We have also shown that combing CIP with constrained DFT enables setting up an electrode potential difference (bias) between two electrodes in a simulation cell -this is simply impossible with E DF T f -based GCE-DFT approaches. A particularly appealing feature of CIP-cDFT is the construction of bias potential without using local orbitals or Green's function approaches, making the method compatible with plane-wave or real-space codes. The prospect of describing a bias between two electrodes without using Green's function methods creates new possibilities in simulating the applied electrode potential in two-electrode electrochemical cells with DFT or addressing non-equilibrium charge transfer dynamics through single-molecule junctions (see Supplementary section S4) . In addition, we envision that CIP-cDFT can be used to e.g. prevent unphysical and instantaneous electron transfer events in molecular dynamics simulations and to include the impact of explicit bias in STM simulations. As the cDFT method is already available in several solid-state DFT codes, only minimal implementation work is needed to make CIP-cDFT widely applicable.