  Constant potential methods (CPM) enable computationally efficient simulations
of the solid-liquid interface at conducting electrodes in molecular dynamics
(MD). They have been successfully used, for example, to realistically model the
behavior of ionic liquids or water-in-salt electrolytes in supercapacitors and
batteries. The CPM models conductive electrodes by updating charges of
individual electrode atoms according to the applied electric potential and the
(time-dependent) local electrolyte structure. Here we present a feature-rich
CPM implementation, called ELECTRODE, for the Large-scale Atomic/Molecular
Massively Parallel Simulator (LAMMPS), which includes a constrained charge
method and a thermo-potentiostat. The ELECTRODE package also contains a
finite-field approach, multiple corrections for non-periodic boundary
conditions of the particle-particle particle-mesh solver, and a Thomas-Fermi
model for using non-ideal metals as electrodes. We demonstrate the capabilities
of this implementation for a parallel-plate electrical double-layer capacitor,
for which we have investigated the charging times with the different
implemented methods and found an interesting relationship between water and
ionic dipole relaxations. To prove the validity of the one-dimensional
correction for the long-range electrostatics, we estimated the vacuum
capacitance of two co-axial carbon nanotubes and compared it to structureless
cylinders, for which an analytical expression exists. In summary, the ELECTRODE
package enables efficient electrochemical simulations using state-of-the-art
methods, allowing one to simulate even heterogeneous electrodes. Moreover, it
allows unveiling more rigorously how electrode curvature affects the
capacitance with the one-dimensional correction.
