Quasi-saddles as relevant points of the potential energy surface in the dynamics of supercooled liquids

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The supercooled dynamics of a Lennard-Jones model liquid is numerically investigated studying relevant points of the potential energy surface, i.e. the minima of the square gradient of total potential energy V. The main findings are: (i) the number of negative curvatures n of these sampled points appears to extrapolate to zero at the mode coupling critical temperature Tc; (ii) the temperature behavior of n(T) has a close relationship with the temperature behavior of the diffusivity; (iii) the potential energy landscape shows an high regularity in the distances among the relevant points and in their energy location. Finally we discuss a model of the landscape, previously introduced by Madan and Keyes [J. Chem. Phys. 98, 3342 (1993)], able to reproduce the previous findings.