1.IntroductionThe highlight in this area over the past two years is the rapid development of computing power and the proliferation of graphics-led packages that exploit this. This has made feasible the study of problems involving unit cells with large numbers of atoms and solids that are disordered or stable at high temperatures/and or pressures, for example studies of the role of water in zeolites1and the properties of solids found in planetary interiors.2The previous Annual Report in this area3introduced the techniques and demonstrated the wide applicability of solid state modelling with examples mainly taken from the author’s laboratory. I shall not, therefore, repeat the methodologies, but concentrate on applications covering the period 2005–2007, attempting to widen the coverage to areas given less emphasis in the previous article, whilst updating work on important areas, and to major groups worldwide. Even so there are major areas that I do not have room to cover. The most important of these is modelling of surfaces.Zeolites and related solids continue to be a lively area of research. An increasing number of studies are using quantum mechanical methods and/or molecular dynamics to study these solids. Many zeolites contain water and this has not been easy to model. Water itself is difficult to deal withviaclassical methods and the size of the unit cell and the numbers of water molecules in the structure have made quantum mechanical approaches prohibitively expensive. In recent years, however, great progress has been made on describing water in zeolites and related solids;1both the siting of water molecules and,viamolecular dynamics, its diffusion through the solid.Oxides, particularly those with industrially important properties, have also attracted much work. The description of strongly correlated solids, that is those in which metal d electrons are highly localised, is currently a very active field with several approaches being explored. Such solids often have interesting properties such as colossal magnetoresistance (CMR) and there have been a number of studies aimed at linking crystal and/or electronic structure to properties. A recently-introduced method, Dynamic Mean Field Theory (DMFT),4currently shows potential for calculations on strongly correlated solids and, in particular, for band gap transitions. Calculations on isolated defects have generally used interatomic potential methods, however recent work has shown that it is now possible to performab initioruns on supercells that are sufficiently large that defect–defect interaction is negligible. Atomistic simulation has proved valuable for investigating the mechanism of ionic conduction in solids. Such studies involve following changes in energy as a particular ion migrates through the solid and classical interatomic potential methods have proved well-suited to this task. The advantage of the method being that it enables local lattice relaxation around the migrating ion, whereasab initiomethods generally relax the whole lattice. A recent notable example of such an investigation is the identification of novel oxide ion and proton diffusion mechanisms for solids containing tetrahedral MO4groups.5Increases in computer power and memory have led to studies of solids at high temperatures and pressures becoming feasible. This is particularly important for minerals and an interesting example of this is work on minerals of the Earth’s mantle. The lowest layer of the mantle has interesting seismic properties but with temperatures of around 4000 K and pressure of about 135 GPa, it is not very easy to study possible components of this layer experimentally. A form of MgSiO3that could be a major component has been identified using both theory and experiment6,7and a number of studies8–13calculate properties for comparison with experimental observation.The final area I address is nanotubes and related structures. Modelling of these can be approached either from a molecular point of view or as an example of a solid. There has been much work on carbon nanotubes, both single-walled (SWCNTs) and multiwalled (MWCNTs) and on graphene, the single graphite layer. Defects in carbon nanotubes and nanotubes constructed from other materials have also attracted interest. An unusual angle on carbon nanotubes is the prediction of the structure of crystals formed inside