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

Defining a theoretical model systematically deliveringaccurate ab initio predictions of the fluorescencequantum yieldsof organic dyes is highly desirable for designing improved fluorophoresin a systematic rather than trial-and-error way. To this end, thefirst required step is to obtain reliable radiative rates (k (r)), as low k (r) typicallyprecludes effective emission. In the present contribution, using aseries of 10 substituted phenyls with known experimental k (r), we analyze the impact of the computational protocolon the k (r) determined through the thermalvibration correlation function (TVCF) approach on the basis of time-dependentdensity functional theory (TD-DFT) calculations of the energies, structures,and vibrational parameters. Both the electronic structure (selectedexchange-correlation functional, application or not of theTamm-Dancoff approximation) and the vibronic parameters (line-shapeformalism, coordinate system, potential energy surface model, anddipole expansion) are tackled. Considering all possible combinationsyields more than 3500 cases, allowing to extract statistically-relevantinformation regarding the impact of each computational parameter onthe magnitude of the estimated k (r). Itturns out that the selected vibronic model can have a significantimpact on the computed k (r), especiallythe potential energy surface model. This effect is of the same orderof magnitude as the difference noted between B3LYP and CAM-B3LYP estimates.For the treated compounds, all evaluated functionals do deliver reasonabletrends, fitting the experimental values.

Automated summary

Defining a theoretical model for accurately predicting the fluorescence quantum yields of organic dyes is important in designing improved fluorophores systematically. This study analyzed the impact of different computational parameters on the determination of reliable radiative rates (k (r)) using time-dependent density functional theory calculations. The results showed that the chosen vibronic model, especially the potential energy surface model, had a significant impact on the computed k (r) and the difference observed between different exchange-correlation functionals. However, all evaluated functionals yielded reasonable trends for the treated compounds, fitting the experimental values.