A number of physical processes, such as autoionization, predissociation, ac-or dc-field-induced ionization, multiphoton dissociation, or chemical transformations, can be formulated as problems involving a nonstationary state satisfying a time-independent complex eigenvalue S c w i n g e r equation (CESE). The CESE gives rise to all the conceptual and practical difficulties associated with the polyelectronic structures of excited states, as well as novel ones due to the presence of external fields and to the physical significance of the continuous spectrum. In a series of articles from this institute, it has been shown how advanced electronic structure theory and methods suitable for excited states can be integrated in a practical way into selected elements of the rigorous theory of discrete states interacting with the continuous spectrum in order to solve the CESE nonperturbatively and efficiently and compute properties such as positions and widths of inner hole or multiply excited states, multiphoton ionization rates, multichannel predissociation lifetimes, nonlinear static and frequency-dependent polarizabilities, and tunneling rates. The present article constitutes a review of the basic features of this theory and its computational methods. 0 1994 John Wiley & Sons, Inc.
I. Nonstationary States and the Complex Eigenvalue Schrodinger Equation (CESE)The discrete spectrum of field-free multiparticle Hamiltonians, H, is defined by the stationary states of H satisfying the real eigenvalue Schrodinger equation (RESE):with ' P, , square-integrable. Considerable effort has been spent for the development of formalism and accurate computation of ' P,, and of related properties for ground or low-lying discrete states in the Born-Oppenheimer approximation. The methods are based on some form of hierarchical incorporation of electron correlation effects beyond a zeroth-order single or multiconfigurational model that is computable accurately. The conceptual foundations of these many-body methods and their degree of suitability for computing and interpreting the *,, of ground (especially) and of low-lying excited states have been understood since the early developments of quantum theory and since the advances that occurred in the 1950s and 1960s.On the other hand, the continuous spectrum is defined by stationary states, 'P(E), satisfying