On asymptotic behavior of density functional theory

The performance of several previously proposed as well as of some novel approaches for correcting the asymptotic behavior of electron densities in density functional theory (DFT) is evaluated. The comparisons are made for molecular properties that are known to be sensitive to the asymptotic behavior of densities such as polarizabilities, energies of excitations to Rydberg states, and interaction energies (computed using symmetry-adapted perturbation theory). We find that whereas DFT-based methods without asymptotic corrections predict the investigated properties with errors often as large as a dozen or so percent relative to the best known values, the best performing asymptotically corrected hybrid functionals reduce these errors to below 2%. In many cases, the errors are just a fraction of one percent and in a few cases DFT reproduces benchmark values to all figures. These errors are also very close to those produced by the coupled-cluster methods at the highest levels of electron excitations applicable in practice. Such performance is unprecedented for any applications of DFT and is due to high sensitivity of the investigated properties to tails of the electron densities. Range-separated hybrid (RSH) functionals are also examined and found to perform comparably to the asymptotically corrected hybrid functionals for excitation energies and only somewhat worse for polarizabilities. However, very surprisingly, RSH functionals fail completely in interaction energy calculations. We explain the latter problem by showing that, despite some expectations in the literature reflected by the alternative name, long-range corrected, used for the RSH functionals, these methods give densities that are not better in the asymptotic region than those produced by asymptotically uncorrected standard DFT methods. We further show that this failure can be corrected by cutting, displacing, and splicing the exchange-correlation potentials of RSH methods such that these potentials approach the correct value at infinity.