The dominant nature of Herzberg-Teller terms in the photophysical description of naphthalene compared to anthracene and tetracene

The first order and second order corrected photoluminescence quantum yields are computed and compared to experiment for naphthalene in this manuscript discussing negative results. Results for anthracene and tetracene are recalled from previous work [J. Chem. Phys. 155, 054108 (2021)], and the results for all three polyacenes are juxtaposed to each other. While at the Franck-Condon point, each of the three noted polyacenes were found to possess a quantum yield near unity. Following the consideration of Herzberg-Teller effects, quantum yields stabilised for anthracene and tetracene to 0.19 and 0.08 respectively. Conversely, the second order corrected quantum yield for naphthalene was found to be 0.91. Analysis of this result showed that while the predicted non-radiative pathways correlate well with what should be expected, the approximation used to calculate second order corrected fluorescence, which yielded very positive results for many other molecular systems, here is unable to account for strong second order contributions, resulting in a grossly overestimated rate of fluorescence. However, substitution of an experimental radiative rate results in a quantum yield of 0.33. This work extols the importance of Herzberg-Teller terms in photophysical descriptions of chromophores, and highlights those cases in which a treatment beyond the above approximation is required.