Effective Hamiltonians for Electronic Fine Structure and Polyatomic Vibrations

The effective Hamiltonian, H[[sup]]eff[[/sup]], is an important tool for analyzing and representing the spectra, energy levels, and dynamics of atoms and molecules. By replacing the rigorous but intractable exact Hamiltonian, H[[sup]]exact[[/sup]], with a model that is designed to share most of its essential qualitative and quantitative characteristics, the spectroscopist can derive valuable insights from raw, incomplete, and partially assigned spectra. These insights guide the optimal design of information-rich new experiments and computations and can reveal the dynamical mechanisms encoded in the spectra. Here we describe the theory, construction, and limitations of effective Hamiltonians, drawing examples primarily from the electronic fine structure of diatomic molecules and the vibrational structure of polyatomic molecules. Current ideas for extending the accuracy, flexibility, and mechanistic transparency of effective Hamiltonian models to future areas of research, especially at extremely high excitation energies, are discussed. Unconventional applications of traditional effective Hamiltonians are illustrated by example, especially schemes to visualize and classify large-amplitude motions. Quantum and classical mechanical H[[sup]]eff[[/sup]] models derived from frequency-domain spectra are the best possible sources for insights into time-domain phenomena. In particular, the existence of large-amplitude regular eigenstates embedded in a principally ergodic bath is uniquely relevant to schemes for external control of intramolecular dynamics and the validity of ergodicity-based predictions of the rates of unimolecular processes.