  A problem of defining the quantum analogues for semi-classical twists in
$U(\mathfrak{g})[[t]]$ is considered. First, we study specialization at $q=1$
of singular coboundary twists defined in $U_{q}(\mathfrak{g})[[t]]$ for
$\mathfrak{g}$ being a nonexceptional Lie algebra, then we consider
specialization of noncoboundary twists when $\mathfrak{g}=\mathfrak{sl}_{3}$
and obtain $q-$deformation of the semi-classical twist introduced by Connes and
Moscovici in noncommutative geometry.
