This paper is devoted to conditionally negative definite functions on a locally compact group $G$, and their relation to representation theory and 1-cohomology. More precisely, we prove first that a normalized, conditionally negative definite function $\psi$ on $G$ is indecomposable if and only if the orthogonal representation of $G$ constructed by GNS-construction is irreducible. Next we define conditionally negative definite measures on $G$ and we prove that a Radon measure $\text{d}\mu$ absolutely continous with respect to Haar measure $\text{d}x$ is conditionally negative definite if and only if the Radon-Nikodym derivative $\frac{\text{d}\mu}{\text{d}x}$ is a conditionally negative definite function. We use this to prove that, on a compactly generated group $G$, any normalized conditionally negative definite function is the limit, uniformly on compact subsets of $G$, of convex combinations of indecomposable normalized conditionally negative definite functions. As a consequence, if a compactly generated group has the property that the reduced 1-cohomology is zero for every irreducible representation of $G$, then the same holds for every unitary representation of $G$. This is related to a characterisation, by Y. Shalom, of Property (T) for compactly generated groups.