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

The Differential Virial Theorem with Gradient Formulas for the Operators