  We consider the clustering of Lennard-Jones particles by using an energetic
connectivity criterion proposed long ago by T.L. Hill [J. Chem. Phys. 32, 617
(1955)] for the bond between pairs of particles. The criterion establishes that
two particles are bonded (directly connected) if their relative kinetic energy
is less than minus their relative potential energy. Thus, in general, it
depends on the direction as well as on the magnitude of the velocities and
positions of the particles. An integral equation for the pair connectedness
function, proposed by two of the authors [Phys Rev. E 61, R6067 (2000)], is
solved for this criterion and the results are compared with those obtained from
molecular dynamics simulations and from a connectedness Percus-Yevick like
integral equation for a velocity-averaged version of Hill's energetic
criterion.
