Ab initio cluster calculations for an excited state of the system CO/Cr2O3 (0001) are presented. A CO(a (3)Pi)-like state generated by an internal electronic excitation of the CO molecule (5sigma --> 2pi*) is considered to be a possible intermediate for the laser-induced desorption of CO from Cr2O3 (0001). A four-dimensional potential energy surface (PES) for this state is calculated at the CASSCF level of theory. A few possible alternatives for the desorption intermediate are also discussed. The interaction mechanism between the excited CO molecule and the-surface is analyzed, and it is shown that the change of symmetry of the quadrupole moment of the CO molecule is responsible for the topology of the calculated PES.