The proposal objective is to invent new approaches for manipulating quantum systems to enhance their nonlinear-optical response. Rather than studying specific systems, this work seeks to discover universal properties that are key to optimizing a material for a given task, which may identify altogether new and transformative materials paradigms and applications. The intellectual merit of this proposal is in the development of fundamental quantum mechanical concepts that build an understanding of the performance limit of optical materials and practical methods for attaining the limit. The fundamental knowledge gained will guide chemists and nanotechnologists in designing new materials and nanostrucutures, provide new paradigms to physicists/materials scientists for making novel functional materials, and generate ideas for engineers to develop novel devices. The broader impacts are diverse by virtue of the generality of the approach, which is based on sum rules that apply to all materials that interact with light including organic molecules, inorganic crystals, nanoparticles, smart materials, nanowires, etc. For example, medical imaging and diagnostics based on selective two-photon absorption would be made more efficient with better tagging chromophores. Other applications of this project include ultra fast switching for telecommunications, logic elements for computing, light-emitting materials for displays, and 3D photolithographic materials for optical memory. In addition to visits to local schools, online interactive resources will be developed to disseminate information to high-school and undergraduate-level students; and, numerical code that is developed as part of our work will be distributed over the web so that students can participate in publishable research.