What Do the Kohn−Sham Orbitals and Eigenvalues Mean?

Abstract

Kohn−Sham orbitals and eigenvalues are calculated with gradient-corrected functionals for a set of small molecules (H 2 O, N 2, CrH 6 6 -, and PdCl 4 2 - ), varying basis sets and functionals. The calculated Kohn−Sham (KS) orbital shapes, symmetries, and the order and absolute energy of the associated eigenvalues are investigated and compared with those of Hartree−Fock (HF) and one-electron extended Hückel (eH) calculations, as well as experimental ionization potentials. The shape and symmetry properties of the KS orbitals are very similar to those calculated by HF and eH methods. The energy order of the occupied orbitals is in most cases in agreement among the various methods. The order of empty orbitals of a minimal basis set is sometimes interchanged, within that group or with some orbitals resulting from a larger basis calculation. Overall the KS orbitals are a good basis as Baerends suggested for qualitative interpretation of molecular orbitals. For the Kohn−Sham eigenvalues we find an approximately linear dependency of |ε i KS − ε i HF | vs ε i HF (≈−IP) for the occupied as well as for the unoccupied orbital eigenvalues. We suggest an ax + b scaling for quantitative interpretation of KS eigenvalues, at least if these are calculated utilizing commonly used functionals.