The virial expression valid in density-functional theory contains an integral over the gradient of the effective exchange-correlation potential. The significance of this term in correcting the noninteracting kinetic and electrostatic energies is discussed in this work. From the gradient integral in the local density approximation an expression is derived for the kinetic-energy part of the exchange-correlation energy density, and its connection with the derivation of von Barth and Williams is discussed. To illustrate the application of these developments to the molecular case, results are presented from Gaussian-orbital cluster calculations for ${\mathrm{H}}_2$. In this study the forces in the dimer are calculated using the Hellmann-Feynman and virial theorems, and results are compared with the force obtained by direct interpolation from the binding-energy curve. The usefulness of the various methods for calculating the force is discussed.

• Received 29 June 1981

DOI:https://doi.org/10.1103/PhysRevB.24.6795