We carry out a systematic study on the microscopic morphology and its relat
ionship with the signatures of the traces swept over the potential energy s
urface in a soft-sphere fluid system interacting via a truncated Lennard-Jo
nes potential. The state of the model system is tuned by changing its tempe
rature obtained in a molecular dynamics simulation, ranging from the equili
brium fluid phase to the deeply quenched supercooled states. The density an
d the range of interaction are chosen so that the instantaneously barely is
olated centers are present. We analyze the microscopic structural origin of
the features in the instantaneous-normal-mode (INM) spectrum and search fo
r evidence of state transformation. It is found that the presence of drasti
c changes in the INM spectra upon entering the deep supercooled regime is a
ccompanied by the reduction in the spatial connectivity. We develop a metho
d to characterize the spatial configuration ration in an attempt to address
the origin of the temperature-dependent changes in the spectra. (C) 2000 E
lsevier Science B.V. All rights reserved.