Internal-Rotation in Hydrogen Peroxide: The Far-Infrared Spectrum and the Determination of the Hindering Potential

Abstract

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+V3cos3xV(x)=V1cosx+V2cos2x+V3cos3x. The internal‐rotation wave equation [αpx2+V(x)]M(x) = EM(x)[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