Pressure formulae for liquid metals and plasmas based on the density-functional theory

First, pressure formulae for electrons under the external potential produced by fixed nuclei are derived both in surface integral and volume integral forms for an arbitrary volume chosen in the system; the surface integral form is based on a pressure tensor which is the sum of the kinetic and exchange-correlation parts in the density-functional theory, and the volume integral form represents the virial theorem with subtraction of the nuclear virial term. Secondly, on the basis of these formulae, the thermodynamical pressure of liquid metals and plasmas is represented in the forms of a surface integral and a volume integral including the nuclear contribution. From these results, we obtain a virial pressure formula for liquid metals, which is more accurate and simpler than the standard representation. On the basis of our formulation, some comments are made on pressure formulae derived previously and on a definition of pressure used widely. (author)