Rigidity of Lie Algebra

Question

I Know the theorem: if $\mathfrak{g}$ is a lie algebra and $H^{2}(\mathfrak{g},\mathfrak{g})=0$ (second space of cohomology in Chevaley-Eilenberg complex) then $\mathfrak{g}$ is rigid ... but I am interested in to Know when The reciprocal of this theorem is true?.