  Constant-potential molecular dynamics (MD) simulations are indispensable for
understanding the capacitance, structure, and dynamics of electrical double
layers (EDLs) at the atomistic level. However, the classical constant-potential
method, relying on the so-called 'floating charges' to keep electrode
equipotential, overlooks quantum effects on the electrode and always
underestimates EDL capacitance for typical electrochemical systems featuring
metal electrodes in aqueous electrolytes. Here, we propose a universal
theoretical framework as moment-tensor-based constant potential method (mCPM)
to capture electronic structure variations with electric moments. For EDLs at
Au(111) electrodes, mCPM-based MD reveals bell-shaped capacitance curves in
magnitude and shape both quantitatively consistent with experiments. It further
unveils the potential-dependent local electric fields, agreeing with
experimental observations of redshift vibration of interfacial water under
negative polarization and predicting a blueshift under positive polarization,
and identifies geometry dependence of two time scales during EDL formation.
