Vibronic coupling in indole: I. Theoretical description of the 1La–1Lb interaction and the electronic spectrum

Abstract

The properties of the three lowest singlet electronic states (ground, ¹L_b, and ¹L_a states) 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 multi-reference 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 ¹L_b bands will have positive signs for both the axis reorientation angle θ_T and the angle θ of the transition dipole moment with respect to the inertial a axis. For ¹L_a bands the signs of both angles will be reversed. Vibronically coupled bands can exhibit opposite signs for θ and θ_T. 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 ¹L_b and ¹L_a states, which can be accessed to varying extents via different Herzberg–Teller active modes is found approximately 2000 cm⁻¹ above the ¹L_b minimum.