Dan Neuhauser is supported by a grant from the Theoretical and Computational Chemistry Program to continue his research on quantum molecular dynamics calculations of four-atom reactions. The method development will involve time-dependent simulations with spatial-grid reduction, and a Filter-Diagonalization-based hybrid approach. Crucial elementary combustion reactions will be chosen as the applications. A smaller portion of this research will concern extension of the Filter-Diagonalization method to semiclassical methodology, which is routinely employed for systems with many more degrees of freedom. Modern dynamical methods will be developed and applied to the study of four-atom chemical reactions. This class of reactions is fundamental to the fields of enviromental and combustion chemistry. Methodological extensions to reactions of more than four atoms will also be developed, since larger scale reactions are of interest in elucidating, for example, surface chemistry phenomena.