Ann. Rev. Phys. Chem. 1982. 33:223-55 Copyright © 1982 by Annual Reviews Inc. All rights reserved COMPLEX COORDINATES IN THE THEORY OF ATOMIC AND MOLECULAR STRUCTURE AND DYNAMICS William P. Reinhardt Department of Chemistry, University of Colorado and Joint Institute for Laboratory Astrophysics, University of Colorado and National Bureau of Standards, Boulder, Colorado 80309 INTRODUCTION During the past ten years there has been rapid developmentand applica- tion of a theory variously known as complex scaling, complex coordinates, coordinate-rotation, and dilatation analyticity, to problems of resonances in atomic and molecular physics and in chemistry. Resonances are ubiquitous. A few examples: 1. an excited species radiates; 2. a multiply excited atom autoionizes; 3. an atomic or molecular system in an external field is subject to field or multiphoton ionization; 4. an appropriately excited molecule dissociates unimolecularly; 5. electrons attach to molecules and the resulting quasibound molecular ions dissociate into stable ionic and neutral subsystems. Each of these processes is typified by the formation and decay of an intermediate state, or resonance, which is a nonstationary (or quasi- bound) state with a lifetime long enough to be well characterized, and long enough to make its explicit recognition of experimental and theoreti- cal importance. The simplest, and most naive, mathematical description of such states is that they resemble bound stationary states in that they are "localized" in space (at t =0), and their time evolution 223 0066-426X/82/1101-0223502.00 www.annualreviews.org/aronline Annual Reviews Annu. Rev. Phys. Chem. 1982.33:223-255. Downloaded from arjournals.annualreviews.org by University of California - Los Angeles on 05/27/08. For personal use only.