Energy landscape, two-level systems, and entropy barriers in Lennard-Jones clusters

In order to study the tunneling dynamics of glasses, we develop an efficient numerical algorithm for the identification of a large number of saddle points of the potential energy function of Lennard-Jones clusters. Knowledge of the saddle points allows us to find many thousands of adjacent minima of clusters containing up to 160 argon atoms and to locate many pairs of minima with the right characteristics to form two-level systems. The true two-level systems are singled out by calculating the quantum-mechanical ground-state tunneling splitting by means of the one dimensional WKB approximation. The many-dimensions correction to the splitting is evaluated by studying a simple model potential; we find that it consists of a splitting enhancement in all isolated tunneling centers observed. [S0163-1829(99)06529-7].