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

Abstract

Experimentally a large number of linear relations have been found between the change in OH stretching frequency, Δν̅, on hydrogen bonding and the hydrogen bond energy, ΔH. A least square treatment of these Δν̅ 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 Δν̅ should go to zero when there is no interaction, it is suggested that the complete Δν̅ against ΔH, relation could be nonlinear. Molecular orbital calculations have been employed to throw light on the Δν̅ 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 (ν̅²₀−[ν̅²)^½ where ν̅₀ and ν̅, are the free and perturbed OH stretching frequencies.