Exchange potential eigenvalues

He where both approaches coincide. Also the corresponding highest occupied eigenvalues are essentially identical. The same holds for the longitudinal x-only energies (see Table 5.1). Here the maximum difference of 106 mhartree is found for No. The x-only ROPM thus demonstrates explicitly that one can obtain RHF-level results for all interesting atomic properties with a local exchange potential. 

It is known (Chap. A) that Koopmans theorem is not vahd for the wavefunctions and eigenvalues of strongly bound states in an atom or in the cores of a solid, i.e. for those states which are a solution of the Schrodinger (or Dirac) equation in a central potential. In them the ejection (or the emission) of one-electron in the electron system means a strong change in Coulomb and exchange interactions, with the consequent modification of the energy scheme as well as of the electronic wavefunction, in contradiction to Koopmans theorem. 

In Kohn-Sham density functional theory, the ionization potential is the negative of the eigenvalue of the highest occupied Kohn-Sham orbital. 86-88 The IP = —sH0M0 relation holds, however, only for the exact exchange-correlation potential. Numerical confirmations for this relation exist for model systems such as the... 

The wave eigenfunctions and energy eigenvalues were obtained by real space electronic state calculations, which were performed by the use of the program code SCAT of the DV-Xx molecular orbital (MO) cluster method with the Hartree-Fock-Slater approximation [8,9]. In the method, the exchange-correlation term Vxc in the one-electron Hamiltonian was expressed in terms of the statistical local potential (1),... 

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