TIME-DEPENDENT THEORETICAL TREATMENTS OF THE DYNAMICS OF ELECTRONS AND NUCLEI IN MOLECULAR-SYSTEMS

An overview is presented of methods for time-dependent treatments of m olecules as systems of electrons and nuclei. The theoretical details o f these methods are reviewed and contrasted in the light of a recently developed time-dependent method called electron-nuclear dynamics. Ele ctron-nuclear dynamics (END) is a formulation of the complete dynamics of electrons and nuclei of a molecular system that eliminates the nec essity of constructing potential-energy surfaces. Because of its gener al formulation, it encompasses many aspects found in other formulation s and can serve as a didactic device for clarifying many of the princi ples and approximations relevant in time-dependent treatments of molec ular systems. The END equations are derived from the time-dependent va riational principle applied to a chosen family of efficiently parametr ized approximate state vectors. A detailed analysis of the END equatio ns is given for the case of a single-determinantal state for the elect rons and a classical treatment of the nuclei. The approach leads to a simple formulation of the fully nonlinear time-dependent Hartree-Fock theory including nuclear dynamics. The nonlinear END equations with th e ab initio Coulomb Hamiltonian have been implemented at this level of theory in a computer program, ENDyne, and have been shown feasible fo r the study of small molecular systems. Implementation of the Austin M odel 1 semiempirical Hamiltonian is discussed as a route to large mole cular systems. The linearized END equations at this level of theory ar e shown to lead to the random-phase approximation for the coupled syst em of electrons and nuclei. The qualitative features of the general no nlinear solution are analyzed using the results of the linearized equa tions as a first approximation. Some specific applications of END are presented, and the comparison with experiment and other theoretical ap proaches is discussed.