¹L _a and ¹L _b states of indole and azaindole: Is density functional theory inadequate?

The applicability of time-dependent density functional theory (TD-DFT) is tested in describing ¹L _a and ¹L _b π-π*states in indole, azaindole, indene, and benzimidazole. Several density functionals including popular three hybrid functionals (B3LYP, PBE0, and mPW1PW91), two meta-GGA functionals (M06-L and M06-2X), and four long-range corrected (CAM-B3LYP, ωB97XD, LC-BLYP, and LC-ωPBE) density functionals have been considered for the present study. The 6-311+G(2d,p) basis set incorporated with two sets of Rydberg sp functions for carbon and nitrogen atoms is utilized. The range-separation parameters for the calculations with the long-range corrected density functionals were tuned by enforcing the DFT version of Koopmans' theorem, and the effect of this tuning on the accuracy of the results is also examined. Results show that all of the hybrid and meta-GGA functionals predict a wrong order of ¹L _a and ¹L _b π-π*states in indole and azaindole. Although all of the LC functionals correctly predict that ¹L _b is the lowest excited state in indole, the energy gap calculated between the ¹L _b and ¹L _a state is much smaller than the value observed in the experimental studies. In the case of azaindole, only LC-ωPBE and LC-BLYP functionals could manage to reproduce the correct order of states; however, here too, the calculated energy gap between the two π-π*states is very small compared to the experimental value. Overall, the ¹L _b state excitation energies derived with all of the functionals are overestimated. In contrast, all of the nine selected functionals correctly reproduce the order of states in indene and benzimidazole. The origin of this differing performance is analyzed. Also in the study, oscillator strengths and dipole moments of the excited states are derived, and two other important states, π-δ*and n-π*states, that could play important role in the photochemistry of these molecules are examined.