Differential projective modules over algebras with radical square zero

Let $Q$ be a finite quiver and $\mathrm{\Lambda }$ be the radical square zero algebra of $Q$ over a field. We give a full and dense functor from the category of reduced differential projective modules over $\mathrm{\Lambda }$ to the category of representations of the opposite of $Q$. If moreover $Q$ has oriented cycles and $Q$ is not a basic cycle, we prove that the algebra of dual numbers over $\mathrm{\Lambda }$ is not virtually Gorenstein.