A large-scale study of the ''inherent structures'' (IS) associated wit
h equilibrium two-dimensional Lennard-Jones systems is presented. The
results validate, for simple 2D fluids, an essential premise of inhere
nt-structures theory: there are consistent, qualitative differences be
tween the IS associated with distinct equilibrium phases. The hexatic
IS show free dislocations plus some nonpercolating grain boundaries. T
he liquid IS always contain percolating grain boundaries, but no evide
nce of free disclinations. Our results are consistent with the disloca
tion-unbinding scenario for the hexatic phase, but leave open the ques
tion of the microscopic melting mechanism leading to the isotropic liq
uid.