About the Author: ILYA PRIGOGINE is Director of the Instituts Internationaux de Physique et de Chimie, E. Solvay, Brussels, Belgium. One of the foremost figures in his field, Professor Prigogine is the Ashbel Smith Professor of Physics and Chemical Engineering at the University of Texas at Austin, where he is also Director of the Ilya Prigogine Center for Studies in Statistical Mechanics and Complex Systems. He is the holder of many scientific prizes, 35 honorary degrees, special chairs, and visiting professorships. In 1977 he was awarded the Nobel Prize in chemistry. Professor Prigogine is a member of many national academies, including the Russian National Academy of Sciences. In 1989 he was given the title of viscount by the King of Belgium. STUART A. RICE is the Frank P. Hixon Distinguished Service Professor in the James Franck Institute and the Department of Chemistry of the University of Chicago. A former dean of the university's Division of Physical Sciences, Professor Rice is a world-renowned authority on chemical physics who has received scores of awards and honors. A former Alfred P. Sloan Fellow and Guggenheim Fellow, Professor Rice is also a Fellow of the American Academy of Arts and Sciences, the National Academy of Sciences, and the American Philosophical Society. Contributors: Douglas J. Doren, Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware. Dominik Marx, Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany Keiji Morokuma, Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, Atlanta, Georgia Djamaladdin G. Musaev, Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, Atlanta, Georgia Sanford A. Safron, Department of Chemistry, Florida State University, Tallahassee, Florida Horst Wiechert, Institut fu Physik, Johannes Gutenberg-Universität, Mainz, Germany