  We construct a new order parameter from the normal modes of vibration, based
on the consideration of energy equipartition, to quantify the structural
heterogeneity in disordered solids. The order parameter exhibits strong spatial
correlations with low-temperature single particle dynamics and local structural
entropy. To characterize the role of particles with the most defective local
structures identified by the order parameter, we pin them and study how
properties of disordered solids respond to the pinning. It turns out that these
particles are responsible to the quasilocalized low-frequency vibration,
instability, softening, and nonaffinity of disordered solids.
