EXCHANGE AND CORRELATION-ENERGY IN DENSITY-FUNCTIONAL THEORY - COMPARISON OF ACCURATE DENSITY-FUNCTIONAL THEORY QUANTITIES WITH TRADITIONALHARTREE-FOCK BASED ONES AND GENERALIZED GRADIENT APPROXIMATIONS FOR THE MOLECULES LI-2, N-2, F-2

The density functional definition of exchange and correlation differs from the traditional one. In order to calculate the density functional theory (DFT), quantities accurately, molecular Kohn-Sham (KS) solutio ns have been obtained from ab initio wave functions for the homonuclea r diatomic molecules Li-2, N-2, F-2. These afford the construction of the KS determinant Psi(S) and the calculation of its total electronic energy E-KS and the kinetic, nuclear-attraction and Coulomb repulsion components T-S, V, W-H as well as the (DFT) exchange energy E-x and co rrelation energy E-c. Comparison of these DFT quantities has been made on one hand with the corresponding Hartree-Fock (HF) quantities and o n the other hand with local density approximation (LDA) and generalize d gradient approximation (GGA). Comparison with HF shows that the corr elation errors in the components T, V, and W-H Of the total energy are much larger for HF than KS determinantal wave functions. However, the total energies E-KS and E-HF appear to be close to each other, as wel l as the exchange energies E-x and E-x(HF) and correlation energies E- c and E-c(HF). The KS determinantal wave function and the KS orbitals therefore correspond to much improved kinetic and Coulombic energies, while having only a slightly larger total correlation energy. It is st ressed that these properties of the Kohn-Sham orbitals make them very suitable for use in the molecular orbital theories of chemistry. Compa rison of the accurate Kohn-Sham exchange and correlation energies with LDA and GGA shows that the GGA exchange energies are consistently too negative, while the GGA correlation energies are not negative enough. It is argued that the GGA exchange functionals represent effectively not only exchange, but also the molecular non-dynamical correlation, w hile the GGA correlation functionals represent dynamical correlation o nly. (C) 1997 American Institute of Physics.