Representation of the delta distribution as an element of the dual of $H^1$

Question

I'm working with some Sobolev spaces and I just wanted to consider the elements of $H^{-1}$ as elements on $H^1$ (Riez Theorem). Since the delta function $\delta(f) = f(0)$ is an element of the dual of $H^1$, who is his representative?

i.e. I want some $g \in H^1$ such that$$ \int g h dx + \int g' h' dx = h(0) \quad \forall h \in H^1$$