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, ${\mathrm{V(x)=V}}_1\cos {\mathrm{x+V}}_2\cos {\text{2x+V}}_3\cos \text{3x}$ 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 $\text{V(x)=994}\cos \text{x+641}\cos \text{2x+55}\cos \text{3x}$ 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°.