SCF-MO-LCGO calculations are performed for H502+ as a model illustrating the properties of a symmetrical hydrogen bond with a double-minimum potential well. The potential curves for the proton in the hydrogen bond with and without electrical fields for various 0-0 distances are calculated, along with the dipole moments, polarizabilities, hyperpolarizabilities, and transition moments of the OH stretching vibrations in the hydrogen bond. The total dipole moment is almost twice as large as the contribution of the proton alone for displacements which are not too large. The relation between the dipole moment and the displacement cannot be approximated linearly. Thus hyperpolarizabilities are of importance. The most important result obtained is that the polarizability is about two orders of magnitude larger than usual polarizabilities. The polarizability of unsymmetric hydrogen bonds may also be considerably larger. The large polarizability causes three interaction effects: an interaction between symmetrical hydrogen bonds via proton dispersion forces, an induced-dipole interaction of the hydrogen bonds with the anions and the dipole fields of the solvation molecules, and an interaction between the transitions in the hydrogen bond and other, especially the intermolecular, vibrations. These interactions cause the strong continuous absorption which is observed in the ir spectra with liquid systems containing such hydrogen bonds. The smaller polarizability of unsymmetrical hydrogen bonds causes band broadening.A continuous absorption was observed in the infrared spectrum on investigating acid and base solutions in the range of the fundamental vibrations1 2 and in the range of the overtones,3•4 567as well as with acidic and basic polyelectrolytes.5-8 This is caused in the acid solutions by H502+ groupings and with bases by H302_ groupings.8 The continuum is not only observed in the presence of these bonds between water molecules

The influence of the coupling of the proton movement and the H bond stretching vibration in a double minimum potential energy surface on the energy levels, transitions, induced dipole moments and polarisabilities is calculated ub initio as a function of an electric field for the H,O: system. The high polarisability of the hydrogen bonds remains to a large extent unchanged due to the coupling. New types of transitions occur, particularly when the tunnelling frequency and the frequency of the bond stretching vibration are comparable in size. Especially in this case numerous Fermi resonances occur due to the shift of the energy levels in the electric field, which leads to a considerable increase in the number of transitions. It is shown that the change of the frequencies of the transitions due to the induced dipole interaction of the bonds with fields from their environment is a decisive cause of the variety of energy level differences observed as a continuous absorption in the i.r. spectrum of such systems.

The displacement of the excess charge of the proton in acid solutions is caused by a structure migration of groupings H5O2+ or H9O4+ . The processes which take place during structure migration are discussed on the basis of results gained in IR-investigations. In an electrical field the structure migration is given a preferred direction. The hydrogen bond with the tunneling proton in H5O2+ and the grouping H3O+ in H5O2+ become polarized. Comparison of both polarizabilities demonstrates that, contrary to previous assumptions, the polarization of the hydrogen bond is the field-dependent mechanism. This conclusion is reached upon calculating the polarizability of the hydrogen bond with a symmetrical double minimum potential well. It is shown that the polarizability is extremely large, being approximately two orders of magnitude greater than that of H3O+ . Despite the large polarizability, the shift of the weights of the proton boundary structures is very small for the external fields usually applied in conductivity measurements. It is demonstrated, however, that this slight shift is large enough for the structure diffusion to obtain a preferred direction consistent with the anomalous high proton conductivity.

The wavenumber dependence of the continuous ir absorbance of strong aqueous acid solutions is calculated on the basis of SCF calculations on H5O2+. The two strongly coupled modes (νOH and νOO stretching vibrations) of the hydrogen bond in H5O2+ are treated exactly. A distribution of the local electrical field strength is taken into account since the hydrogen bond is easily polarizable. Furthermore, a distribution of OO bond lengths is used with these calculations. The calculated continua—wavenumber dependence, the absolute intensity, and the structure—are in close agreement with the ir continua observed with aqueous solutions of strong acids. The intensity of the calculated continuum decreases with increasing strength of the mean local electrical field at the polarizable hydrogen bonds, and it is independent of temperature over a very large temperature range, both of which are in very good agreement with experiment. The influence of the hydrogen bond lengths is studied, considering the system as a model for short, medium, and long hydrogen bonds. Relatively short polarizable hydrogen bonds show continua only below 1500 cm−1. With relatively long polarizable hydrogen bonds, the continuum is much more intense in the region 3000–1600 cm−1. Medium long polarizable hydrogen bonds show a continuous absorption in the whole region below 3400 cm−1. The results demonstrate that the electrical field as well as the bond length distributions are necessary conditions for the occurrence of ir continua. The continua occur in the whole range below 3400 cm−1 when the OO distribution includes the typical double minimum case with a moderate barrier.

On the basis of former ab initio calculations on H50:, the deuterium bond of D50: is treated by considering vibrations in two dimensions. Vibrational energy levels, intensities and polarizabilities dependent on the electrical field strengths at the deuterium bond are calculated for a variety of bond lengths. From the absorption intensities continuous absorption spectra are calculated, taking into account distributions of electrical field strengths and 0-0 distances. These continua are compared with i.r. spectra of aqueous solutions of HCI or DCI and H2S04 or D2S04 in H 2 0 or D20, respectively. The calculated isotope factor of the intensity I v ~~/ l v ~~, which is dependent on wavenumber, agrees with experimental data.