  Metallic glasses deform elastically under stress. However, the atomic-level
origin of elastic properties of metallic glasses remain unclear. In this paper
using {\em ab initio} molecular dynamics simulations of the Cu$_{50}$Zr$_{50}$
metallic glass under shear strain, we show that the heterogeneous stress
relaxation results in the increased charge transfer from Zr to Cu atoms,
enhancing the softening of the shear modulus. Changes in compositional
short-range order and atomic position shifts due to the non-affine deformation
are discussed. It is shown that the Zr subsystem exhibits a stiff behavior,
whereas the displacements of Cu atoms from their initial positions, induced by
the strain, provide the stress drop and softening.
