  A gradient dependent formula is derived for the spinless one-particle
density-matrix operator z from the differential virial theorem. A gradient
dependent formula is also derived for a spinless one-particle density-matrix
operator that can replace the two operators of the differential virial theorem
that arise from the kinetic energy operator. Other operators are also derived
that can replace the operators mentioned above in the differential virial
theorem; these operators depend on the real part of spinless one-particle
density-matrix.
