Energy landscape of a Lennard-Jones liquid: statistics of stationary points

Molecular dynamics simulations are used to generate an ensemble of saddles of the potential energy of a Lennard-Jones liquid. Classifying all extrema by their potential energy u and number of unstable directions k, a well-defined relation k(u) is revealed. The degree of instability of typical stationary points vanishes at a threshold potential energy u(th), which lies above the energy of the lowest glassy minima of the system. The energies of the inherent states, as obtained by the Stillinger-Weber method, approach u(th) at a temperature close to the mode-coupling transition temperature T-c.