Mean-field models for molecular states and dynamics: New developments

For accurate description of vibration/rotation eigenstates of molecules, and for discussion of reactions and relaxation processes, simple independent-mode pictures are generally inadequate. Mean-field methods, in which each mode acts subject to a mean potential (static or dynamic) that is just the exact potential averaged over all other modes of the system, are attractive for treating such problems for several reasons: they are conceptually simple, numerically tractable, quantitatively quite accurate, and generally applicable to a wide variety of molecular species, energies, and coupling conditions. For these reasons, such mean-field, or self-consistent-field, techniques have been applied to molecular problems quite extensively within the last decade. We discuss several aspects of recent and current work on mean-field applications to molecular problems. In the class of static mean-field, or self-consistent-field, methods such situations include inversion of vibration/ rotation spectra to obtain potential energy surfaces, distorted-wave Born approximation work on vibrational predissociation lifetimes of long-lived van der Waals complexes, and an extension of the Slater theory for unimolecular decay rates in the weak-coupling regime. Applications of time-dependent SCF, or TDSCF, include a linearized approximation for investigation of long-time processes and study of the Fourier representation to derive random-phase approximations for direct calculation both of excitation energies and of instabilities and lifetimes. Several intriguing problems remain in the general area of mean-field methods for molecular systems: these include optimal choice of coordinate systems, selection of initial state in dynamical problems, and methods for tractable extension of mean-field approximations.