Comparison of inherent, instantaneous, and saddle configurations of the bulk Lennard-Jones system

Abstract

The configurational energies, order parameters and normal mode spectra associated with inherent structure, inherent saddle, and instantaneous configurations of the bulk Lennard-Jones system are compared. Instantaneous structures are generated by sampling configurations from an isothermalisobaric ensemble Monte Carlo simulation. Local minimization of the potential, starting from a given instantaneous configuration is used to determine the corresponding inherent structure. The inherent saddles are obtained by local minimization on a pseudo-potential surface defined in terms of the square magnitude of the potential gradient. In the solid phase, no stationary points of order greater than zero are sampled and minimizations of both the potential, as well as of the pseudo-potential, always lead to the same global minimum energy crystalline configuration. The energies of instantaneous configurations of the solid show a clear negative correlation with the second-order bond orientational parameters. The instantaneous normal mode spectrum of the solid close to melting has a fairly prominent imaginary branch and is sufficiently smoothed out by local disorder that it qualitatively resembles the liquid phase INM spectrum. In the liquid phase, the inherent, saddle, and instantaneous structures form distinct sets of configurations. The thermal averages of the saddle energies and force constants lie between that of the instantaneous and inherent structures. The temperature dependence of the mean saddle energy and force constant is essentially parallel to that of the corresponding instantaneous quantities. The fraction of imaginary modes for the saddle configurations is approximately half that of the instantaneous configurations. The most striking similarity between the instantaneous and saddle configurations is the linear relationship between the index density and the configurational energy. The most notable difference between the two sets of configurations is the reduction to zero of the fraction of imaginary modes of the saddle configurations on freezing, making the saddle normal mode spectra qualitatively different in the liquid and solid phases.