A Simple and Efficient Lattice Summation Method for Metallic Electrodes in Constant Potential Molecular Dynamics Simulation

This work extends a well-known constant potential simulation method (SR-CPM) in the LAMMPS MD simulation package. The SR-CPM method has been widely applied to investigate the metallic electrolyte/electrode interface, especially for conducting nanochannels with complex connectivity, e.g., carbide-derived carbon or graphene assembled membrane. Compared with this seminal work, the computational efficiency of our work has drastically improved by about one order of magnitude. It can be attributed to several newly developed techniques in this work (e.g., preconditioning) and the employment of mesh-based Ewald summation method (P3M). First, a general method has been proposed to efficiently calculate the Ewald interaction matrix $\mathbf{E}$ using existing highly optimized electrostatic codes. Second, we introduce a preconditioning technique into the conjugate gradient (PCG) method to considerably increase computational efficiency of a linear equation system that determines electrode atomic charges. As a result, our SR-CPM code can handle extra-large systems, e.g., with over 8.1 million electrode atoms. Moreover, the importance of the electroneutrality condition is demonstrated. We propose a general method to enforce electroneutrality in CPM. In the end, the choice of adjustable parameter $\alpha_{i}$, namely the atomic Hubbard-U $U_{i}^{0}$, is an unsolved issue in SR-CPM. We found that the optimized $\alpha_{i}$ or $U_{i}^{0}$ compensates for the gaps in energy between the discrete atom model and the continuum limit. As a result, a series of analytical $\alpha_{i}^{0}$ values for some typical 2D lattices are derived, which excellently resembles the behaviour of a metallic surface.