Internal-Rotation in Hydrogen Peroxide: The Far-Infrared Spectrum and the Determination of the Hindering Potential
The torsional oscillation between the two OH groups of the hydrogen peroxide molecule is investigated through a study of the far-infrared absorption spectrum of the molecule. A 1-m-focal-length vacuum grating monochromator was used to scan the region from 15 to 700 cm-1 with an average resolution of 0.3 cm-1. The observed spectrum contains seven perpendicular-type bands of which only the Q branches are resolved. The centers of the seven bands are at 11.43, 116.51, 198.57, 242.76, 370.70, 521.68, and 557.84 cm-1. These bands result from transitions between different states of the internal rotation and their identification makes it possible to construct the internal-rotation energy level scheme through the first five excited states. Relative to the torsional ground state, these levels occur at 11.43, 254.2, 370.7, 569.3, and 775.9 cm-1.A theory of internal rotation in the hydrogen peroxide molecule is developed for use in the analysis of the far-infrared spectra. In this theory, the Hamiltonian is constructed assuming all structural distances and angles fixed except the dihedral angle x defining the relative position of the two OH bars. By the use of a contact transformation the Hamiltonian is put in the form H (asymmetric top)+H(internal rotation) where the interaction between the internal and over-all rotations arises through the x dependence of the inertial parameters of H(asymmetric top). It is assumed that the relative position of the two OH bars is governed by a potential-energy function of the form V(x)=V1cosx+V2cos2x+V3cos3x. The internal-rotation wave equation [αpx2+V(x)]M(x)=EM(x) is solved numerically by an electronic-computer and the potential function parameters V1=993 cm-1, V2=636 cm-1, and V3=44 cm-1 are chosen to fit the internal-rotation energy-level scheme. The trans and cis potential barrier heights are 386 and 2460 cm-1, respectively, and the potential-function minima are located 111.5° from the cis configuration. Diagonalization of the matrix of the complete Hamiltonian to second order by the use of perturbation theory is sufficient to account for the observed Q-branch shapes in the far infrared region. Two microwave frequencies observed by Massey and Bianco at 22 054.5 and 27 639.6 Mc/sec are identified from their Stark effects as the first excited-state transitions J, K, n, τ=8, 6, 1, 1→7, 5, 1, 3 and J, K, n, τ=8, 5, 1, 3→9, 6, 1, 1, respectively, where the internal-rotation quantum number n=1 denotes the first excited torsional state and where τ denotes trans symmetric (τ=1 and 2) or antisymmetric (τ=3 and 4) states. The form of the dipole moment operator is assumed to be μ0 cos(x/2) and μ0 is found to be 3.15 D in agreement with the value obtained from the torsional ground-state transitions. Two J=0 microwave series observed by Massey, Beard, and Jen in a mixed sample of the deuterated species D2O2 and HOOD give confirmation of the potential function determined from the H2O2 analysis. The K=4→5 series is identified as the D2O2 first excited torsional state transition n=1→1, τ=4→2. The K=0→1 series is identified as the HOOD torsional ground-state transition n=0→0, τ=4→2. Only very small changes in the trans barrier height are necessary to fit the constant terms of these series exactly. These changes, which are expected to arise from vibration-internal rotation interactions, show a reasonable progression from H2O2 to D2O2: V (trans, HOOH) = 386 cm-1, V (trans, HOOD) = 381 cm-1 and V (trans, DOOD) = 378 cm-1.