Pair density functional theory — a generalized density functional theory

Abstract

The idea of a pair density functional theory for fermions is presented. Whereas in the conventional Hohenberg-Kohn-Sham theory for the ground state of an interacting N-particle system the particle density is the key quantity and the sum of the kinetic and the interaction energy is a universal functional of this density, here the pair distribution function (PDF) is the key quantity and the kinetic energy alone is a universal functional of this PDF. With an appropriate ansatz for the PDF and the kinetic energy in terms of antisymmetric geminals a two-particle equation with an effective local interaction potential and a corresponding expression for the total energy are derived. Besides this a way is described how to obtain from the solution of the effective two-particle equation also the one-particle density matrix via the first link of the equation of motions for the reduced density matrices.