In this project in the Theoretical and Computational Program of the Chemistry Division, Professor Harriman will study new methodologies in the field of quantum chemistry. His contributions to density matrix theory have the potential for allowing chemists to improve their understanding of laser and nuclear magnetic resonance phenomena, as well as to perform accurate calculations on larger molecules than is possible at present. This project deals with reduced density matrices, which provide one of the best ways of summarizing the essential information about a many-electron system in compact and useful form, and density functional theory, which is an effective method for dealing with large systems.