Density-functional theory calculations with correct long-range potentials

A variational method for forcing the exchange-correlation potential in density-functional theory (DFT) to have the correct asymptotic decay is developed. The resulting exchange-correlation potentials are much improved while the total energies remain essentially the same, compared with conventional density-functional theory calculations. The highest occupied orbital energies from the asymptotically corrected exchange-correlation potentials are found to provide significantly more accurate approximations to the ionization potential (for a neutral molecule) and the electron affinity (for an anion) than those from conventional calculations, although the results are usually inferior to direct methods by computing energy differences. Extending recent results from exchange-only DFT, we show that exact exchange-correlation potential is nonuniform asymptotically. Correcting the asymptotic decay of approximate exchange-correlation potentials towards the exact functional form binds the highest occupied orbitals for atomic and molecular anions, which supports the use of DFT calculations for negatively charged molecular species. With this technique, even hybrid functionals have local exchange-correlation potentials, effectively removing the largest objection to including these functionals in the panoply of Kohn–Sham DFT methods.