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Deep multi-scale modelling of electrified metal oxide nanostructures

Periodic Reporting for period 1 - DeepProton (Deep multi-scale modelling of electrified metal oxide nanostructures)

Reporting period: 2021-01-01 to 2022-06-30

One promising solution toward a sustainable society and a green economy is to use metal oxide-based materials. Metal oxides are a class of inorganic materials that have various energy and environmental applications such as heterogeneous catalyst, fuel cells, lithium-ion batteries, supercapacitors, water treatment, and antimicrobial applications. Most metal oxides are synthesized as nanostructures which leads to unique properties and reduced economical costs. The very properties that make the metal oxide nanostructures attractive and indispensable in modern science and technology also cause an issue for the environment and human safety.

In both the functioning and the degradation of metal oxide nanostructures, the aqueous interface plays a vital role. The metal oxide-aqueous solution aqueous interface is electrified in working conditions due to acid-base chemistry and is composed of the protonic electric double layer. Given the importance of metal oxide surfaces in practical applications, surprisingly little is known about the relation between the atomic structure of the protonic double layer and the interfacial reactivity. This is largely due to the fact that our knowledge is mostly based on macroscopic observations such as current and concentration in electrochemistry and microscopic information of protonic double layer is difficult to be obtained in experiments.

Therefore, developing a novel deep-learning empowered multi-scale modelling framework and providing a revolutionizing understanding at the microscopic level of the functioning and degradation of electrified metal oxide nanostructures are the aims
of this proposal. The outcome of this project will not only lead to the knowledge discovery about the impact of protonic electric double layer on porous metal oxide-based supercapacitors and on the degradation of metal oxide nanoparticles, but it will also propose useful design principles for synthesis and fabrication.
In the work of Jia, Zhang, and Cheng, J. Phys. Chem. Lett., 20201, 12: 4616, 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 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 main objectives in the DeepProton project.

In the work of Knijff and Zhang, Mach. Learn.: Sci. Technol., 2021, 2: 03LT03, 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. 4 (2022) 014012, 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 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.
The most recent work on introducing the finite-field coupling through learning the charge response kernel is an example of our progress that goes beyond the state-of-the-art. i) We showed that the ACSK2 method is equivalent to Dyson's equation. This provides a new route to handle charge systems by introducing the dielectric function to the Fukui function. ii) We showed that by employing machine learning models, one can fix the long-standing problem of superlinear scaling which plagues the EEM type of models. iii) We established the PiNet-chi framework to generate the charge response kernel by learning from the molecular polarizability data. This provides a way to model the heterogeneous electrode model in constant potential simulations, which goes beyond what the Siepmann-Sprik approach and its Thomas-Fermi extension can provide.
The atomistic machine-learning framework developed in the DeepProton project