Validity of the Hammett equation for isolated molecules: basicity of 3- and 4-substituted benzonitriles

Abstract

Atomic and electronic energies of 27 3- and 4-substituted benzonitriles and of their protonated forms were calculated within the framework of density functional theory (DFT) at the B3LYP/6-311 + G(d,p) level. The substituent effects were expressed by isodesmic homodesmotic reactions, separately for the molecule of benzonitrile [eqn. (7)], for the protonated form [eqn. (8)] and for the resulting basicity [eqn. (6)]. With several molecules, actual site of protonation may be ambiguous and was determined in most cases from the energies of both protonated forms. In particular 4-aminobenzonitrile, 3-formylbenzonitrile and both nitrobenzonitriles are protonated on the CN group, while 3-aminobenzonitrile and both dimethylaminobenzonitriles on the substituent. The behaviour of methylsulfonylbenzonitriles is still doubtful. The validity of the Hammett equation was tested by correlation with the energies of equally substituted benzoic acids. It holds within the gradually extended range of validity with gradually decreased accuracy: Strictly speaking, it is valid only for meta derivatives; para derivatives with acceptor substituents can be still included at the cost of accuracy but para donors deviate significantly. The DFT model is not the best for the protonated nitriles. From several models tested, best agreement with the experimental gas-phase basicities was achieved with MP2/6-311 + G(d,p) but for the purpose of testing the Hammett equation the DFT model is good when only relative energies are compared.