First-principles study on vibrationally resolved fluorescence of fused 5,15-(diphenyl)-10,20-(dibromo)porphyrin molecule.

The vibrationally resolved fluorescence spectrum of a narrow-line single-molecule transducer, fused 5,15-(diphenyl)-10,20-(dibromo)porphyrin (fused-H2P) molecule, has been calculated by time-dependent density functional theory with the inclusion of both Franck-Condon and Herzberg-Teller contributions. Analytical transition dipole derivatives are used for the calculations of Herzberg-Teller terms to eliminate the possible errors caused by numerical differentials. The performance of different exchange-correlation functionals including B3LYP, ωB97X-D, and M06-2X has been examined. The comparison with the high-resolution experimental emission spectrum indicates that all three functionals can satisfactorily describe the fluorescence spectral profile, while ωB97X-D and M06-2X give slightly better excitation energy than B3LYP. Detailed analysis shows that the fluorescence spectrum is dominated by the Franck-Condon contribution, while the Herzberg-Teller term contributes mostly to its low energy tail. It is found that the size of the basis set has limited influence on the fluorescence spectrum, and a standard 6-31G(d, p) basis set is adequate for the purpose. The substitution of terthiophene side chains is found to have minor effects on the fluorescence spectrum. Our study provides unambitious assignments for all the vibronic structures in the experimental spectrum.