In this project in the Physical Chemistry Program, Hayden and Wells address basic mathematical and computational problems inherent in determining the structure of macromolecules from various experimental data, especially nuclear magnietc resonance spectroscopy. Presently this category of nonlinear optimization problems is completely solvable only for small molecules. A new characterization of Euclidean distance matrices has provided new insight into these problems and provides the foundation for the development of an algorithm for the embedding problem of computational chemistry. This algorithm, based on von Neumann's idea of alternating projections, promises a dramatic reduction in computational time for certain phases of the overall structure determination. In numerous test cases the time reduction is from exponential order to polynomial growth of order four.
