Applications to atoms, ions, and molecules of a novel form of the correlation energy density functional

The Liu-Parr new local form of the correlation energy functional [Phys. Rev. A 53 (1996) 2211] has been applied to first- and second-row neutral atoms, positive ions, and both diatomic and polyatomic molecules. This local form originates from the adiabatic connection and functional expansion formulation in density functional theory. It consists of a sum of three or four integrals of density to the 1, 23, 13, and 0 powers. Hartree-Fock densities are used. Numerical results show that among five commonly used local forms of the correlation energy, this one best reproduces the experimental values, and in some cases it is even comparable with the LYP non-local form. Its connections with the Wigner form are discussed.