the distribution of molecular dipole inferred from the machine learning model is surprisingly similar to those calculated using the established method of maximally localised Wannier centres. This is an example of how ML can be reinforced by physics to learn physics. This publication serves as a stepping stone for the follow-up development of machine learning potential for modelling electrified interfaces in the DeepProton projects, where the description of supercell polarisation in condensed phase systems using ML model is a key objective.
In the work of Shao, Andersson, Knijff, and Zhang, Electron. Struct. 2022, 4: 014012, the authors have extended their graph convolution neural network model PiNet for describing the charge response kernel (CRK). The CRK provides the connection between polarizability and the response charge and can be used in the constant potential MD simulation of the electrode/electrolyte system. By reformulating the CPE and ACKS2 methods in terms of the CRK and elaborating on the advantages of using the CRK to describe molecular polarizability, the authors showed how different PiNet-χ models perform regarding molecular polarizability, size scaling as well as examples of response charge and atom-condensed CRK. Therefore, it provides a viable and efficient route to describing the electrochemical systems with ML models. This work is a key step forward in the DeepProton projects, in which the coupling between the finite field and the polarization is incorporated in ML models.
In the work of Dufils, Knijff, Shao, and Zhang, J. Chem. Theory Comput. 2023, 19: 5199, the authors demonstrated the first stage of the ongoing development for coupling electrochemical systems to the external potential or external electric field using atomistic machine learning. This was done 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 modelling of electrochemical systems. This leads to the development of the PiNNwall interface, which will serve as an example showing how physics-based models and machine learning models can be integrated for modeling heterogeneous and complex electrode materials often under potential control.
