  In this paper we derive a general expression for the transmission coefficient
using the method of reactive flux for a particle coupled to a harmonic bath
surmounting a one dimensional inverted parabolic barrier. Unlike Kohen and
Tannor [J. Chem. Phys. 103, 6013 (1995)] we use a normal mode analysis where
the unstable and the other modes have a complete physical meaning. Importantly
our approach results a very general expression for the time dependent
transmission coefficient not restricted to overdamped limit. Once the spectral
density for the problem is know one can use our formula to evaluate the time
dependent transmission coefficient. We have done the calculations with time
dependent friction used by Xie [Phys. Rev. Lett 93, 180603 (2004)] and also the
one used by Kohen and Tannor [J. Chem. Phys. 103, 6013 (1995)]. Like the
formula of Kohen and Tannor our formula also reproduces the results of
transition state theory as well as the Kramers theory in the limits t->0 and
t->infinity respectively.
