Oxygen vacancies on ceria (CeO(2)) surfaces play a crucial role in catalytic applications, yet whether vacancies are at surface or subsurface sites on reduced CeO(2)(111), and whether vacancies agglomerate or repel each other, is still under discussion, with few and inconsistent experimental results. By combining density-functional theory (DFT) in the DFT+U (U is an effective onsite Coulomb interaction parameter) approach and statistical thermodynamics, we show that the energetically most stable near-surface oxygen vacancy structures for a broad range of vacancy concentrations, Θ (1/16 ≤ Θ ≤ 1 monolayer) have all vacancies at subsurface oxygen sites and predict that the thermodynamically stable phase for a wide range of reducing conditions is a (2 × 2) ordered subsurface vacancy structure (Θ = 1/4). Vacancy-induced lattice relaxations effects are crucial for the interpretation of the repulsive interactions, which are at the basis of the vacancy spacing in the (2 × 2) structure. The findings provide theoretical data to support the interpretation of the most recent experiments, bringing us closer to solving the debate.

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Quantum control of the wave function of two interacting electrons confined in quasi-onedimensional double-well semiconductor structures is demonstrated. The control strategies are based on the knowledge of the energy spectrum as a function of an external uniform electric field. When two low-lying levels have avoided crossings our system behaves dynamically to a large extent as a two-level system. This characteristic is exploited to implement coherent control strategies based on slow (adiabatic passage) and rapid (diabatic Landau-Zener transition) changes of the external field. We apply this method to reach desired target states that lie far in the spectrum from the initial state.PACS numbers: 78.67.Hc The control of quantum systems is a fundamental challenge in physical chemistry, nanoscience, and quantum information processing [1,2]. Quantum control is the manipulation of the temporal evolution of a system in order to obtain a desired target state or value of a certain physical observable. From the experimental point of view, the techniques of quantum control are highly developed in the area of magnetic resonance, and more recently great progress has been made in quantum chemistry thanks to the development of ultrafast laser pulses [3].Coherent control in semiconductor quantum dots has become an active field of research in the last 15 years. Early works on electron localization in double well systems spurred intense theoretical activity. In a seminal paper, Grossmann et al. [4] showed that, by applying an appropriate AC electric field, the tunneling of the electron between the wells could be coherently destroyed, thereby maintaining an existing localization in one of the wells. Shortly after, Bavli and Metiu [5] found ways to, starting from the delocalized ground state, localize the electron wave function and then to preserve the localization with a precisely taylored time-dependent electric field. A large body of literature followed these pioneering works. A decade later, the first steps in the theoretical exploration of localization and control of two interacting electrons in quantum dots were made [6,7,8]. Whereas Zhang and Zhao studied a model two-level system, Tamborenea and Metiu studied a more realistic multi-level system inspired by quasi-one-dimensional semiconductor nanorods. The study of two-electron localization and control in double dots has remained active ever since [9,10,11,12,13].In this Letter we propose an efficient method to control the wave function of two interacting electrons confined in quasi-one-dimensional nanorods [8,14]. The control method is based on the knowledge of the energy spectrum as a function of an external uniform electric field. The method requires that the system behaves locallynear avoided level crossings-as the Landau-Zener (LZ) two-level model [15]. This fact is exploited to navigate the spectrum using slow (adiabatic) and rapid (diabatic) changes of the external control parameter. Although this characteristic may seem rather restrictive, it is, in fact, a general ...