Modelling metal centres, acid sites and reaction mechanisms in microporous catalysts.

We discuss the role of QM/MM (embedded cluster) computational techniques in catalytic science, in particular their application to microporous catalysis. We describe the methodologies employed and illustrate their utility by briefly summarising work on metal centres in zeolites. We then report a detailed investigation into the behaviour of methanol at acidic sites in zeolites H-ZSM-5 and H-Y in the context of the methanol-to-hydrocarbons/olefins process. Studying key initial steps of the reaction (the adsorption and subsequent methoxylation), we probe the effect of framework topology and Brønsted acid site location on the energetics of these initial processes. We find that although methoxylation is endothermic with respect to the adsorbed system (by 17-56 kJ mol(-1) depending on the location), there are intriguing correlations between the adsorption/reaction energies and the geometries of the adsorbed species, of particular significance being the coordination of methyl hydrogens. These observations emphasise the importance of adsorbate coordination with the framework in zeolite catalysed conversions, and how this may vary with framework topology and site location, particularly suited to investigation by QM/MM techniques.

Determination of the nitrogen vacancy as a shallow compensating center in GaN doped with divalent metals.

We report accurate energetics of defects introduced in GaN on doping with divalent metals, focusing on the technologically important case of Mg doping, using a model that takes into consideration both the effect of hole localization and dipolar polarization of the host material, and includes a well-defined reference level. Defect formation and ionization energies show that divalent dopants are counterbalanced in GaN by nitrogen vacancies and not by holes, which explains both the difficulty in achieving p-type conductivity in GaN and the associated major spectroscopic features, including the ubiquitous 3.46 eV photoluminescence line, a characteristic of all lightly divalent-metal-doped GaN materials that has also been shown to occur in pure GaN samples. Our results give a comprehensive explanation for the observed behavior of GaN doped with low concentrations of divalent metals in good agreement with relevant experiment.

The reactivity of CO2 and H2 at trapped electron sites at an oxide surface.

We investigate the reactivity to H2 of a chemisorbed CO2 species at electron traps on oxide surfaces, taking the single electron F(+) oxygen vacancy of the MgO(100) terrace as a model system. We find that multiple hydrogen addition steps form three interacting catalytic cycles, leading to the evolution of formaldehyde, methanol or methane. Our results have general implications for the reactivity of CO2 on metal oxides.

Double bubbles: a new structural motif for enhanced electron-hole separation in solids.

Electron-hole separation for novel composite systems comprised of secondary building units formed from different compounds is investigated with the aim of finding suitable materials for photocatalysis. Pure and mixed SOD and LTA superlattices of (ZnO)12 and (GaN)12, single-shell bubbles are constructed as well as core@shell single component frameworks composed of larger (ZnO)48 and (GaN)48 bubbles with each containing one smaller bubble. Enthalpies of formation for all systems are comparable with fullerenes. Hole and electron separation is achieved most efficiently by the edge sharing framework composed of (GaN)12@(ZnO)48 double bubbles, with the hole localised on the nitrogen within the smaller bubbles and the excited electron on zinc within the larger cages.

The reactivity of CO2 on the MgO(100) surface.

We investigate the adsorption of CO2 over an MgO(001) terrace, as calculated using an embedded cluster method. We find adsorbed geometries for CO2 on the perfect surface with energies which differ appreciably from previous studies, and observe that it is polarization of the surface rather than the inclusion of electron correlation which leads to this discrepancy. Our results suggest that both monodentate and tridentate carbonate formation on the MgO(001) surface are favourable processes, with the monodentate structure being of lower energy. Adsorption of CO2 is found to be favourable at both F(0) and F(+) terrace sites, but not at F(2+). We also find that chemisorption at oxygen vacancy sites with a single localized electron (F(+)) could provide a route for the conversion of CO2 to other products, and that this system may be a useful model for other, more effective catalysts.

One-dimensional embedded cluster approach to modeling CdS nanowires.

We present an embedded cluster model to treat one-dimensional nanostructures, using a hybrid quantum mechanical/molecular mechanical (QM/MM) approach. A segment of the nanowire (circa 50 atoms) is treated at a QM level of theory, using density functional theory (DFT) with a hybrid exchange-correlation functional. This segment is then embedded in a further length of wire, treated at an MM level of theory. The interaction between the QM and MM regions is provided by an embedding potential located at the interface. Point charges are placed beyond the ends of the wire segment in order to reproduce the Madelung potential of the infinite system. We test our model on the ideal system of a CdS linear chain, benchmarking our results against calculations performed on a periodic system using a plane-wave DFT approach, with electron exchange and correlation treated at the same level of approximation in both methods. We perform our tests on pure CdS and, importantly, the system containing a single In or Cu impurity. We find excellent agreement in the determined electronic structure using the two approaches, validating our embedded cluster model. As the hybrid QM/MM model avoids spurious interactions between charged defects, it will be of benefit to the analysis of the role of defects in nanowire materials, which is currently a major challenge using a plane-wave DFT approach. Other advantages of the hybrid QM/MM approach over plane-wave DFT include the ability to calculate ionization energies with an absolute reference and access to high levels of theory for the QM region which are not incorporated in most plane-wave codes. Our results concur with available experimental data.

