When, on an electrode surface, the applied potential is changed, electrons flow into or out of the surface and some ions from the electrolyte may adsorb specifically while others remain in the diffuse double layer. An equilibrium is reached with the surface work function changed by an amount equal to the applied potential change, according to work function measurements on emersed electrodes with intact double layers. This suggests a band shift model is appropriate for quantum calculations of electrode phenomena. The use of the atom superposition and electron delocalization molecular orbital (ASED-MO) theory to calculate properties of isolated adsorbate molecules as functions of band shifts is demonstrated and the use of perturbation theory to interpret the calculational results is explained in this paper. For adsorbed CO and CN, calculated CO and PtC and CM- and AgC bond vibrational frequency dependencies on potential changes are found to agree with experiment in a qualitative if not quantitative way. The phenomenological Stark-effect approach and semiempirical as well as self-consistent field single determinant cluster-in-a-field approaches from other laboratories for the potential dependencies of adsorbed CO and CN- vibrational frequencies are discussed and evaluated. Additional results of the ASED-MO band shift theory are presented. These include the potential dependence of CO adsorption sites on Pt and Pd surfaces, activation of CC and C-H bonds in C2H2 on Pt and Fe electrodes, the dissolution of FeOH+ from Fe anodes, leading to passive film formation, and the anodic generation of O2 on SrFeO3. © 1990.