Extensive Analysis of the Parameters Influencing Radiative Rates Obtained through Vibronic Calculations

Defining a theoretical model systematically delivering
accurate ab initio predictions of the fluorescence
quantum yields
of organic dyes is highly desirable for designing improved fluorophores
in a systematic rather than trial-and-error way. To this end, the
first required step is to obtain reliable radiative rates (kr), as low kr typically
precludes effective emission. In the present contribution, using a
series of 10 substituted phenyls with known experimental kr, we analyze the impact of the computational protocol
on the kr determined through the thermal
vibration correlation function (TVCF) approach on the basis of time-dependent
density functional theory (TD-DFT) calculations of the energies, structures,
and vibrational parameters. Both the electronic structure (selected
exchange–correlation functional, application or not of the
Tamm–Dancoff approximation) and the vibronic parameters (line-shape
formalism, coordinate system, potential energy surface model, and
dipole expansion) are tackled. Considering all possible combinations
yields more than 3500 cases, allowing to extract statistically-relevant
information regarding the impact of each computational parameter on
the magnitude of the estimated kr. It
turns out that the selected vibronic model can have a significant
impact on the computed kr, especially
the potential energy surface model. This effect is of the same order
of magnitude as the difference noted between B3LYP and CAM-B3LYP estimates.
For the treated compounds, all evaluated functionals do deliver reasonable
trends, fitting the experimental values.