  We report on numerical procedures for, and preliminary results on the search
for, tunnelling centres in Lennard-Jones clusters, seen as simple model systems
of glasses. Several of the double-well potentials identified are good
candidates to give rise to two-level systems. The role of boundary effects, and
the application of the semiclassical WKB approximation in multidimensional
spaces for the calculation of the ground state splitting are discussed.
