Quantum aspects of torsional vibrations in the HO₃H, DO₃H and DO₃D molecules

The hydrogen trioxide (HT) molecule HOOOH is 1) a prototype for a class of molecules of the form X(ZY)₂ with two equivalent internal tops (ZY) and 2) the second representative of the polyoxides series of the form HO_nH (n ≥ 2). Due to this, it is the subject of close attention of researchers. In this paper, we performed a group theory analysis of the torsional and spin states of the HOOOH, DOOOH, and DOOOD molecules. The relationships have been established between the symmetry species of the C_2V(M) molecular symmetry group to which the HOOOH and DOOOD molecules belong, and the symmetry species of the C₂ and C_S point groups to which the equilibrium configurations of trans- and cis-conformers of the above molecules belong, respectively. 2D PES and 2D surfaces of kinematic coefficients related to torsional vibrations of hydroxyl groups were calculated at the complete basis set (CBS) limit by extrapolating the results of calculations at the MP2/cc-pVTZ and MP2/cc-pVQZ levels of theory. For all the three molecules, the energies of the stationary torsional states were computed using the Fourier method for a numerical solution of the 2D vibrational Schrödinger equation. Symmetry species of torsional states and the values of quantum numbers defining the types of torsional vibrations were found by analyzing the torsional wave functions. The selection rules for transitions between torsional states in the dipole approximation were also formulated.