Energy landscapes of some model glass formers

The potential energy surfaces of several model atomic glass formers have been studied using eigenvector-following techniques. Barrier distributions, cooperativity indices, path lengths, and vibrational densities of states (VDOS) are presented based upon data sets containing more than 250 000 pathways in total. We find that rearrangements can usefully be separated into ``nondiffusive'' processes, which do not change the nearest-neighbor contacts and ``diffusive'' processes, which do. We suggest a criterion to separate these classes: nondiffusive processes are those in which no atoms move more than a threshold distance. Energy barriers for the two classes of rearrangement differ much more in the ``strong'' system (Stillinger-Weber silicon) than in the ``fragile'' Lennard-Jones systems. Our results indicate that the system is not trapped in a single local minimum below the glass transition temperature, because there are numerous ``nondiffusive'' rearrangements with low barriers still accessible. Disconnectivity graphs for low-energy regions of the potential energy surface illustrate how the crystal is rapidly located once a critical nucleus is present. Finally, the calculated VDOS show a pronounced excess over the Debye density of states in the low-frequency region. Transition state searches following the eigenvectors corresponding to these soft modes converge to low-lying transition states, including some that separate nearly degenerate minima. This result provides support for the hypothesis that two-level systems and the boson peak are related.