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Multiscale Modeling of the Electrode/Electrolyte Interface Using Charge Optimized Many Body (ECOMB3) Potentials

**Introduction**

Present day advances in computer simulation have greatly accelerated material discovery and the investigation of bulk and surface properties that are relevant to the reactivity and performance of the material. Electrocatalytic systems present unique challenges to atomistic and electronic structure modeling due to the presence of an electrode/electrolyte interface and the integration of electrical currents and chemical reactions.

Our objective is to develop robust methods that can provide a reasonable atomistic description of the electrode/electrolyte interface that can be used to investigate the complex underlying interfacial chemistry. We combine Density Functional Theory (DFT)* *and a force field (FF) based classical approach to construct an atomistic modeling tool to consider this interface. Two key features of the electrochemical interface are incorporated - metal polarizability and the interfacial electrolyte chemistry in the presence of a potential-controlled field. In our previous study [1], we employ a reactive modified central force-field (mCF) model that uses simple point charges with pairwise interactions to model reactive water that can dissociate under the influence of potential controlled Pt (111) electrodes. The electrodes are held at constant potential by using a charge fluctuation approach called Electrode Charge Dynamics (ECD) [2]. However the mCF model assigns a fixed charge/oxidation state to the water species and the ECD scheme does not permit charge exchange between the electrode and the electrolyte. In this work, we report third-generation Charge Optimized Many Body potentials (COMB3) [3] in conjunction with an electrode charge equilibration scheme (ECOMB3) for modeling the electrified interface. This model advantageously has a on-the-fly partial charge assignment and allows for a multi-body charge equilibration within a constant potential controlled environment.

**Materials and Methods**

All molecular dynamics (MD) simulations have been carried out in Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The DFT calculations were conducted using the Vienna ab-initio package using a generalized gradient approximation (GGA) with the Perdew, Burke and Ernzerhof (PBE) functional. For complete simulation details and a detailed description of the COMB3 formalism, please refer to Ref. [1] and [3].

**Results and Discussion**

An atomistic representation of the electrode/electrolyte interface is shown in Figure 1. In order to apply an electrode potential drop (Δ*V*) across two electrodes that are modeled as two halves of a metal slab in a periodic representation, the ECOMB3 scheme inserts a constant offset potential *V*, in the self-consistent charge equilibration scheme, biasing one side of the metal slab relative to the other. The atom-centered charge equilibration scheme treats transferred charge as continuous variables subject to overall charge conservation. To compute the partial charges on the individual atoms, the overall electrostatic energy (*U*) of the system is minimized relative to the each partial charge (*q _{i}*) (also defined as the electronegativity

*Χ*) within the constraint that overall system is charge-balanced. When a voltage offset

*V*is applied, the electronegativity at all sites is no longer the same and is biased at the electrodes by a magnitude of

*V*as shown in Equation (1). The equations of motion are then modified to accommodate the bias (Equations 2 and 3).

δ*U*_{cathode}/δ*q _{i}* − δ

*U*

_{anode}/δ

*q*=

_{i}*V*(1)

Cathode:* m _{q}q_{i}*″ =

*Χ*

_{avg}+ (

*N*/

_{C}*N*)

_{T}*V*−

*Χ*+

_{i}*νq*′ (2)

_{i}Anode:* m _{q}q_{i}*″ =

*Χ*

_{avg}− (

*N*/

_{A}*N*)

_{T}*V*−

*Χ*+

_{i}*νq*′ (3)

_{i}where *m _{q}* denotes the fictitious mass of the charge

*q*on atom

*i*and

*ν*represents the velocity.

*N*and

_{A}*N*represent the number of Cu atoms at the anode and cathode respectively with the total number of atoms

_{C}*N*=

_{T}*N*+

_{A}*N*. The average electronegativity

_{C}*Χ*

_{avg}of the system is computed as the sum of the electrongativity of each atom

*i*averaged over all atoms. We will demonstrate the use of the ECOMB3 method to study the environment in which electrocatalysis occurs. Specifically, we report the distribution and dynamics of the interfacial species, the fluctuation and distribution of charge on the electrode, and the distribution of electrostatic potential at the interface.

**References**

- Yeh, K.-Y., Janik, M. J. and Maranas, J. K.
*, Electrochimica Acta,*101, 308 (2013). - Guymon, C. G., Rowley, R. L., Harb, J. N. and Wheeler, D. R.,
*Condens. Matter Phys,*8, 335 (2005). - Liang, T., Shan, T.-R., Cheng, Y.-T., Devine, B. D., Noordhoek, M., Li, Y., Lu, Z., Phillpot, S. and Sinnott, S.,
*Materials Science and Engineering: R: Reports*, 74(9), 255 (2013)*.*

**Figure 1. A simulation cell of 5352 atoms consisting of Cu (111) layers acting as the cathode (Right) and anode (Left) and water (O = red, H=white) as electrolyte. **