This grant is funded from the Theoretical and Computational Chemistry program under the Computational Science and Engineering Initiative. Its purpose is to study simple chemical reactions in full quantum-mechanical detail to gain understanding of the complex changes that take place when an atom reacts with a two-atom molecule. The general area of this research has been singled out by the National Research Council in its recent report, "Opportunities in Chemistry," as one of the most important unsolved problems in chemistry. The recently developed Adiabatically adjusting Principal axis Hyperspherical (APH) coordinate formalism will be used to study three-body rearrangement processes. Exact three-dimensional reactive scattering cross sections will be calculated for the systems D + H2 = HD + H and e+ + H = Ps + p+, using accurate potential energy surfaces. The results will be used to interpret existing and future experimental data obtained at other research laboratories. Also, exact S-matrices will be determined at several values of the total angular momentum for the systems F + H2 = HF + H and LiH + F = Li + HF. The work involves close collaboration between Professor Parker's research group at Oklahoma and that of Dr. Russell Pack at Los Alamos Scientific Laboratory.