Moore's Law states that the number of active components on an microchip doubles every 18 months. Variants of this Law can be applied to many measures of computer performance, such as memory and hard disk capacity, and to reductions in the cost of computations. Remarkably, Moore's Law has applied for over 50 years during which time computer speeds have increased by a factor of more than 1 billion! This remarkable rise of computational power has affected all of our lives in profound ways, through the widespread usage of computers, the internet and portable electronic devices, such as smartphones and tablets. Unfortunately, Moore's Law is not a fundamental law of nature, and sustaining this extraordinary rate of progress requires continuous hard work and investment in new technologies most of which relate to advances in our understanding and ability to control the properties of materials. Computer software plays an important role in enhancing computational performance and in many cases it has been found that for every factor of 10 increase in computational performance achieved by faster hardware, improved software has further increased computational performance by a factor of 100. Furthermore, improved software is also essential for extending the range of physical properties and processes which can be studied computationally. Our EPSRC Centre for Doctoral Training in Computational Methods for Materials Science aims to provide training in numerical methods and modern software development techniques so that the students in the CDT are capable of developing innovative new software which can be used, for instance, to help design new materials and understand the complex processes that occur in materials. The UK, and in particular Cambridge, has been a pioneer in both software and hardware since the earliest programmable computers, and through this strategic investment we aim to ensure that this lead is sustained well into the future.

Wherever advanced materials are required for technology theory and simulation have a vital role to play. That role may be in making a safety case, or reducing costs by narrowing down the selection of materials, or predicting and preventing failures. It may also be to establish whether and how materials may be designed to meet engineering specifications, or to interpret experimental characterizations of materials over a range of length and time scales.The need for this DTC cannot be overstated: there are no longer PhD graduates produced anywhere in the UK with a foundation knowledge of theoretical and computational materials physics. Current PhD graduates in theory and simulation of materials (TSM), with a first degree in a subject other than materials science, know extremely little about materials physics beyond the topic of their own research. On the other hand very few students with a first degree in materials science have sufficient training in mathematical techniques to engage in TSM at any level beyond the use of standard simulation packages. The need for breadth in the training of PhD graduates in TSM stems directly from the multi-scale and multi-physics nature of the vast majority of challenging problems in materials technology. The need exists both in industrial and academic research. The education and training provided by the DTC will be unique in the UK. For the first time in decades students will be taught theoretical materials physics at a sophisticated mathematical level, which will enable them to model the principal classes of materials across the length and time scales. They will also learn about the principal techniques of simulating materials at different length and time scales, and how information is transferred up and down the length and time scale hierarchies. The multidisciplinary training and research environment of the DTC, in combination with a wide range of cohort building and student empowerment activities, will provide a far richer educational and professional experience than a standard PhD funded through the DTA. The scientific network students will be able to form through the DTC with their peers, academics, industrialists and leading visiting scientists will be a lasting benefit for them.The DTC will bring together key staff of 4 departments across 2 faculties at Imperial College. Students will have 2 supervisors, whose expertise will not be centred at the same length scale. This will usually mean that their supervisors are in different departments. Similarly, no single department has the expertise to provide the range of courses that students will receive in their first year. For these reasons the multidisciplinary training and research environment can be delivered only through a DTC. Conversely, if the DTC is not funded then narrowly focused PhDs in TSM will continue to be generated with the same limited usefulness for industry, academe and the students themselves as they have in the past 2-3 decades.With nuclear power once again a key component of the Government strategy for energy there will be a significant demand from this sector for graduates of the DTC, as confirmed by the letter of support from UKAEA. Other forms of producing energy such as wind and solar power will also benefit. But TSM is needed in all advanced materials technologies, including aerospace and land-based transportation, building and construction, the processing, storage and communication of information, sport, prostheses and health-care, sensors and security, defence and more. The need from academic groups in the UK and overseas is also very significant. Indeed the absence of suitably trained PhD graduates is universally recognised in the attached letters of support from academics, national labs and industry, as one of their principal concerns. Judging by these letters the 50 graduates of the DTC funded by EPSRC are likely to be in very strong demand.

