The concept of pressure in density functional theory

Using density functional theory, a prescription is given for determining the internal scalar pressure at a point within an atom or molecule. From this expression for the pressure, a thermodynamic expression for the energy is obtained in terms of the chemical potential of the reference system, forces acting on the system, the internal pressure and an additional component X[ρ]; namely, Here μ0 is the chemical potential in the absence of fields, v is the potential due to nuclei, φ is the potential due to electrons, P is the scalar pressure, and X[ρ] is defined by the formula where T[ρ] and K[ρ] are the exact kinetic energy and exchange–correlation functionals. The functional X[ρ] vanishes as N approaches infinity, or in Thomas–Fermi or Thomas–Fermi–Dirac approximation, yet it is necessary to account for chemical binding.