Tunneling splittings in vibrational spectra of non-rigid molecules: VIII. Six-dimensional tunneling dynamics of hydrogen peroxide and its isotopomers Original Research Article

The six-dimensional torsion–vibration Hamiltonian of H2O2 is derived. This Hamiltonian includes a tunneling coordinate dependent kinetic energy operator and a potential energy surface, quartic in the small-amplitude transverse coordinates. The parameters of this Hamiltonian are derived from the equilibrium geometries and the eigenvectors and eigenfrequencies of the normal modes in the ground and the two (cis/trans) transition states. The quantum dynamical problem is solved within the perturbative instanton approach developed in previous papers of this series, which is generalized here for excited states situated above the barrier and for anharmonic transverse vibrations. Globally uniform semiclassical wave functions and tunneling splittings in the ground and low-lying excited states are calculated. The strong kinematic and squeezed potential couplings between the wide-amplitude torsional motion and bending vibrations are shown to be responsible for vibrationally assisted tunneling and for the significant dependence of the tunneling splittings on the quantum numbers of transverse vibrations. Mode specific isotope effects of tunneling splittings are predicted. The dependence on the quantum numbers of overall rotation is found to be insignificant.