Analysis of density functionals and their density tails in H2

The total energy, internuclear distance, vertical ionization potential, and electron density function were determined for the hydrogen molecule (H2) with a configuration interaction calculation, a Hartree–Fock calculation, all 22 density functional theory (DFT) methods built into Gaussian 92/DFT, and the Davidson and Jones natural orbital expansion of the Kolos and Roothaan wave function. These data were used to explore the performance of DFT methods in modeling the chemical bond. We noted that although the vertical ionization potentials suggested by the highest occupied molecular orbital energies of DFT methods are generally quite poor, the medium‐range bahavior of the electron density from DFT methods is close to that of more accurately determined electron densities. Accordingly, we propose a method of finding an approximate vertical ionization potential for a density functional calculation from the medium‐range behavior of the electron density. We explain why the density functionals' electron densities decay in a manner different from that which their orbital energies lead us to expect and explore the relationship between the errors in the exchange‐correlation potentials, electron densities, and the orbital energies. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 541–550, 1998