The last decade has seen an explosion of interest in two-dimensional materials, which now can be synthesized in either single or a few atomic layer forms. The discovery of novel fabrication methods for creating single-layer materials such as graphene, zinc oxide, silicon carbide, boron nitride, and molybdenum disulfide has opened a new field of materials research with promising applications for energy technologies. Single-layer materials not only represent the ultimate scaling in the vertical direction, but also show a variety of novel and useful electronic, optical, and mechanical properties. Using a data-mining and first-principles design approach we identify several previously unrecognized families of single-layer materials. We determine their energetic and dynamical stability, study their electronic and optical properties, and determine their suitability for electronic and energy applications using a combination of density-functional calculations with semi-local and hybrid density functionals, the many-body G0 W0 method, and the Bethe-Salpeter equation. To determine their suitability for photocatalytic water splitting we also determine their solubility in water. We discover several single-layer materials with promising properties for electronic devices such as for dielectric barriers in graphene field-effect tunneling transistors and for photocatalytic water splitting. Our results provide guidance for experimental synthesis efforts and future searches of materials suitable for applications in electronic device and energy technologies.