  In this article, we propose a generalized model for nonequilibrium
vibrational energy distribution functions. The model can be used, in place of
equilibrium (Boltzmann) distribution functions, when deriving reaction rate
constants for high-temperature nonequilibrium flows. The distribution model is
derived based on recent \textit{ab initio} calculations, carried out using
potential energy surfaces developed using accurate computational quantum
chemistry techniques for the purpose of studying air chemistry at high
temperatures. Immediately behind a strong shock wave, the vibrational energy
distribution is non-Boltzmann. Specifically, as the gas internal energy rapidly
excites to a high temperature, overpopulation of the high-energy tail (relative
to a corresponding Boltzmann distribution) is observed in \textit{ab initio}
simulations. As the gas excites further and begins to dissociate, a depletion
of the high-energy tail is observed, during a time-invariant quasi-steady state
(QSS). Since the probability of dissociation is exponentially related to the
vibrational energy of the dissociating molecule, the overall dissociation rate
is sensitive to the populations of these high vibrational energy states. The
non-Boltzmann effects captured by the new model either enhance or reduce the
dissociation rate relative to that obtained assuming a Boltzmann distribution.
This article proposes a simple model that is demonstrated to reproduce these
non-Boltzmann effects quantitatively when compared to \textit{ab initio}
simulations.
