Electronic Excitations of Simple Cyanine Dyes: Reconciling Density Functional and Wave Function Methods

The simplest cyanine dye series [H2N(CH)nNH2]+ with n = 1, 3, 5, 7, and 9 appears to be a challenge for all theoretical excited-state methods since the experimental spectra are difficult to predict and the observed deviations cannot be easily explained with standard arguments. We compute here the lowest vertical excitation energies of these dyes using a variety of approaches, namely, complete active space second-order perturbation theory (CASPT2), quantum Monte Carlo methods (QMC), coupled cluster linear response up to third approximate order (CC3), and various flavors of time-dependent density functional theory (TDDFT), including the recently proposed perturbative correction scheme (B2PLYP). In our calculations, all parameters such as basis set, active space, and geometry dependence are carefully analyzed. We find that all wave function methods give reasonably close excitation energies, with CASPT2 yielding the lowest values, and that the B2PLYP scheme gives excitations in satisfactory agreement with CC3 and DMC, significantly improving on the generalized gradient and hybrid approximations. Finally, to resolve the remaining discrepancy between predicted excitation energies and experimental absorption spectra, we also investigate the effect of excited-state relaxation. Our results indicate that a direct comparison of the experimental absorption maxima and the theoretical vertical excitations is not possible due to the presence of nonvertical transitions. The apparent agreement of earlier CASPT2 calculations with experiments was an artifact of the choice of active space and the use of an older definition of the zero-order Hamiltonian.