Relation between O—H stretching frequency and hydrogen bond energy: re-examination of the Badger–Bauer rule

Experimentally a large number of linear relations have been found between the change in OH stretching frequency, Δ, on hydrogen bonding and the hydrogen bond energy, ΔH. A least square treatment of these Δ against ΔH relations is carried out for constant acceptor, variable donor as well as constant donor, variable acceptor systems. Generally, the constant-acceptor plots have much higher values of intercepts than the constant-donor plots. The slopes of the constant-donor plots seem to vary with the basicity of the donor . However, since Δ should go to zero when there is no interaction, it is suggested that the complete Δ against ΔH, relation could be nonlinear. Molecular orbital calculations have been employed to throw light on the Δ against ΔH relation. It is also shown that charge transfer theory when applied to the hydrogen bond predicts a relation between shown that charge transfer theory when applied to the hydrogen bond predicts a relation between ΔH and the quantity (20–2)½ where 0 and , are the free and perturbed OH stretching frequencies.