Atomistic simulation of the electrochemical
double layer is an
ambitious undertaking, requiring quantum mechanical description of
electrons, phase space sampling of liquid electrolytes, and equilibration
of electrolytes over nanosecond time scales. All models of electrochemistry
make different trade-offs in the approximation of electrons and atomic
configurations, from the extremes of classical molecular dynamics
of a complete interface with point-charge atoms to correlated electronic
structure methods of a single electrode configuration with no dynamics
or electrolyte. Here, we review the spectrum of simulation techniques
suitable for electrochemistry, focusing on the key approximations
and accuracy considerations for each technique. We discuss promising
approaches, such as enhanced sampling techniques for atomic configurations
and computationally efficient beyond density functional theory (DFT)
electronic methods, that will push electrochemical simulations beyond
the present frontier.