  Based on a quantum Langevin equation and its corresponding Hamiltonian within
a c-number formalism we calculate the vibrational dephasing rate of a cubic
oscillator. It is shown that leading order quantum correction due to
anharmonicity of the potential makes a significant contribution to the rate and
the frequency shift. We compare our theoretical estimates with those obtained
from experiments for small diatomics $N_2$, $O_2$ and $CO$.
