Excited vibrational states of polyatomic molecules: The semiclassical self-consistent field approach

An outline is given of self-consistent field methods for treating the coupled vibrations of polyatomic systems and some applications to energy level structure and dissociation dynamics of molecules and clusters are described. The SCF approximation describes each mode as moving in an average field of all other modes; the mean fields for the single modes are determined by a self-consistency condition. The method is computationally simple, applicable to relatively large systems, and can be formulated for static or for time-dependent problems, in classical, semiclassical, or quantum representations. We discuss several aspects of static SCF, including vibrational energy level and eigenstate determination, with applications to spectroscopy of highly excited states, inversion methods for obtaining polyatomic potential surfaces, metastable states, and finally the validity range of SCF and its extensions. For time-dependent SCF, we discuss dissociation of van der Waals molecules both in the strong coupling (Ar₃, RRKM-like) and weak coupling (I₂Ne, Slater-like) regimes, and vibrational relaxation in polyatomic clusters (I₂Ne_N). In each of these cases, SCF techniques are fairly accurate, and offer convenient physical interpretation. We believe that these advantages will result in an important place for these SCF methods in the theoretical discussion of vibrational energy states, flow, and dynamics.