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.

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