THEORY OF INTERNAL ROTATION IN HYDROGEN PEROXIDE

$^{\dag}$Corning Glass Works Foundation Fellow 1962-63. $^{1}$K. T. Hecht and D.M. Dennison, J. Chem. Phys. 26, 40 (1957). $^{2}$J.T. Massey and D. R. Bianco, J. Chem. Phys. 22, 442 (1954).Author Institution: Harrison, M. Randall Laboratory of Physics, The University of Michigan“An internal rotation Hamiltonian for hydrogen peroxide is constructed assuming the relative position of the two O-H groups is governed by a potential of the form $V(x) = V_{1} \cos x + V_{2} \cos 2x + V_{3} \cos 3x$ where x is the dihedral angle between the two groups. By the use of a contact transformation1 the Hamiltonian is put in the form H (asymmetric top) + H (internal motion) where the interaction between internal and overall rotation arises through the x-dependence of the inertial parameters in H (asymmetric top) which are expanded in Fourier series of x. The internal motion wave equation $[(1/2 I]\stackrel{2}{Px} + V(x)] \Psi = E \Psi$ is solved on an IBM 7090 computer where the potential constants $V_{1}, V_{2}, V_{3}$ are chosen to fit the infrared spectra of Hunt and Peters (see following abstract). Digitalization of the Hamiltonian to second order by perturbation theory is sufficient is account for the observed Q-branch shapes in the infrared. Using centrifugal detention energy terms and the above theory the microwave $lines^{2}$ $\nu_{3} = 22054.5$ Mc/sec and $\nu_{4} = 27639.6$ Mc/sec are identified as $\tau, J, K = 1,1,8,6\rightarrow 1,3,7,5$ and $1,3,8,5\rightarrow 1,1,9,6$ respectively. The $n=1, \tau=1$ and 3 torsional levels lie 254.2 and $370.8\;cm^{-1}$ above the ground state. The form of the dipole moment operator is assumed to be $\mu_{0} \cos \stackrel{x}{2}$ and $\mu_{0}$ is found to be 3.15 D in agreement with the value obtained from the torsional ground state transitions. The deuterated species H--O--O--D and $D_{2}O_{2}$ will be discussed.