The virial of Clausius in condensed phases and in free molecules

Abstract

The virial theorem of Clausius is first applied to classical bulk liquids in its original integral form. Thermodynamic consistency between the virial equation of state and that derived from the compressibility form in terms of long wavelength structures is then discussed within a pair-force framework. Coulomb liquids are treated as a special case of the above.

Attention is then focused on the fully quantal ground state of the homogeneous electron gas. Forms of the total correlation energy yield separately the correlation kinetic and potential energies via the virial theorem. Following a brief discussion of the extension to treat the weakly inhomogeneous electron gas, a differential form of the virial theorem is introduced, in a fully interacting and strongly inhomogeneous electronic assembly. This form is then utilized, together with the definitions of low-order density matrices, to obtain, following Holas and March, the exact exchange-correlation potential in terms of the first-order density matrix and the electron pair correlation function. Finally, the exchange-only limit is considered, and the virial is employed to find the exchange energy from this exchange potential.