The prediction of new materials is, in theory, a completely straightforward problem. The fundamental equations of quantum mechanics for solids are well-established and can be numerically solved, at least approximately, by powerful first-principles methods developed over the last decade. It remains, then, only to examine the solutions to find those systems that will exhibit the properties desired.

The number of possibilities to be considered and sorted is many orders of magnitude larger than can be managed in a case-by-case first-principles analysis. Therefore, in practice, the approach to theoretical prediction of new materials is to establish easy-to-apply rules for screening large numbers of candidate stoichiometrics (which might or might not be known compounds). These rules are based on physical understanding of the occurrence of the structure or property, inference from known examples, and general principles governing chemical trends in the structure and stability of known compounds. Data from the scientific literature on the occurrence and structure of crystalline compounds are now organized into a number of crystallographic databases, providing a unique opportunity to investigate, from a global perspective, the factors that influence structure and stability. To display, access, and extract general principles from this enormous amount of information, a graphical method such as the “quantum diagram” method is essential, and can be thought of as providing a convenient “roadmap” for navigation around the database. Useful conclusions about individual compounds or small sets of compounds can also be drawn from this type of analysis. These conclusions form the basis for rules for predicting new representatives that direct attention to special regions on the roadmap, as illustrated on the cover of this issue. Systems that satisfy these rules are the most likely to reward experimental investigation.