We report accurate calculations of vibrational energy levels of HOOH, DOOD, and HOOD up to 10 000 cm−1 above the zero-point energy levels on a high-quality ab initio potential energy surface. These energies were determined by the Lanczos algorithm based on repetitive matrix-vector multiplication. The six-dimensional vibrational Hamiltonian in the diatom–diatom Jacobi coordinate system was discretized in a mixed basis/grid representation. A direct product potential optimized discrete variable representation was used for the radial coordinates, while nondirect product spherical harmonics were employed for the angular degrees of freedom. The calculation and storage of the potential matrix in the angular finite basis representation were avoided by using a series of one-dimensional pseudo-spectral transformations to a direct product angular coordinate grid. The diatom–diatom exchange symmetry, when applicable, was incorporated into the basis, which significantly enhanced the efficiency for symmetric isotopomers. A few hundred low-lying vibrational levels of each isotopomer were assigned and compared with experimental data.

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The vibrational spectrum of SO2 up to 15 000 cm−1 is calculated using a low-storage filter-diagonalization method based on the Chebyshev propagation. The Hamiltonian in the Radau coordinates is expressed on a direct product of one-dimensional discrete variable representation (DVR) grids. The extended symmetry-adapted discrete variable representation (ESADVR) is implemented to accelerate the calculation of the action of kinetic energy operators, and multiple symmetry-adapted autocorrelation functions are obtained from the propagation of a single wave packet. Approximately 1000 vibrational energy levels are identified and some of them are assigned according to the nodal structure of the eigenstates. Comparison with experimental data indicates reasonably good agreement (<1%). The agreement, however, deteriorates with increasing energy, implicating imperfection in the potential energy surface used in the calculation. Statistical analyses indicate that the system is mostly regular in this energy range. There is some evidence of a normal-to-local mode transition at higher energies.

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