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PiNNAcLe is an implementation of our adaptive learn-on-the-fly algorithm for running machine-learning potential (MLP)-based molecular dynamics (MD) simulations -- an emerging approach to simulate the large-scale and long-time dynamics of systems where empirical forms of the PES are difficult to obtain. The algorithm aims to solve the challenge of parameterizing MLPs for large-time-scale MD simulations, by validating simulation results at adaptive time intervals. This approach eliminates the need of uncertainty quantification methods for labelling new data, and thus avoids the additional computational cost and arbitrariness thereof. The algorithm is implemented in the NextFlow workflow language (Di Tommaso et al., 2017). Components such as MD simulation and MLP engines are designed in a modular fashion, and the workflows are agnostic to the implementation of such modules. This makes it easy to apply the same algorithm to different references, as well as scaling the workflow to a variety of computational resources. The code is published under BSD 3-Clause License, the source code and documentation are hosted on Github. It currently supports MLP generation with the atomistic machine learning package PiNN (Shao et al., 2020), electronic structure calculations with CP2K (K\"uhne et al., 2020) and DFTB+ (Hourahine et al., 2020), and MD simulation with ASE (Larsen et al., 2017).

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.

Transference number is a key design parameter for electrolyte materials used in electrochemical energy storage systems. However, the determination of the true transference number from experiments is rather demanding. On the other hand, the Bruce-Vincent method is widely used in the lab to measure transference numbers of polymer electrolytes approximately, which becomes exact in the limit of infinite dilution. Therefore, theoretical formulations to treat the Bruce-Vincent transference number and the true transference number on an equal footing are clearly needed. Here we show how the Bruce-Vincent transference number for concentrated electrolyte solutions can be derived in terms of the Onsager coefficients, without involving any extrathermodynamic assumptions. By demonstrating it for the case of PEO-LiTFSI system, this work opens the door to calibrating molecular dynamics (MD) simulations via reproducing the Bruce-Vincent transference number and using MD simulations as a predictive tool for determining the true transference number.

The transport coefficients, in particular the transference number, of electrolyte solutions are important design parameters for electrochemical energy storage devices. Recent observation of negative transference numbers in PEO-LiTFSI under certain conditions has generated much discussion about its molecular origins, by both experimental and theoretical means. However, one overlooked factor in these efforts is the importance of the reference frame (RF). This creates a non-negligible gap when comparing experiment and simulation, because the fluxes in the experimental measurements of transport coefficients and in the linear response theory used in the molecular dynamics simulation are defined in different RFs. In this work, we show that by applying a proper RF transformation, a much improved agreement between experimental and simulation results can be achieved. Moreover, it is revealed that the anion mass and the anion-anion correlation, rather than ion aggregates, play a crucial role for the reported negative transference numbers.

One hidden yet important issue for developing neural network potentials (NNPs) is the choice of training algorithm. Here we compare the performance of two popular training algorithms, the adaptive moment estimation algorithm (Adam) and the Extended Kalman Filter algorithm (EKF), using the Behler-Parrinello neural network (BPNN) and two publicly accessible datasets of liquid water [Proc. Natl. Acad. Sci. U.S.A. 2016, 113, 8368-8373 and Proc. Natl. Acad. Sci. U.S.A. 2019, 116, 1110-1115]. This is achieved by implementing EKF in TensorFlow. It is found that NNPs trained with EKF are more transferable and less sensitive to the value of the learning rate, as compared to Adam. In both cases, error metrics of the validation set do not always serve as a good indicator for the actual performance of NNPs. Instead, we show that their performance correlates well with a Fisher information based similarity measure.

Ion-pairing is commonly considered as a culprit for the reduced ionic conductivity in polymer electrolyte systems. However, this simple thermodynamic picture should not be taken literally, as ion-pairing is a dynamical phenomenon. Here we construct model PEO-LiTFSI systems with different degree of ion-pairing by tuning solvent polarity, and examine the relation between the cation-anion distinct conductivity $\sigma^\rm{d}_{+-}$ and the lifetime of ion-pairs $\tau_{+-}$ using molecular dynamics simulations. It is found that there exist two distinct regimes where $\sigma^\rm{d}_{+-}$ scales with $1/\tau_{+-}$ and $\tau_{+-}$ respectively, and the latter is a signature of longer-lived ion-pairs which contribute negatively to the total ionic conductivity. This suggests that ion-pairs are kinetically different depending on the solvent polarity, which renders the ion-pair lifetime highly important when discussing its effect on ion transport in polymer electrolyte systems.

Alkaline electrolyte solutions are important components in rechargeable batteries and alkaline fuel cells. As the ionic conductivity is thought to be a limiting factor in the performance of these devices, which are often operated at elevated temperatures, its temperature dependence is of significant interest. Here we use NaOH as a prototypical example of alkaline electrolytes, and for this system we have carried out reactive molecular dynamics simulations with an experimentally verified high-dimensional neural network potential derived from density-functional theory calculations. It is found that in concentrated NaOH solutions elevated temperatures enhance both the contributions from proton transfer to the ionic conductivity and deviations from the Nernst-Einstein relation. These findings are expected to be of practical relevance for electrochemical devices based on alkaline electrolyte solutions.

Atomic neural networks (ANNs) constitute a class of machine learning methods for predicting potential energy surfaces and physico-chemical properties of molecules and materials. Despite many successes, developing interpretable ANN architectures and implementing existing ones efficiently are still challenging. This calls for reliable, general-purpose and open-source codes. Here, we present a python library named PiNN as a solution toward this goal. In PiNN, we designed a new interpretable and high-performing graph convolutional neural network variant, PiNet, as well as implemented the established Behler-Parrinello high-dimensional neural network. These implementations were tested using datasets of isolated small molecules, crystalline materials, liquid water and an aqueous alkaline electrolyte. PiNN comes with a visualizer called PiNNBoard to extract chemical insight "learned" by ANNs, provides analytical stress tensor calculations and interfaces to both the Atomic Simulation Environment and a development version of the Amsterdam Modeling Suite. Moreover, PiNN is highly modularized which makes it useful not only as a standalone package but also as a chain of tools to develop and to implement novel ANNs. The code is distributed under a permissive BSD license and is freely accessible at https://github.com/Teoroo-CMC/PiNN/ with full documentation and tutorials.