Quasisaddles as relevant points of the potential energy surface in the dynamics of supercooled liquids

we describe and revisit in a detailed way an additional approach, that has been very useful to give new insight in the analysis of the relevant processes taking place in the supercooled liquid regime. This approach focuses on the minima of the square gradient of the total potential energy, ‘‘closest’’ to the instantaneous points of the molecular dynamics trajectory. This approach allows one to obtain a microscopic interpretation of the relevant processes, the main result being the characterization of the dynamics above and below the mode coupling temperature Tc . 14 Moreover, the analysis of these points allows one to obtain information about some relevant characteristics of the PES, of great importance to construct simplified models of the landscape. Let us briefly resume the two main PES approaches, the INM and the IS approach. The INM method is based on the investigation of the PES around the instantaneous configurations r ~r represents the 3 N-dimensional vector of the representative point in the configuration space! during the molecular dynamics evolution of the system. The diffusive quantities are supposed to be related to the shape of the energy surface at r, that is to say the eigenvalues and eigenvectors of the Hessian matrix ~the second derivative of the potential energy!. The main hypothesis of the INM approach is that the relevant diffusive directions have to be searched among the downward curvatures ~eigenvectors with negative eigenvalues!. Many attempts have been devoted to extend this approach to different liquid systems and to develop a theory of the supercooled liquid state based on INM concepts. Moreover many efforts have been spent to recognize the true diffusive directions among all the downward ones, as it is known there are downward curvatures that do not correspond to diffusive directions, notably in the crystalline state. The INM negative curvature directions are classified as shoulder modes ~related to anharmonicities of the PES! and double wells ~with a double well shaped one-dimensional profile!. Diffusive directions are finally identified as those leading to different minima 15 ~this analysis involves the