Failure of Time-Dependent Density Functional Theory for Long-Range Charge-Transfer Excited States:  The Zincbacteriochlorin−Bacteriochlorin and Bacteriochlorophyll−Spheroidene Complexes

It is well-known that time-dependent density functional theory (TDDFT) yields substantial errors for the excitation energies of charge-transfer (CT) excited states, when approximate standard exchange-correlation (xc) functionals are used, for example, SVWN, BLYP, or B3LYP. Also, the correct 1/R asymptotic behavior of CT states with respect to a distance coordinate R between the separated charges of the CT state is not reproduced by TDDFT employing these xc-functionals. Here, we demonstrate by analysis of the TDDFT equations that the first failure is due to the self-interaction error in the orbital energies from the ground-state DFT calculation, while the latter is a similar self-interaction error in TDDFT…