Are Hartree–Fock atoms too small or too large?

Abstract

We address the simple question, whether Hartree–Fock atoms are smaller or larger than exact (Schrödinger) atoms. As a measure, we use 〈r²〉. We study the ground state of the atoms He–Kr. The unrestricted Hartree–Fock method is used. To obtain the Schrödinger values we use the finite field CASPT2 approach, and the full CI scheme where possible. CASSCF calculations are also reported. Very large basis sets are employed. We find that for those atoms for which the CASSCF wavefunction is distinct from the HF wavefunction, the Schrödinger values are distinctly smaller than the HF values. Most other atoms are also smaller than the HF values, (or the same within a numerical uncertainty), the exceptions being the hard atoms N–Ne, and Cl, Ar and Kr. We interpret our results in terms of categories of correlation contribution. It is also of interest to test the performance of density functional theory (DFT); we find on the whole that the predictions are good, with B3LYP giving close agreement with finite field CASPT2 for nearly all atoms, in particular for the transition metals.