The overall objective of this project is to develop a new generation of methods, algorithms and software that address the challenges of modeling chemical reactivity in applications such as C-H activation catalysis for chemical up-cycling of polymers. A layered approach will be taken that addresses length and timescale challenges using machine learning to explore chemical space, advances in the theory of rare events and non-equilibrium processes to address timescale challenges, and new developments in electronic structure methods of both low accuracy and high accuracy to overcome present system size limitations. Each of the above developments represent a partnership between theoretical chemists and chemical engineers as domain scientists, and applied mathematicians associated with the FastMath Institute. The partnership will enable a fusion of new physically motivated ideas from the domain scientists with advances in linear algebra and scalable libraries from applied math, to deliver computational tools that can utilize the resources of leadership class computing, in order to address present and future target applications in chemical reactivity modeling.