Structural and vibrational analysis of indole by density functional and hybrid Hartree–Fock/density functional methods
Accurately assigned vibrational frequencies for indole and its derivatives, particularly tryptophan, are critical for analyses of vibronic coupling, excited state fluorescence spectra and resonance Raman spectra. Examination of published, assigned, experimental vibrational frequencies for indole reveals that while most observed bands assigned to fundamentals are in agreement among the different reports, there are notable exceptions in six different spectral regions. We have calculated the structure and assigned the harmonic vibrational spectrum of indole by application of local and gradient-corrected density functional theory methods (DFT) and a hybrid Hartree–Fock/density functional (HF/DFT) method. The hybrid method B3LYP predicts the structure of indole within 0.005 Å and 1.1° of a recently published CASSCF structure. Unscaled harmonic frequencies calculated with the gradient-corrected method BLYP with the 6-31G(d) basis set exhibit the best overall agreement with experiment with an RMSD of 31 cm–1 for all modes including hydrogen stretching and bending. The hybrid B3LYP method gives frequencies in closest agreement for the out-of-plane modes, except for the NH wagging mode. Our calculations, which include electron correlation effects for approximately the same computational resources as a Hartree–Fock calculation, predict two fundamentals in the 1330–1360 cm–1 region, where a Fermi resonance pair has previously been hypothesized. This report demonstrates the utility of DFT and HF/DFT methods for heteroaromatic molecules such as indole. We provide the first complete assignment of vibrational modes for indole based on unscaled calculated frequencies which have not been empirically fit to experiment.