In the present contribution we perfomed ab initio calculations within the supermolecule approach on the vertical excitation spectra of the diatomic van der Waals CO-H2 molecule in its linear most stable O-C⋯H-H structure. They indicated the existence of at least one vibrational state in the ground CO(X1Σ+)-H2(X1Σ g) state, and of five vibrational states in the electronic CO(A1Π)-H2(X1Σg) excited configuration. Since ab initio correlation energy calculations for the excited electronic state are extremely demanding on computational resources, we are forced in practice to use medium-size highly optimized basis sets, suggesting to investigate the use of less demanding ab initio methods to represents the complete interaction energy surface of the excited states of interest. © 1998 Elsevier Science B.V.