Evert Jan Baerends
Theoretical Chemistry,Vrije Universiteit, Amsterdam, The Netherlands
We will first review many wrong statements in the literature on the nature and the (lack of) physical meaning of Kohn-Sham orbitals.
Next the nature of the occupied KS orbitals, and their advantages over Hartree-Fock orbitals are highlighted.
Then we address orbital energies. Exact KS orbitals have many virtues:
- the orbital energies of the occupied orbitals are close to ionization potentials (an order of magnitude better agreement than the Koopmans’ type agreement in Hartee-Fock) ;
- virtual orbital energies are realistic: occupied-unoccupied orbital energy differencies are very close to excitation energies. There is no “gap problem” in DFT! [2,3]
- the KS virtual orbitals are typically bound states and have good (valence type) shapes (not unphysically diffuse like the Hartree-Fock virtuals); excitations can be described in most cases as simple single orbital-to-orbital transitions [2,3].
Unfortunately, orbital energies in the common LDA and GGA calculations are very wrong: they are typically 5 eV (more than 100 kcal/mol) higher than the exact Kohn-Sham orbital energies, an error that would be completely unacceptable in total energies. We will first analyze where this error comes from - it is not due to wrong asymptotic behavior of LDA/GGA potentials, or to a “self-interaction error” but it is caused by erroneous density dependence of the standard Exc[ρ] functionals, hence a wrong derivative (= potential). We will demonstrate that approximate potentials can be formulated that have similar good properties for ionization and excitation energies as the exact KS potential .