Electronic structure data and analytical representations of the potential energy surface for the adsorption of carbon monoxide on a crystalline copper Cu(100) substrate are reviewed. It is found that a previously published and widely used analytical hypersurface for this process [J. C. Tully, M. Gomez, and M. Head-Gordon, J. Vac. Sci. Technol. A 11, 1914 (1993)] represents rather poorly the data obtained from a slab type calculation of the electronic structure. A new, global analytical representation of the potential energy surface for this process is derived via a nonlinear adjustment of parameters. It is more general and fits qualitatively better the electronic structure data. Key characteristic elements of the new surface are the "top" equilibrium adsorption site in the perpendicular arrangement Cu-C-O with Cu-C and C-O distances of 184 and 115 pm, the desorption energy of 0.76 eV and the barrier for lateral diffusion of 33 meV, including approximative corrections for the variation of zero point energy. Anharmonic vibrational fundamentals and overtones are also calculated from six dimensional variational calculations. All these values agree equally well or better with experimental data than previous published theoretical data within estimated uncertainties. The analytical representation is compact and robust, and may be used to describe other adsorption processes of diatomic molecules, including dissociative chemisorption. © 2010 American Institute of Physics.