Instantaneous normal mode approach to liquid state dynamics

The instantaneous normal mode (INM) approach to liquid state dynamics is presented. INM is put in historical context, and the underlying physical ideas, including the importance of the potential energy landscape, are explained. It is shown that INM can be the basis of a general starting point for dynamical calculations in liquids, and the theoretical developments necessary for future development are indicated. New results are given for the general INM formalism, as well as for depolarized light scattering, the ''Boson peak'' in supercooled liquids, friction on a vibrating bond, nonadiabatic solvent induced transitions of a quantum system coupled to a liquid, and diffusion in supercooled liquids.