  The flux-flux correlation function formalism is a standard and widely used
approach for the computation of reaction rates. In this paper we introduce a
method to compute the classical and quantum flux-flux correlation functions for
anharmonic barriers essentially analytically through the use of the classical
and quantum normal forms. In the quantum case we show that the quantum normal
form reduces the computation of the flux-flux correlation function to that of
an effective one dimensional anharmonic barrier. The example of the computation
of the quantum flux-flux correlation function for a fourth order anharmonic
barrier is worked out in detail, and we present an analytical expression for
the quantum mechanical microcanonical flux-flux correlation function. We then
give a discussion of the short-time and harmonic limits.
