Recently, several empirical models of the potential energy function (PEF) of the ground electronic state of CO have been developed by Coxon and Hajigeorgiou using the direct-potential-fit (DPF) analysis. These models reproduce more than twenty thousand of observed ro-vibrational line positions within their experimental accuracies and follow the theoretically predicted long-range asymptotic behavior of the potential beyond Le Roy's radius. However, the applicability of these models to calculations of the intensities of weak transitions is not obvious due to limitations discussed in this work. Here, we make the next step by imposing an additional requirement that the model has to display physical behavior outside the region to which the available spectroscopic data pertain. We perform ab initio calculations of the potential in the short-range region r = 0.3-0.8 Å where the potential increases well above the dissociation limit and include these data along with the estimated uncertainties in the DPF analysis. At smaller r, our PEF tends to the well-known united-atom limit. In the long-range region, it follows the ab initio data with their estimated accuracies available in the literature. On top of the above, the model is analytical, i.e. it has continuous derivatives of all orders. The model constructed is a linear function of twenty three adjustable parameters, and a non-linear function of additional five parameters. The properties of the new PEF are investigated in comparison with the previous empirical model due to Coxon and Hajigeorgiou (2004). Our PEF provides reproduction of all observed lines at the same level of accuracy. The new potential changes the intensities of high overtone transitions dramatically. In addition, we find that the anomalies in the purely rotational and ro-vibrational spectra change their intensities between the two PEFs even for the low-v bands.