Advances in computational studies of energy materials.

We review recent developments and applications of computational modelling techniques in the field of materials for energy technologies including hydrogen production and storage, energy storage and conversion, and light absorption and emission. In addition, we present new work on an Sn2TiO4 photocatalyst containing an Sn(II) lone pair, new interatomic potential models for SrTiO3 and GaN, an exploration of defects in the kesterite/stannite-structured solar cell absorber Cu2ZnSnS4, and report details of the incorporation of hydrogen into Ag2O and Cu2O. Special attention is paid to the modelling of nanostructured systems, including ceria (CeO2, mixed Ce(x)O(y) and Ce2O3) and group 13 sesquioxides. We consider applications based on both interatomic potential and electronic structure methodologies; and we illustrate the increasingly quantitative and predictive nature of modelling in this field.

The effect of local environment on photoluminescence: a time-dependent density functional theory study of silanone groups on the surface of silica nanostructures.

The optical absorption spectrum and lowest photoluminescence (PL) signal for silanone terminated silica nanostructures are studied using time-dependent density functional theory calculations on a range of realistic low energy silica nanocluster models. We show that the broad experimental absorption spectrum for silanone centers [V. A. Radtsig and I. M. Senchenya Russ. Chem. Bull. 45, 1849 (1996)] is most likely the result of a synergetic combination of inhomogeneous broadening, thermal broadening and the small energy differences between different excitations. We further demonstrate that upon relaxation of the excited state the excited electron and hole localize on only one silanone center, and that there is a clear and distinct link between the local environment of a silanone center and its absorption and PL spectra. Finally, we provide strong evidence that the silanone center does not have a double bond between the constituent silicon and oxygen atoms but rather can be probably more aptly described as the =Si(+)-O(-) charge-transfer species.

Construction of nano- and microporous frameworks from octahedral bubble clusters.

We report a general method of constructing microporous, cubic frameworks from eight different high symmetry small clusters of ZnO, which were previously predicted via the application of an evolutionary algorithm. Using interatomic potentials, the lattice energies of the structures formed are computed. We analyse the relative stabilities within particular subsets of these periodic structures, and show that frameworks constructed from edge-sharing units of clusters with the T(h) point group are predicted to be much more stable than those with T(d). Our results have general implications for the nanostructures of systems whose bulk structures are based on tetrahedral coordination.

Bubbles and microporous frameworks of silicon carbide.

We report the results of density functional theory calculations on nanostructures of SiC, including single clusters, cluster dimers, and nanoporous cluster frameworks. Our results show that at the nanoscale, there is significant charge transfer of 2.5|e| from Si to C atoms, which results in the adoption of the same structural motifs for nanoparticles of SiC that occur for ZnO, with clusters of T(h), T(d), and O symmetry. Experimental support for our models is provided by comparison of optical gaps and ionisation potentials. With the exception of the (SiC)(28) cluster, the T(h) or T(d) nanoparticles can bind into kinetically stable agglomerates on either tetragonal or hexagonal faces, with tetragonal binding energetically preferred for larger nanoclusters, which enables the construction of cubic nanoporous frameworks of varying porosities. Frameworks composed of larger clusters are softer; with bulk moduli of ca. 20 GPa while frameworks assembled from smaller clusters tend to be harder. The electronic structure of all frameworks can be analysed in terms of the adopted short-range order of the clusters, we predict that frameworks containing topological features similar to the rock-salt phase are metallic in nature.

Optical excitations of defects in realistic nanoscale silica clusters: comparing the performance of density functional theory using hybrid functionals with correlated wavefunction methods.

