Why is the density of inherent structures of a Lennard-Jones-type system Gaussian?

The thermodynamics of glass-forming systems can be expressed in terms of the density of inherent structures, which correspond to the minima of the potential energy landscape. In previous work this approach has been applied to Lennard-Jones-type systems, yielding a density of inherent structures which to a very good approximation turned out to be Gaussian. In this work we clarify whether the Gaussian distribution is just a consequence of the central-limit theorem or whether it also contains information about the local structure of the glass-forming system.