This article describes the variational and fixed-node diffusion quantum Monte Carlo methods and how they may be used to calculate the properties of many-electron systems. These stochastic wave-function-based approaches provide a very direct treatment of quantum many-body effects and serve as benchmarks against which other techniques may be compared. They complement the less demanding density-functional approach by providing more accurate results and a deeper understanding of the physics of electronic correlation in real materials. The algorithms are intrinsically parallel, and currently available high-performance computers allow applications to systems containing a thousand or more electrons. With these tools one can study complicated problems such as the properties of surfaces and defects, while including electron correlation effects with high precision. The authors provide a pedagogical overview of the techniques and describe a selection of applications to ground and excited states of solids and clusters. CONTENTS

Advances in renewable and sustainable energy technologies critically depend on our ability to design and realize materials with optimal properties. Materials discovery and design efforts ideally involve close coupling between materials prediction, synthesis and characterization. The increased use of computational tools, the generation of materials databases, and advances in experimental methods have substantially accelerated these activities. It is therefore an opportune time to consider future prospects for materials by design approaches. The purpose of this Roadmap is to present an overview of the current state of computational materials prediction, synthesis and characterization approaches, materials design needs for various technologies, and future challenges and opportunities that must be addressed. The various perspectives cover topics on computational techniques, validation, materials databases, materials informatics, high-throughput combinatorial methods, advanced characterization approaches, and materials design issues in thermoelectrics, photovoltaics, solid state lighting, catalysts, batteries, metal alloys, complex oxides and transparent conducting materials. It is our hope that this Roadmap will guide researchers and funding agencies in identifying new prospects for materials design.

We demonstrate that electrochemically etched, hydrogen capped Si n H x clusters with n larger than 20 are obtained within a family of discrete sizes. These sizes are 1.0 (Si 29 ), 1.67 (Si 123 ), 2.15, 2.9, and 3.7 nm in diameter. We characterize the particles via direct electron imaging, excitation and emission optical spectroscopy, and colloidal crystallization. The band gaps and emission bands are measured. The smallest four are ultrabright blue, green, yellow and red luminescent particles. The availability of discrete sizes and distinct emission in the red, green and blue ͑RGB͒ range is useful for biomedical tagging, RGB displays, and flash memories.