HARDNESS FUNCTIONAL

The hardness functional for the ground state of an electronic system with electron density rho is defined by the formula H[rho] = integral dr. Rho(r)(deltaF[p]/deltarho(r)) - F[rho], where F[rho] is the universal functional of density-functional theory, the sum of the electronic kinetic energy and the electron-electron repulsion energy. It is shown that H[rho] is the negative of the equilibrium grand potential OMEGA[rho] and that for any change of equilibrium state DELTA(E - Nmu) = -DELTAH, where E is the total electronic energy and mu is the chemical potential. The maximum hardness principle is proved and discussed, and the relationship between H[rho] and the global and local hardness is elucidated.