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The energy of the ground state of the carbon monoxide molecule has been calculated by multi-configuration methods of self-consistent field (MC-SCF), configuration interaction (MR-CI+Q), and the averaged coupled pair functional (MR-ACPF) on a detailed grid and in a wide range of internuclear distances 0.1 < R < 17.0 Å. The scalar relativistic correction is systematically taken into account using the effective second-order Douglas–Krol–Hess (DKH) Hamiltonian. Quantum electrodynamic (QED) correction to mass invariant potential has been estimated for the first time using a model one-electron operator, which has been built independently for each atom. The calculations have been carried out using the family of correlation-consistent aug-cc-pwCVnZ-DK (n = 3, 4, 5) bases for both atoms followed by extrapolation to the complete basis set (CBS) in the framework of the empirical three-point scheme. The resulting potential has been found to be very close to its semi-empirical counterpart near the equilibrium position and at the dissociation limit. It is expected that the most significant clarification ab initio potential corresponds to the intermediate region 2.0 < R < 4.5 Å, where reliable experimental data are not yet available. [ABSTRACT FROM AUTHOR]