Vibronic coupling in indole: I. Theoretical description of the ¹L_a-¹L_b interaction and the electronic spectrum

The properties of the three lowest singlet electronic states (ground, ¹Lb, and ¹La state) of indole (C₈H₇N) have been calculated with second-order approximate coupled-cluster theory (CC2) within the resolution-of-the-identity approximation. Refined electronic energies at the CC2 optimized structures and transition dipole moments were calculated using a density-functional theory multireference configuration-interaction (DFT/MRCI) approach. Structures, energies, and dipole moments are reported for all three states and compared to experimental values. From the optimized structures and calculated transition dipole moments, we predict that pure ¹Lb bands will have positive signs for both the axis reorientation angle θT and the angle θ of the transition dipole moment with respect to the inertial a axis. For ¹La bands the signs of both angles will be reversed. Vibronically coupled bands can exhibit opposite signs for θ and θT. The absorption and emission spectra of indole are calculated based on the Franck-Condon Herzberg-Teller approximation using numerical transition dipole moment derivatives at the DFT/MRCI level of theory. Implications for the experimentally observed vibronic spectra are discussed. Predictions are made for rotationally resolved spectra of various rovibronic bands. A conical intersection, connecting the ¹Lb and ¹La states, which can be accessed to varying extents via different Herzberg-Teller active modes is found approximately 2000cm-1 above the ¹Lb minimum