The van der Waals intermolecular potential for the dimer O2–O2 is determined as a function of both intermolecular and bond coordinates from ab initio calculations for two selected orientations of the diatomic molecules. A recent empirical method based on correlation formulae between the polarizability of the diatoms and some potential features is also employed and extended to determine a model potential which incorporates the dependence on the bond coordinate. The main features of the ab initio and empirical potential energy surfaces are compared and discussed. Quantum scattering calculations of the vibrational relaxation of O2(v) are performed by using both types of potentials for each selected geometry, providing evidence for the key role played by the representation of the vibrational dependence of the potential.