Schatz is a theoretician who studies the optical, structural and thermal properties of nanomaterials, including plasmonic nanoparticles, DNA and peptide nanostructures, and carbon-based materials, with applications in chemical and biological sensing, electronic and biological materials, high performance fibers, and solar energy. His past work has also been concerned with understanding the dynamics of chemical reactions in the gas phase and in gas-surface collisions.

In the field of chemical reaction dynamics, Schatz was one of the pioneers in the application of quantum scattering methods to determine the cross sections and rates of simple gas phase reactions such as H + H2. He was also active in using these methods to describe the spectra of transition states, and he was involved in the discovery of resonances in a number of chemical reactions, including F + H2, Cl + HCl and I + HI. In addition, he has developed quasiclassical methods for describing state-resolved collision processes involving polyatomic molecules, and he has developed potential energy surfaces for many benchmark reactions. With these methods and surfaces, he was involved in early studies of many reactions important in combustion and atmospheric chemistry, including OH + H2 and OH + CO, and he has contributed to studies of reactions involved in the low earth orbit environment and nonequilibrium materials chemistry, including reactions of hyperthermal atomic oxygen ( and other atoms) with small molecules and with surfaces. In addition, he has worked actively in the theory and modeling of the mechanical properties of hard materials, including diamond films, graphene and carbon nanotubes.