Quantum Chemical Investigation on Indole: Vibrational Force Field and Theoretical Determination of Its Aqueous p<i>K</i><sub>a</sub> Value

Indole and its derivatives are molecules which play important roles in different fields, from biology to pharmacology. Here we report a thorough investigation on the anharmonic force fields of indole as well as the ab initio determinations of its gas phase basicity and aqueous p<i>K</i><sub>a</sub> value. For the geometry optimizations, the calculations have been performed using both density functional (DFT) and second-order Møller–Plesset (MP2) levels of theory employing different basis sets. Anharmonic force fields have been obtained employing both the B3LYP and the B97-1 functionals and an hybrid approach: the best agreement to the experimental data has been determined employing the B3LYP functional combined with the recently developed N07D basis set (mean unsigned error, MUE, of 5.1 cm<sup>–1</sup> and a root-mean-square error, RMSE, of 7.2 cm<sup>–1</sup>). Gas phase basicity and proton affinity have been computed employing several computational schemes, namely the G3 and G4 Gaussian models, the complete basis set (CBS) extrapolation methods of Petersson and co-workers, several DFT calculations, and different hybrid extrapolation schemes based on combining single-point energy calculations performed at MP2 as well as at coupled cluster level of theory with single, double and perturbative triple excitations, CCSD­(T). Regarding the aqueous p<i>K</i><sub>a</sub> computations, two implicit solvation models (SMD and SM8) have been employed to determine the free energy of solvation and the corresponding p<i>K</i><sub>a</sub> value.