Estimations of FH···X hydrogen bond energies from IR intensities: Iogansen's rule revisited

Abstract

In this work the possibility of using the IR intensity of the stretching vibration ν_s of proton donor group for estimation of hydrogen bond strength was investigated. For a set of complexes with FH···X (X = F, N, O) hydrogen bonds in the wide range of energies (0.1-49.2 kcal/mol) vibrational frequencies ν_s and their intensities A were calculated (CCSD at complete basis set limit). The validity of the previously proposed linear proportionality between the intensification of the stretching vibration ν_s in IR spectra and hydrogen bond enthalpy -ΔH = 12.2 $\text{∆}\sqrt{A}$ (A. V. Iogansen, Spectrochimica Acta A 1999) was examined. It is shown that for a range of similar hydrogen bond types with complexation energies ∆E <15 kcal/mol the ∆E( $\text{∆}\sqrt{A}$ ) function remains similar to that proposed in the Iogansen's work, while upon strengthening this dependency becomes significantly nonlinear. We examined two other parameters ( $\text{∆}\sqrt{\frac{A}{{\nu }_s}}$ and $\text{∆}\sqrt{A\bullet m_R}$ ) related to IR intensity as descriptors of hydrogen bond strength which are proportional to transition dipole moment matrix element and mass-independent dipole moment derivative. It was found that the dependency ∆E( $\text{∆}\sqrt{\frac{A}{{\nu }_s}}$ ) stays linear in the whole studied range of complexation energies and it can be used for evaluation of ∆E from infrared spectral data with the accuracy about 2 kcal/mol. The mass-independent product $\text{∆}\sqrt{A\bullet m_R}$ is an appropriate descriptor for sets of complexes with various hydrogen bond types. Simple equations proposed in this work can be used for estimations of hydrogen bond strength in various systems, where experimental thermodynamic methods or direct calculations are difficult or even impossible.

Keywords: IR intensities; IR spectroscopy; hydrogen bond strength; hydrogen bonds; quantum-chemistry.