A classical determination of vibrationally adiabatic barriers and wells of a collinear potential energy surface

Abstract

A necessary and sufficient condition for the existence of a classical vibrationally adiabatic barrier or well in collinear systems is the existence of periodic orbit dividing surfaces. Knowledge of all pods immediately provides all adiabatic barriers and wells. Furthermore, the classical equation connecting the barriers and wells to the masses and potential energy surface of the system is shown, under mild conditions, to be identical in form to the corresponding quantal equation. The only difference is in the determination of the vibrational state which is obtained by WKB quantization classically. The classical barriers and wells can therefore be used to analyze quantal computations. Such analysis is provided for the hydrogen exchange reaction and the F+HH system. A novel result is the existence of vibrationally adiabatic barriers even where no saddle point exists on the static potential energy surface. These barriers are an outcome of competition between the increase of potential energy and decrease of vibrational force constant along the reaction coordinate. Their existence is therefore of general nature — not limited to the specific structure of a given potential energy surface. The experimental significance of these barriers is discussed. The implications on the use of forward or reverse quasiclassical computations is analyzed. A definite conclusion is that one should not average over initial vibrational action in such calculations.