Fully coupled four-dimensional quantum-mechanical calculations are presented for intermolecular vibrational states of rigid carbon dioxide dimer for J=0. The Hamiltonian operator is given in collision coordinates. The Hamiltonian matrix elements are evaluated using symmetrized products of spherical harmonics for angles and a potential optimized discrete variable representation (PO-DVR) for the intermolecular distance. The lowest ten or so states of each symmetry are reported for the potential energy surface (PES) given by Bukowski [J. Chem. Phys. 110, 3785 (1999)]. Due to symmetries, there is no interconversion tunneling splitting for the ground state. Our calculations show that there is no tunneling shift of the ground state within our computation precision (0.01 cm(-1)). Analysis of the wave functions shows that only the ground states of each symmetry are nearly harmonic. The van der Waals frequencies and symmetry adapted force constants are found and compared to available experimental values. Strong coupling between the stretching coordinates and the bending coordinates are found for vibrationally excited states. The interconversion tunneling shifts are discussed for the vibrationally excited states. (C) 2000 American Institute of Physics. [S0021-9606(00)00911-9].