Density-functional approach to obtaining excited states: Study of some open-shell atomic systems

There are two density-functional approaches to obtaining the transition energies of many-electron systems. One involves taking the difference of the excited-state and the ground-state energies, both obtained by static density-functional calculation, and the other involves applying the time-dependent density-functional method. In this paper, we apply both methods to get transition energies of low-lying excited states of some open-shell atomic systems and compare their accuracy. We find that while both methods give accurate energies for most of the systems, they lead, inexplicably, to substantial errors in some cases.