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. (C) 2001 American Institute of Physics.