Optical excitations of low energy silica (SiO(2))(4) clusters obtained by global optimization, as opposed to constructed by hand, are studied using a range of theoretical methods. By focusing on the lowest energy silica clusters we hope to capture at least some of the characteristic ways by which the dry surfaces of silica nanosystems preferentially terminate. Employing the six lowest energy (SiO(2))(4) cluster isomers, we show that they exhibit a surprisingly wide range of geometries, defects, and associated optical excitations. Some of the clusters show excitations localized on isolated defects, which are known from previous studies using hydrogen-terminated versions of the defect in question. Other clusters, however, exhibit novel charge-transfer excitations in which an electron transfers between two spatially separated defects. In these cases, because of the inherent proximity of the constituent defects due to the small cluster dimensions, the excitation spectrum is found to be very different from that of the same defects in isolation. Excitation spectra of all clusters were calculated using time-dependent density functional theory (TD-DFT) and delta-SCF DFT (DeltaDFT) methods employing two different hybrid density functionals (B3LYP and BB1K) differing essentially in the amount of incorporated Hartree-Fock-like exchange (HFLE). In all cases the results were compared with CASPT2 calculated values which are taken as a benchmark standard. In line with previous work, the spatially localized excitations are found to be well described by TD-DFT/B3LYP but which gives excitation energies that are significantly underestimated in the case of the charge-transfer excitations. The TD-DFT/BB1K combination in contrast is found to give generally good excitation energies for the lowest excited states of both localized and charge-transfer excitations. Finally, our calculations suggest that the increased quality of the predicted excitation spectra by adding larger amounts of HFLE is mainly due to an increased localization of the excited state associated with the elimination of spurious self-interaction inherent to (semi-)local DFT functionals.

Structure, optical properties and defects in nitride (III-V) nanoscale cage clusters.

Density Functional Theory calculations are reported on cage structured BN, AlN, GaN and InN sub- and low nanosize stoichiometric clusters, including two octahedral families of T(d) and T(h) symmetry. The structures and energetics are determined, and we observe that BN clusters in particular show high stability with respect to the bulk phase. The cluster formation energy is demonstrated to include a constant term that we attribute to the curvature energy and the formation of six tetragonal defects. The (BN)(60) onion double-bubble structure was found to be particularly unstable. In contrast, similar or greater stability was found for double and single shell cages for the other nitrides. The optical absorption spectra have been first characterised by the one-electron Kohn-Sham orbital energies for all compounds, after which we concentrated on BN where we employed a recently developed Time Dependent Density Functional Theory approach. The one-electron band gaps do not show a strong and consistent size dependency, in disagreement with the predictions of quantum confinement theory. The density of excited bound states and absorption spectrum have been calculated for four smallest BN clusters within the first ionisation potential cut-off energy. The relative stability of different BN clusters has been further explored by studying principal point defects and their complexes including topological B-N bond rotational defects, vacancies, antisites and interstititials. The latter have the lowest energy of formation.

The nature of the oxidation states of gold on ZnO.

The interaction between gold in the 0, i, ii and iii oxidation states and the zinc-terminated ZnO(0001) surface is studied via the QM/MM electronic embedding method using density functional theory. The surface sites considered are the vacant zinc interstitial surface site (VZISS) and the bulk-terminated island site (BTIS). We find that on the VZISS, only Au(0) and Au(i) are stable oxidation states. However, all clusters of i to iii oxidation states are stable as substitutionals for Zn2+ in the bulk terminated island site. Au(OH)(x) complexes (x= 1-3) can adsorb exothermically onto the VZISS, indicating that higher oxidation states of gold can be stabilised at this site in the presence of hydroxyl groups. CO is used as a probe molecule to study the reactivity of Au in different oxidation states in VZISS and BTIS. In all cases, we find that the strongest binding of CO is to surface Au(i). Furthermore, CO binding onto Au(0) is stronger when the gold atom is adsorbed onto the VZISS compared to CO binding onto a gas phase neutral gold atom. These results indicate that the nature of the oxidation states of Au on ZnO(0001) will depend on the type of adsorption site. The role of ZnO in Au/ZnO catalysts is not, therefore, merely to disperse gold atoms/particles, but to also modify their electronic properties.

Computational approaches to the determination of active site structures and reaction mechanisms in heterogeneous catalysts.

We apply quantum chemical methods to the study of active site structures and reaction mechanisms in mesoporous silica and metal oxide catalysts. Our approach is based on the use of both molecular cluster and embedded cluster (QM/MM) techniques, where the active site and molecular complex are described using density functional theory (DFT) and the embedding matrix simulated by shell model potentials. We consider three case studies: alkene epoxidation over the microporous TS-1 catalyst; methanol synthesis on ZnO and Cu/ZnO and C-H bond activation over Li-doped MgO.

The surgical repair of a defect of tendinous distortion of the patella and of the joint capsule during an arthrolysis of the knee joint.

The suture of tissues resected during surgical tendomyolysis and arthrolysis of the knee joint required by its extension contracture is carried out during tibial flexion at an angle of 90 degrees. This can lead to the development of a diastasis of the tendinous distortion of the patella and of the joint capsule which prevents the suture of the wound. It is suggested to repair the resulting tissue defect with the use of a split flap of local tissues with a wide base situated in front of the defect. The flap is dissected from the lateral part of the tendinous distortion and of the capsule. The flap is turned by 180 degrees around its base and extended to cover the defect with its subsequent suture to the opposite edge of the defect. The described supplementary surgical procedure is technically uncomplicated and results in stable anterior and lateral joint structures, in a reduction of the risk of complications due to infection, and allows an early initiation of active kinesitherapy in the early postoperative period.