The Industrial Doctorate Centre in Molecular Modelling and Materials Science (M3S) at University College London (UCL) trains researchers in materials science and simulation of industrially important applications. As structural and physico-chemical processes at the molecular level largely determine the macroscopic properties of any material, quantitative research into this nano-scale behaviour is crucially important to the design and engineering of complex functional materials. The M3S IDC is a highly multi-disciplinary 4-year EngD programme, which works in partnership with a large base of industrial sponsors on a variety of projects ranging from catalysis to thin film technology, electronics, software engineering and bio-physics research. The four main research themes within the Centre are 1) Energy Materials and Catalysis; 2) Information Technology and Software Engineering; 3) Nano-engineering for Smart Materials; and 4) Pharmaceuticals and Bio-medical Engineering. These areas of research align perfectly with EPSRC's mission programmes: Energy, the Digital Economy, and Nanoscience through Engineering to Application. In addition, per definition an industrial doctorate centre is important to EPSRC's priority areas of Securing the Future Supply of People and Towards Better Exploitation. Students at the M3S IDC follow a tailor-made taught programme of specialist technical courses, as well as professionally accredited project management courses and transferable skills training, which ensures that whatever their first degree, on completion all students will have obtained thorough technical and managerial schooling as well as a doctoral research degree. The EngD research is industry-led and of comparable high quality and innovation as the more established PhD research degree. However, as the EngD students spend approximately 70% of their time on site with the industrial sponsor, they also gain first hand experience of the demanding research environment of a successful, competitive industry. Industrial partners who have taken up the opportunity during the first phase of the EngD programme to add an EngD researcher to their R&D teams include Johnson Matthey, Pilkington Glass, Exxon Mobil, Silicon Graphics, Accelrys and STS, while new companies are added to the pool of sponsors each year. Materials research in UCL is particularly well developed, with a thriving Centre for Materials Research and a newly established Materials Chemistry Centre. In addition, the Bloomsbury campus has perhaps the largest concentration of computational materials scientists in the UK, if not the world. Although affiliated to different UCL departments, all computational materials researchers are members of the UCL Materials Simulation Laboratory, which is active in advancing the development of common computational methodologies and encouraging collaborative research between the members. As such, UCL has a large team of well over a hundred research-active academic staff available to supervise research projects, ensuring that all industrial partners will be able to team up with an academic in a relevant research field to form the supervisory team to work with the EngD student. The success of the existing M3S Industrial Doctorate Centre and the obvious potential to widen its research remit and industrial partnerships into new, topical materials science areas, which are at the heart of EPSRC's strategic funding priorities for the near future, has led to this proposal for the funding of 5 annual cohorts of ten EngD students in the new phase of the Centre from 2009.

Quantum mechanics has had a profound and pervasive influence on science and technology. Phenomena that are intrinsically quantum mechanical, such as magnetism, electron transport in semiconductors, and the effect of impurity atoms in materials, lie at the heart of almost every branch of industry. Quantum mechanical calculations of properties and processes from ``first-principles'' are capable of making accurate quantitative predictions but require solving the Schrdinger equation which is extremely difficult and can only be done using powerful computers. In contrast, empirical modelling approaches are relatively cheap but lack the predictive power of first-principles methods (which are parameter-free and take as input only the atomic numbers of the constituent atoms). The predictive capability is essential, in order to make rapid progress on new and challenging problems where there is insufficient experimental data and to also generate useful empirical approaches or even to check their reliability when these exist. Within the class of first-principles methods, one approach that has been outstandingly successful is the Density Functional Theory (DFT) as it combines high accuracy with moderate computational cost. Nevertheless, the computational effort of performing calculations with conventional DFT approaches increases as the cube of the number of atoms, making them unable to tackle problems with more than a few hundred atoms even on modern supercomputers. Since the pioneering work of the Nobel laureate Walter Kohn, it has been known that it is possible to reformulate DFT so that it scales linearly, which would in principle allow calculations with many thousands or even millions of atoms. The practical realisation of this however, in a method which is as robust and accurate as conventional cubic-scaling DFT approaches has been extremely difficult. The ONETEP approach developed over many years by the applicants of this proposal has achieved just that. ONETEP is at the cutting edge of developments in first principles calculations. However, while the fundamental difficulties of performing accurate first-principles calculations with linear-scaling cost have been solved, only a small core of functionality is currently available in ONETEP which prevents its wide application. In this collaborative project between three Universities, the original developers of ONETEP will lead an ambitious workplan whereby the functionality of the code will be rapidly and significantly enriched. The code development ethic of ONETEP, namely that software is robust, user-friendly, modular, portable and highly efficient on current and future HPC technologies will be of fundamental importance and will be further strengthened by rigorous cross-checking between the three institutions of this proposal. The developments are also challenging from a theoretical point of view as they need to be within the linear-scaling framework of ONETEP, using its highly non-trivial formulation of DFT in terms of in situ optimised localised functions. The program of work provides much added value as the few fundamental enabling technologies that will be developed in its first stages will then underpin many of the functional capabilities that will follow. The result will be a tool capable of a whole new level of materials simulation at the nanoscale with unprecedented accuracy. It will find immediate application in simulations in molecular biology, nanostructures and materials, which underpin solutions in urgent current problems such as energy, environment and health. Through the increasing number of commercial and academic users and developers of ONETEP, the worldwide dissemination and wide use of this novel tool will be rapid; finally the expanding ONETEP Developers' Group will coordinate the best strategies for the future maintenance and development of the software.

