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 $k\left(u\right)$ is revealed. The degree of instability of typical stationary points vanishes at a threshold potential energy $u_{\mathrm{th}}$, 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 $u_{\mathrm{th}}$ at a temperature close to the mode-coupling transition temperature $T_c$.