PiNNwall: Heterogeneous Electrode Models from Integrating Machine Learning and Atomistic Simulation

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.


B Validation and implementation of base charges predicted from PiNet-dipole
To validate the charges predicted from the PiNet-dipole model, molecular analogues of the target structures were used for each of the functionalized graphene models.To validate that the charges predicted from PiNet-dipole have a physical basis, comparisons were made to charges computed using several population analysis techniques.
To perform the population analysis, DFT calculations were run using Gaussian09 [1].The B3LYP [2,3] functional and the cc-pVDZ basis set [4] were used.The population analyses that were performed are: CM5 [5], Mulliken [6], Hirshfeld [7] and Merz-Singh-Kollman (MSK) [8,9].The molecular analogues were deemed fit as a references if the predicted charges corresponded to chemical intuition and the dipole moment was comparable to that calculated using DFT.
For the graphene sheet doped with nitrogen, a planar form of trimethylamine was used as a reference.S2: Base charges from trimethylamine as implemented in the N-doped graphene.
The charges of the methyl groups are placed the carbon atoms when charges are used in the real system, to ensure a charge neutral entity.
For the graphene sheet doped with epoxy groups, ethylene oxide was used as the reference molecule.Here, the charges of the hydrogen atoms are also combined with that of the carbon atoms when the charges are transferred to functionalized graphene.Once again, to ensure charge neutrality and to localize the charges on the graphene sheet.
For the graphene sheet doped with hydroxyl groups, methanol was used as the molecular analogue.The charge on the carbon atom is set so that it includes the charges of the hydrogen atoms as well.In this way, it compensates for the charge on the hydroxyl group, and the whole group is charge neutral.
Finally, for the graphene sheet functionalized with carboxyl groups, a smaller graphene flake with carboxyl groups was used as a reference.This was done because alternative analogues showed large fluctuations in the charges when changing the charge state of the analogue which did not correspond to chemical intuition.While the dipole moment for the carboxyl flake shows discrepancies to that of DFT in the xand y-direction, the z-direction, which is the most important direction when it comes to the carboxyl group, agrees within a reasonable error margin.Table S9: Base charges from the protonated carboxyl flake as implemented in the protonated side of carboxyl-terminated graphene oxide.
Since the investigated structures contain neutral, protonated, and deprotonated forms of the carboxyl groups, these are also the structures for which the charges were predicted.Here the charge of the carbon atom is set such that the total charge of the protonated carboxyl group is +1.Once again the charges of the atoms are predicted using PiNet-dipole.Then, the charge of the carbon atom is simply set to ensure that the charge of the protonated carboxyl group sums to +1.This is done to keep the charges localized, and because it is the simplest way to adjust the charge without the need for an arbitrary charge division.It also prevents unphysical modifications to the other charges from being made.This is supported by Figure S6, as this shows that the charge analysis performed with DFT methods the excess charge is also mostly located on the carbon atom.Table S10: Base charges from the deprotonated carboxyl flake as implemented in the deprotonated side of carboxyl-terminated graphene oxide.
Similarly, for the deprotonated cases, the charge of the carbon atom is set such that the total charge of the deprotonated carboxyl group is -1.As can be seen in Figure S7, for the DFT charge methods the negative charge is spread across the carboyxl flake, mostly at the edges.As a first approximation, the excess charge is localized on the carbon atom in our implementation, which avoids any size-inconsistent charge divisions.

Figure S1 :
Figure S1: Passing the charge response kernel.Response charges predicted by MetalWalls via the PiNNwall interface against the prediction from PiNN using the same kernel PiNet-χ (EEM).

Figure S8 :
Figure S8: Density of adsorbed ions in on a pristine graphene electrode .Surface density in e Å−2 of potassium (yellow to red color bar) and chloride (blue to purple color bar) using the MetalWalls (PM) on the negative (a) and positive (b) electrode, and using the PiNet-χ (EEM) model on the negative (c) and positive (d) electrode, under an applied potential of 2 V.

Figure S9 :
Figure S9: Density of adsorbed ions on a graphene electrode with Nitrogen substitution.Surface density in e Å−2 of potassium (yellow to red color bar) and chloride (blue to purple color bar) using the MetalWalls (PM) model on the negative (a) and positive (b) electrode, and using the PiNet-χ (EEM) model on the negative (c) and positive (d) electrode, for a surface coverage of 20 % and under an applied potential of 2 V.

Figure S10 :
Figure S10: Density of adsorbed ions on a graphene oxide electrode with epoxy terminations.Surface density in e Å−2 of potassium (yellow to red color bar) and chloride (blue to purple color bar) using the MetalWalls (PM) model on the negative (a) and positive (b) electrode, and using the PiNet-χ (EEM) model on the negative (c) and positive (d) electrode, for a surface coverage of 20 % and under an applied potential of 2 V.

Figure S11 :
Figure S11: Density of adsorbed ions on a graphene oxide electrode with hydroxyl terminations.Surface density in e Å−2 of potassium (yellow to red color bar) and chloride (blue to purple color bar) using the MetalWalls (PM) model on the negative (a) and positive (b) electrode, and using the PiNet-χ (EEM) model on the negative (c) and positive (d) electrode, for a surface coverage of 20 % and under an applied potential of 2 V.

Table S3 :
Dipole moment of ethylene oxide.

Table S4 :
Based charges from ethylene oxide as implemented in the epoxy-terminated graphene oxide.

Table S5 :
Dipole moment of methanol.

Table S6 :
Base charges from methanol as implemented in the hydroxyl-terminated graphene oxide.

Table S7 :
Charges from the neutral carboxyl flake.

Table S8 :
Dipole moment from the neutral carboxyl flake.