This Workshop will bring together theoreticians and experimentalists working on reducible oxides such as CeO2,TiO2, VOx, FeOx, CoOx, HfO2, ZrO2, MnOx, PrOx and SmOx in the form of complex materials like bulk materials, nanocrystals and nanostructured or functionalised surfaces, which play a paramount role for many applications in the fields of heterogeneous catalysis, photocatalysis, microelectronics, photovoltaic energy conversion as well as for sensor, filter and fuel cells. The aim of this Workshop is to provide a forum for exchanging ideas on the most urgent questions related to the theoretical modeling of reducible oxide systems, the analysis and tailoring of nanostructured reducible oxide materials, the exploration and control of their chemical reactivity and the exploitation of the unique properties of reducible oxide systems for applications.
Reducible metal oxides are versatile solid state compounds exhibiting a rich chemistry related to changes in the oxidation state of the metal . Ceria is one of the paramount examples and many of the contributions in the workshop will focus on this particular oxide. Among the reasons for this choice are the number of industrial applications and the extensive basic and applied research work done in the last 10 years. Furthermore, Ceria exemplifies the theoretical challenges posed by these materials. The importance of ceria in catalysis originates from its ability to undergo rapid and reversible Ce4+(4f0)/ Ce3+(4f1), redox cycles depending on the conditions in the reactor stream . This feature is strongly related to the facile creation, healing, and diffusion of oxygen vacancies, especially at the ceria surfaces. In addition, metal-ceria catalysts have attracted interest for hydrogen production for fuel cells (water-gas shift reaction) . However, the role played by both, the metal and the oxide phase, and the nature of the metal-oxide interaction are still unclear. A generally accepted mechanism for the water-gas shift reaction does not yet exist. This shallow knowledge also applies to ceria supported metal-oxide systems such as vanadia/ceria catalysts for oxidative dehydrogenation reactions of alkanes to produce alkenes, for which a sizeable economic incentive exists within the petrochemical industry . Vanadia supported on ceria shows a remarkably high activity as compared to other supports . However, the origin of the promoting effect of ceria in oxidation reactions has yet to be fully elucidated. The complexity of the surface structure of the real supported catalysts has been partly responsible for the shallow understanding of the role of reducible oxides in catalysis. The study of well-defined model systems of increasing complexity, both experimentally and theoretically, is of importance for analyzing the structure, properties and catalytic functioning of reducible oxide-based catalysts. Actually, a fundamental understanding of the atomic structure, morphology, electronic and magnetic properties, as well as the reactivity of the reducible oxide-based systems is essential to understand the system functionality in many applications, not just catalysis.
For a theoretical modelling of reducible oxide-based systems providing insight into their functioning, it is important that the chosen computational method is capable of accurately describing the electronic structure of the reduced oxide. The application of density functional theory (DFT) within the local density approximation (LDA) and the generalized gradient approximation (GGA) to materials with strongly localized d and f-electrons such as reduced titania and ceria has not been successful, since spurious self-interactions in these approximations prevent the localization of 4f electrons . A vast number of theoretical studies have been published in recent years on oxidized and reduced bulk and surfaces of reducible oxides using the DFT+U approach [7,8], DFT with hybrid functionals [7,9], cluster MP2  as well as other wavefunction-based methods , and GW . These methods do cure LDA and GGA shortcomings such as the predicted metallicity of actual insulating reduced ceria and significantly improve the description of the commonly underestimated band gaps. Yet, further development is necessary to obtain reliable energies. For instance, DFT+U defect formation energy values depend significantly on the specific implementation, in particular, the nature and extent of the localized d or f orbitals defining the projection operators, the underlying level of theory (LDA or GGA), and the actual value of the effective Coulomb parameter U and, therefore, the quest for improved functionals is still open .
How shallow is our knowledge of the structure and functions of reducible oxide-based systems is exemplified in the following using ceria-based systems in heterogeneous catalysis.
One of the most topical issues related to oxygen vacancies on ceria surfaces is the relative stability of surface and subsurface defects and the location of the Ce3+ ions created upon reduction [13,14]. Recent theoretical work  using DFT with the HSE06 hybrid functional as well as the DFT+U approach has predicted the subsurface position is considerably more stable than the surface one and the excess electrons localize not on Ce ions which are the nearest neighbor to the defect as priorly suggested, but instead on those that are next-nearest neighbors. Notwithstanding recent STM  and atomic force microscope investigations  the location of the Ce3+ ions has remained experimentally undetermined.
Nanostructured ceria-based particles expose special adsorption sites close to edges and corners, giving rise to novel adsorption and reaction properties. They provide a significantly increased degree of complexity and an important advance towards mimicking real catalysts. Hence, there is a rapidly growing interest in ceria-based nanostructures. The theoretical modelling of such particles  and the spectroscopic identification of special adsorption sites represent still a great challenge, however. In this topic a closer connection between theory and experiment is desirable.
Experimental and theoretical studies of model systems using either metal aggregates deposited on a well characterized oxide substrate (conventional catalyst)  or oxidic aggregates deposited on a well characterized metal substrate (inverse catalyst)  as well as a mixed-metal oxide configuration , have proven to give valuable insight into the properties of the real-world catalysts for hydrogen production and highlighted the importance of synergy between experiment and theory in understanding model systems for heterogeneous catalysis. It has become clear that in such model metal-oxide catalysts, both the metal and the oxide can play a crucial role in the water-gas shift reaction and that the nature, size and morphology of both interacting phases needs to be further elucidated. The dissociation of water may be the rate limiting step which is expected to be facilitated by the presence of steps and defects such as oxygen vacancies in the metal-oxide systems. The scenario which is likely taking place in metal-oxide catalysts involves the interaction of CO with the metal, the dissociation of water helped by the oxide, and the reaction at the metal-oxide interface. Notwithstanding the progress, a full mechanistic picture including the identification of the catalytically active phase and the active sites as well as the determination of the relevant reaction pathways does not yet exist, and remains, in most cases, as an elusive goal without the support from theory.
The synergy between theory and experiment has already been been demonstrated for the VOx/CeO2 system. DFT+U calculations on theoretical models of CeO2 (111)-supported vanadia clusters in combination with experiments (STM, IRAS, and) on model catalysts (VOx/CeO2(111)) have been performed to investigate the distinctive properties of vanadia/ceria systems [19, 20]. As a result of these efforts, the atomic structure of low coverage species supported on CeO2(111) has been resolved to a far greater extent than in the past . Moreover, the effect of the support on the reactivity of the system for low vanadia loadings in the methanol ODH reaction has also just recently been elucidated using TPD and (DFT+U) calculated hydrogenation and oxygen vacancy formation energies as reactivity descriptors . At the origin of the support effect is the ability of ceria to stabilize reduced states by accommodating electrons in localized f-states. However, the role played by both oxide phases and a generally accepted mechanism for the oxidation reaction does not yet exist.
Despite some research successes, the field of the theoretical and experimental characterization of reducible oxide-based materials has not quite reached a state of maturity and there are still many important questions to be answered for a full understanding of reducible oxide based systems. One of the more urgent research topics to be addressed is related to the ability of the theoretical methods to provide reliable energies and an accurate description of the electronic structure of reduced oxide-based systems. Equally urgent is the identification of the nature and role of defects in the surface reactivity as well as to elucidate how ceria affects the reactivity of ceria-based catalysts.