  A new approach to calculate the vibrational distribution function of
molecules in a medium providing energy for vibrational excitation is proposed
and demonstrated. The approach is an improvement of solution methods based on
the drift-diffusion Fokker-Planck (FP) equation for a double differentiable
function representing the vibrational populations on a continuum internal
energy scale. A self-consistent numerical solution avoids approximations used
in previous analytical solutions. The dissociation flux, a key parameter in the
FP equation, is fixed using the kinetics of molecular dissociation from
near-continuum levels, so that the vibrational kinetics becomes a functional
problem. The approach is demonstrated for the kinetics of asymmetric stretching
of CO2, showing that it represents an alternative, potentially much more
efficient in computational terms, to the presently usual state-to-state
approach which is based on the kinetics of the populations of individual
levels, and gives complementary insight into the dissociation process.
