  Experiments have shown that pitting corrosion can develop in aluminum
surfaces at potentials $> -0.5$ V relative to the standard hydrogen electrode
(SHE). Until recently, the onset of pitting corrosion in aluminum has not been
rigorously explored at an atomistic scale because of the difficulty of
incorporating a voltage into density functional theory (DFT) calculations. We
introduce the Quantum Continuum Approximation (QCA) which self-consistently
couples explicit DFT calculations of the metal-insulator and insulator-solution
interfaces to continuum Poisson-Boltzmann electrostatic distributions
describing the bulk of the insulating region. By decreasing the number of atoms
necessary to explicitly simulate with DFT by an order of magnitude, QCA makes
the first-principles prediction of the voltage of realistic electrochemical
interfaces feasible. After developing this technique, we apply QCA to predict
the formation energy of chloride atoms inserting into oxygen vacancies in
Al(111)/$\alpha$-Al$_2$O$_3$ (0001) interfaces as a function of applied
voltage. We predict that chloride insertion is only favorable in systems with a
grain boundary in the Al$_2$O$_3$ for voltages $> -0.2$ V (SHE). Our results
roughly agree with the experimentally demonstrated onset of corrosion,
demonstrating QCA's utility in modeling realistic electrochemical systems at
reasonable computational cost.
