Basis functions and orbitals

Let us make a clear distinction between (basis) functions and orbitals, even where these phrases are sometimes mixed up in the traditional terminology. Orbitals are always specific combinations of the basis functions. Orbitals are related to the computed eigenfunctions of some Fock operator or Hamiltonian occurring in the run or in a related preceding calculation. Functions are merely the elementary mathematical entities in which the orbitals are expressed. A Slater Type Orbital (STO), for instance is a function, not an orbital.

The physical meaning of one-electron orbitals in DFT has often been questioned. We believe that they are useful quantities for interpretation, just like the HF orbitals. For a recent discussion see [2].