Joint and grand‐canonical density‐functional theory

Understanding the Electric Double-Layer Structure, Capacitance, and Charging Dynamics

“…In extension of the solvation model to EDL, Nishihara and Otani developed an effective screening medium method (ESM) and Green’s function techniques to describe electrified interfaces with open boundary conditions . Another popular approach to account for electron–ion interactions explicitly is the joint density-functional theory (Joint-DFT). ,, In principle, Joint-DFT can be formulated by applying the Hohenberg–Kohn theorem to open systems of electrons and classical particles as shown in eq . However, further developments are needed to describe the quantum-classical interactions.…”

“…The electronic density of a metallic surface was considered by Rice as early as 1928 based on the Sommerfeld theory of free electrons . Regrettably, little progress was made toward a more accurate description of the electronic structure before the landmark publications by Lang and Kohn on the theory of metal surfaces in the early 1970s. , An integrated approach to account for both the electronic and ionic density profiles in the EDL has been explored since the 1980s and remains an active field of theoretical development today. − …”

Revision of the oxygen reduction reaction on N-doped graphenes by grand-canonical DFT

“…35,50 It is also worth mentioning that it would be promising to improve the solvent model in used joint DFT, which could be done within the framework of classical DFT liquids with an atomic-scale structure. 51 Another option is to use ab initio molecular dynamics simulations; 35,52 however, it is still computationally costly and very tricky to fix the surface potential, which as was shown plays an important role.…”

An Explicit-Implicit Hybrid Solvent Model for Grand Canonical Simulations of the Electrochemical Environment

“…It may also be possible to include the effect of the electrode potential in the calculations through the socalled capacitor model, 14 but such an approach fails to account accurately for the response of the charge on the electrode to the dynamical evolution of the adsorbate, electrolyte, and the catalyst surface to keep the electrode potential constant. Fortunately, such dynamical effects are naturally included in the self-consistent grand canonical DFT (GC-DFT) 15,16 method, but its implementation has been hampered by high computational cost. Efforts 17,18 have also been devoted to the develop the grand-canonical AIMD (or constant potential) simulations, but so far these methods have not been widely applied.…”