Inductive effect of methyl group in a series of methylated indoles: A graph theoretical analysis in the light of density functional theory and correlation with experimental charge transfer transition energies

The inductive effect of methyl group has been quantified by expressing highest occupied molecular orbital (HOMO) and HOMO-1 energies of indole and a series of methylated indoles using a combination of graph theory (GT) and the Coulson-Longuett-Higgins perturbation method. By correlating these expressions with the corresponding Kohn-Sham orbital energies of the indoles obtained by density functional theory (DFT) calculation at the B3LYP/6-31++G(d,p) and M06-2X/6-31++G(d,p) levels of theory, the inductive effect parameter h(Me) has been estimated; the Coulomb integral a of pi-conjugated carbon atom also comes out from the analysis. A correlation of the GT results with the HOMO and HOMO-1 energies obtained by the HF/STO-3G method yield almost the same values of h(Me) and alpha. Finally, when these estimated h(Me) and alpha are used to calculate the vertical ionization potentials of the methylated indoles in the series, an excellent correlation with experimental charge transfer transition energies of their molecular complexes with tetracyanoethylene is obtained which complies with Mulliken's theory of charge transfer.