Applications of time dependent and time independent density functional theory to the first π to π* transition in cyanine dyes

The first π → π* transition in a number of cyanine dyes was studied using both time dependent and time independent density functional methods using a coupled cluster (CC2) method as the benchmark scheme. On the basis of 10 different functionals, it was concluded that adiabatic time dependent density functional theory (ATDDFT) almost independently of the functional gives rise to a singlet-triplet separation that is too large by up to 1 eV, leading to too high singlet energies and too low triplet energies. This trend is even clearer when the Tamm-Dancoff (TD) approximation is introduced and can in ATDDFT/TD be traced back to the representation of the singlet-triplet separation by a HF-type exchange integral between π and π. The time independent DFT methods (ΔSCF and RSCF-CV-DFT) afford triplet energies that are functional independent and close to those obtained by ATDDFT. However, both the singlet energies and the singlet-triplet separations increases with the fraction α of HF exchange. This trend can readily be explained in terms of the modest magnitude of a KS-exchange integral between π and π* in comparison to the much larger HF-exchange integral. It was shown that a fraction α of 0.5 affords good estimates of both the singlet energies and the singlet-triplet separations in comparison to several ab initio benchmarks.