The Centre for Doctoral Training in "Molecular Modelling and Materials Science" (M3S CDT) at University College London (UCL) will deliver to its students a comprehensive and integrated training programme in computational and experimental materials science to produce skilled researchers with experience and appreciation of industrially important applications. As structural and physico-chemical processes at the molecular level largely determine the macroscopic properties of any material, quantitative research into this nano-scale behaviour is crucially important to the design and engineering of complex functional materials. The M3S CDT offers a highly multi-disciplinary 4-year doctoral programme, which works in partnership with a large base of industrial and external sponsors on a variety of projects. The four main research themes within the Centre are 1) Energy Materials; 2) Catalysis; 3) Healthcare Materials; and 4) 'Smart' Nano-Materials, which will be underpinned by an extensive training and research programme in (i) Software Development together with the Hartree Centre, Daresbury, and (ii) Materials Characterisation techniques, employing Central Facilities in partnership with ISIS and Diamond. Students at the M3S CDT follow a tailor-made taught programme of specialist technical courses, professionally accredited project management courses and generic skills training, which ensures that whatever their first degree, on completion all students will have obtained thorough technical schooling, training in innovation and entrepreneurship and managerial and transferable skills, as well as a challenging doctoral research degree. Spending >50% of their time on site with external sponsors, the students gain first-hand experience of the demanding research environment of a competitive industry or (inter)national lab. The global and national importance of an integrated computational and experimental approach to the Materials Sciences, as promoted by our Centre, has been highlighted in a number of policy documents, including the US Materials Genome Initiative and European Science Foundation's Materials Science and Engineering Expert Committee position paper on Computational Techniques, Methods and Materials Design. Materials Science research in the UK plays a key role within all of the 8 Future Technologies, identified by Science Minister David Willetts to help the UK acquire long-term sustainable economic growth. Materials research in UCL is particularly well developed, with a thriving Centre for Materials Research, a Materials Chemistry Centre and a new Centre for Materials Discovery (2013) with a remit to build close research links with the Catalysis Technology Hub at the Harwell Research Complex and the prestigious Francis Crick Institute for biomedical research (opening in 2015). The M3S will work closely with these centres and its academic and industrial supervisors are already heavily involved with and/or located at the Harwell Research Complex, whereas a number of recent joint appointments with the Francis Crick Institute will boost the M3S's already strong link with biomedicine. Moreover, UCL has perhaps the largest concentration of computational materials scientists in the UK, if not the world, who interact through the London-wide Thomas Young Centre for the Theory and Simulation of Materials. As such, UCL has a large team of well over 100 research-active academic staff available to supervise research projects, ensuring that all external partners can team up with an academic in a relevant research field to form a supervisory team to work with the Centre students. The success of the existing M3S CDT and the obvious potential to widen its research remit and industrial partnerships into topical new materials science areas, which lie at the heart of EPSRC's strategic funding priorities and address national skills gaps, has led to this proposal for the funding of 5 annual student cohorts in the new phase of the Centre.