Long wavelength absorbing carbostyrils as test cases for different TDDFT procedures and solvent models

The vertical excitation energies of 3,4-dicyano-6-methoxy and 3,4-dicyano-6,7-dimethoxy carbostyril have been computed with different approximations for the time-dependent density functional theory (TD-DFT) procedure and with different implementations of the continuum solvation model COSMO. Different DFT functionals were tested in TD-DFT and Tamm-Dancoff approximations (TDA) for the excitation energies in the gas phase. TDA-B3LYP showed the best agreement with the experimental data. Then TDA-B3LYP computations were performed combined with the COSMO model of solvation comparing a linear response (LR) and a post-configuration interaction (CI) implementation of the fast solvent reorganization. The post-CI solvent model overestimates the π→π* transitions and strongly underestimates the n→π* transition. The TDA approximation in combination with the linear response implementation of the COSMO solvation model perfectly computes the experimental results. TDA-LR is the most reliable method for the computation of the vertical excitation energies in a solvent. Comparison with explicit solvent calculations shows there is only a minor effect on the energies of the electronic interaction of the solute with the solvent.