On the determination of excitation energies using density functional theory

The use of time-dependent density functional theory (TDDFT) is considered for the determination of electronic excitation energies. Using beryllium and methylene as examples, we highlight (i) problems with Rydberg excitations arising from neglect of the integer discontinuity in the potential; (ii) the absence of pure double excitations in calculations using conventional exchange-correlation functionals; (iii) quantitative differences between excitation energies determined using TDDFT and the 'delta SCF' method; (iv) non-additivity of excitation energies calculated using TDDFT from different electronic states; (v) an apparent failure to predict single excitations to states that are lower than the reference states and (vi) the difference in quality between excitations to singlet and triplet states.