  We classify nontrivial deformations of the standard embedding of the Lie
algebra $\Vect(S^1)$ of smooth vector fields on the circle, into the Lie
algebra~$\PD(S^1)$ of pseudodifferential symbols on $S^1$. This approach leads
to deformations of the central charge induced on $\Vect(S^1)$ by the canonical
central extension of $\PD(S^1)$. As a result we obtain a quantized version of
the second Bernoulli polynomial.
