Orbitals in Quantum Chemistry

Orbitals, on the one hand, are often considered as auxiliary quantities without physical meaning for various reasons. Slater determinants, e.g., Hartree-Fock or Kohn-Sham determinants, are invariant with respect to unitary transformations of the occupied orbitals. Within densityfunctional theory (DFT) orbitals frequently are considered as quantities that merely generate the electron density but have no other meaning. In the limit of a full configuration interaction wave function orbitals just serve as one-electron basis functions. On the other hand, orbitals underly the thinking of quantum chemists. The concept of bonding or antibonding orbitals, the definition of electronic configurations, or the characterization of electronic transitions as excitations of electrons between occupied and unoccupied orbitals are examples that show the ubiquitous use of orbitals in quantum chemistry. Indeed orbitals in some sense can even be ’observed’ in experiment. To demonstrate this point, examples of STM images that can be directly related to individual orbitals obtained by DFT methods are presented [1]. A crucial question is which orbitals are those corresponding to the thinking of quantum chemists or to experimental results. It is shown that one choice could be KohnSham orbitals obtained by novel DFT methods which treat the local Kohn-Sham exchange potential exactly and thus are free of unphysical Coulomb self-interactions [2]. The concept of a new generation of DFT methods based on orbital-dependent functionals is presented [3].