Hartree-Fock calculation exchange energy

Tschinke, V., andT. Ziegler. 1991. Gradient corrections to the Hartree-Fock-Slater exchange and their influence on bond energy calculations. Theor. Chim. Acta 81, 81. 

Here, h is the one electron matrix in the non-orthogonal Gaussian basis and G (P ) is the two electron matrix for Hartree-Fock calculations, but for DFT it represents the Coulomb potential. The term Exc is the DFT exchange-correlation functional (for Hartree-Fock Exc = 0), while Vmn represents the nuclear repulsion energy. In the orthonormal basis, these matrices are h = etc., where the overlap... 

A Hartree-Fock calculation provides a set of orbital energies, e,. What is the significance of these The energy of an electron in a spin orbital is calculated by adding the core interaction to the Coulomb and exchange interactions with the other electrons in the system ... 

Table 8 Energies (in eV) of the highest (HOMO), second-highest (HOMO-1), and third-highest (HOMO-2) occupied orbital as well as of the lowest (LUMO) and second-lowest (LUMO+1) unoccupied orbital for H2O, N2, and CO from exact-exchange (EXX), Hartree-Fock (HF), and local-spin-density (LSDA) calculations in comparison with the experimental first ionization potentials (IP). For N2, the ordering of the HOMO and the HOMO-1 is not correctly reproduced by the Hartree-Fock calculations. The results are from ref. 82...

Pereira JCG, Catlow CRA, Price GD (1999) Ab initio studies of sihca-based clusters. Part I. Energies and conformations of simple clusters. J Phys Chem A 103 3252-3267 Pisani C, Dovesi R (1980) Exact-exchange Hartree-Fock calculations for periodic systems. I. Illustration of the method. Int J Quantum Chem 17 501-516... 

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