Is the Tamm-Dancoff Approximation Reliable for the Calculation of Absorption and Fluorescence Band Shapes?

The reliability of the Tamm-Dancoff approximation (TDA) for predicting vibrationally resolved absorption and emission spectra of several prototypical conjugated molecules has been addressed by performing a series of extensive theoretical calculations. To this end, we have systematically compared the TDA results with the full Time-Dependent Density Functional Theory (TDDFT), the Random Phase Approximation (RPA), as well as the Configuration Interaction Singles (CIS) methods that are routinely employed for the prediction of optical spectra of large molecules. Comparisons have been made with experimental results for both the band shapes and 0-0 energies. They revealed that TDA is generally able to reproduce the experimental band shapes along with the positions of the absorption and emission peaks. With respect to TDDFT, TDA leads to an underestimation of the relative intensities for most cases but does not alter any other feature of the spectra. For the case of 0-0 energies, it leads to a better agreement between theory and experiment compared to TDDFT for the majority of the molecules studied, at least when combined with the popular B3LYP functional.