HOMO energy of indole: A graph-theoretical analysis from charge-transfer bands

Abstract

The effect of methyl (Me-) substitution of the ring hydrogen atoms of indole on the HOMO energy the latter (in HMO formalism) has been analysed gra -theoretically. It has been shown that the apparently scattered values of CT transition energies of the . π-molecular complexes of methylated indoles with tetracyanoethylene follow a systematic trend when the inductive effect (+1) of Me- is considered. The method of calculation involves (i) construction of characteristic polynomial (CP) of relevant graphs through McClelland's graph-factorisation technique, (ii) locating the HOMO from CP's using Budan- Fourier theorem and (III) calculation of squares of eigencoefficients of the HOMO by Ulam subgraph method. The whole scheme of obtaining the HOMO energies of methylated indoles rests on Coulson- Longuet-Higgins perturbation theory in HMO formalism but the main purpose of the present work is to demonstrate how graph-theoretic techniques can be used to carry out perturbational calculations without necessitating complete solution of the Huckel hamiltonian eigenproblem.