On effective potentials in classical mechanical systems

A classical mechanical variational method for computing effective potentials due to exact, first order and adiabatic constraints is presented. The effective potential can be used to envision in configuration space the restricted motion imposed by the constraints relative to the full potential. It can locate effective equilibrium structures and transition barriers and saddles and can be used when combined with semi-classical ideas to delineate regions of quantum packet flow and stationary state localization. The latter gives information on energy flow in a system and on the nature of basis sets needed for full quantum calculations. The advantage of the method is that is does not involve the solution of any equations of motion. The ideas are illustrated by some examples coming from the area of atomic and molecular dynamics.