Electronic π-to-π* Excitations of Rhodamine Dyes Exhibit a Time-Dependent Kohn-Sham Theory "Cyanine Problem".

The longest-wavelength π-to-π* electronic excitations of rhodamine-like dyes (RDs) with different group 16 heteroatoms (O, S, Se, Te) have been investigated. Time-dependent Kohn-Sham theory (TDKST) calculations were compared with coupled-cluster (CC) and equations-of-motion (EOM) CC results for π-to-π* singlet and triplet excitations. The RDs exhibit characteristics in the TDKST calculations that are very similar to previously investigated cyanine dyes, in the sense that the singlet energies obtained with nonhybrid functionals are too high compared with the CC results at the SD(T) level. The errors became increasingly larger for functionals with increasing amounts of exact exchange. TDKST with all tested functionals led to severe underestimations of the corresponding triplet excitations and overestimations of the singlet-triplet gaps. Long-range-corrected range-separated exchange and "optimal tuning" of the range separation parameter did not significantly improve the TDKST results. A detailed analysis suggests that the problem is differential electron correlation between the ground and excited states, which is not treated sufficiently by the relatively small integrals over the exchange-correlation response kernel that enter the excitation energy expression. Numerical criteria are suggested that may help identify "cyanine-like" problems in TDKST calculations of excitation spectra.