Time-dependent density-functional calculations with asymptotically correct exchange-correlation potentials

We implement exchange-correlation functionals with correct asymptotic behavior in the framework of a real-space density-functional pseudopotential method. This formalism is applied to calculate excitation energies and absorption spectra for a number of test systems selected to represent a wide range of electronic and chemical properties. The energies and oscillator strengths of electronic transitions are computed using time-dependent linear-response theory. Compared to calculations based on the time-dependent local-density approximation, asymptotically correct functionals yield more accurate excitation and ionization energies for atoms, molecules, and small clusters. The most notable improvements are observed for transitions to the upper electronic levels and for systems where the local-density approximation predicts close to zero electron affinities. At the same time, asymptotic corrections appear to have almost no effect on the absorption spectra and optical gaps of large atomic clusters and quantum dots. It implies that the asymptotic behavior of the exchange-correlation potential is less important in the limit of large systems, and other, more complex functionals may be needed to further improve the quality of theoretical results for all cluster sizes.