ALTERNATIVE EXPRESSIONS FOR THE FERMI HOLE CURVATURE

The Fermi hole curvature C(r,s) is defined as the Laplacian of the par allel-spin pair distribution, evaluated at zero separation r'=r for a pair of Fermions in a many-Fermion system. It has been used by a numbe r of authors to discuss electron localization, properties of the excha nge and correlation hole, and exchange and correlation energies of inh omogeneous electron gases. Here, the discussion of this quantity is ex tended in two directions. First, for the special case of a single-dete rminant many-electron state, it is shown that a previously derived mac roscopic expression for C can be generalized in a simple fashion to ap ply to current-carrying states. Second, it is shown that a recently gi ven interpretation of C(rs), in terms of relative kinetic energy of pa irs, is valid for a general many-Fermion state and is not limited to t he single-determinant case investigated previously.