A recapFirst principles of previous chapters is followed by recent advancementsDensity Functional Theory (DFT). Density functional theory (DFT) is outlined and when implemented in the Vienna ab initioAb initio simulation package (VASP) it becomes a valuable tool for surface science. Initial applications to electrochemistry explored the effects on surface reaction reversible potentialsReversible potential and activation energies of double layerDouble layer fields. Fields were introduced by charging the surface and modeling compensation with various forms of background charge. Codes such as “interface” were developed in which the surface is charged andModified Poisson-Boltzmann (MPB) modified Poisson–BoltzmannBoltzmann theory determines the double layer charge distribution variationally. The Fermi levelFermi level (Ef) determines the potential. ThisGrand-Canonical Density Functional Theory (GC-DFT) grand-canonical density functional theoryDensity Functional Theory (DFT) (GC-DFT) approach is the current state of the art and is capable of accurately predicting reversible potentials though obtaining activation energies for electron transferElectron transfer is computationally demanding. Research is ongoing to improve GC-DFTDensity Functional Theory (DFT) methods and combine them withMolecular mechanics molecular mechanics. Mention is made of evolving alternative concepts such as orbital-free DFT and programmable electrodes.