Far-Infrared Spectrum and Hindering Potential of Deuterium Peroxide

The hindered-rotation motion in the deuterium peroxide molecule is investigated through a study of the far-infrared absorption of the vapor. A 1-m focal-length vacuum grating spectrometer was used to scan the region from 20 to 400 cm−1 with an average resolution of 0.4 cm−1. Seven perpendicular-type hindered-rotation bands characterized by prominent Q branches and unresolved P- and R-branch structure are observed in the spectrum. The band centers are located at 1.88, 42.3, 123.5, 136.8, 206.7, 250.9, and 302.6 cm−1. From these it is determined that, relative to the ground state, the first five excited hindered-rotation states are at 1.88, 208.6, 250.9, 387.7, and 511.2 cm−1. A theory of internal rotation, developed for an earlier application to the far-infrared spectrum of hydrogen peroxide, is applied to the D2O2 spectrum. In this theory the only internal degree of freedom is the dihedral angle x defining the relative position of the two OD groups. The Hamiltonian is put in the form H (asymmetric top) +H (internal rotation), where the inertial coefficients are functions of the internal angle x. A three-parameter hindering potential is assumed, V(x)=V1cosx+V2cos2x+V3cos3x and the internal-rotation wave equation is solved numerically by computer to obtain the potential parameters which reproduce the internal-rotation energy eigenvalues. In the semirigid model adopted, the effective hindering potentials, bond lengths, and bond angles of H2O2 and D2O2 differ slightly. The data do not yield a complete set of effective bond lengths and angles for D2O2, but the product of the OD distance and the sine of the OOD angle is found to be 0.01 Å smaller than its H2O2 counterpart. As a result, the inertial parameter in the internal-rotation wave equation is 2% larger than is predicted from the H2O2 data. Using this adjusted inertial parameter, the hindering potential V(x)=994cosx+641cos2x+55cos3x provides a good fit to the D2O2 data. For this potential function the cis and trans potential barrier heights are 2470 and 377 cm−1, respectively, and the potential minima are 110.8° from the cis configuration. These parameter values are similar to the corresponding H2O2 values of 2460 cm−1, 386 cm−1, and 111.5°.