Long-range potentials and dipole moments of the CO electronic states converging to the ground dissociation limit

The asymptotic, R → ∞, behavior of the potential-energy and dipole-moment functions (PEFs and DMFs) for all six (1,2)Σ + , (1,2)Π, Σ − , and Δ electronic states converging to the ground C( 3 P) + O( 3 P) dissociation limit of the CO molecule are studied in the framework of long-range (LR) perturbation theory. The analytical expressions for the leading coefficients of the LR expansion, C 5 / R 5 for PEF and d 4 / R 4 for DMF, in terms of the atomic quadrupole constants and static dipole polarizabilities are derived. The exact relationships between the LR coefficients for the states of different spatial symmetry are established as well. The analytical results are complemented with the first-principles calculation of the PEFs and DMFs for all the above states at large distances ( R = 5-20 Å). The electronic structure calculation is conducted by means of the multi-reference configuration interaction and the averaged-coupled-pair functional methods, which both implemented the aug-cc-pwCVXZ (X = T, Q, and 5) basis sets and finite-field approach. The dispersion coefficients, C 5 and C 6 , extracted from the ab initio PEFs, are found to be very close to their present and previous theoretical counterparts. The analytically estimated d 4 = −5 DÅ 4 obtained for the ground X 1 Σ + state perfectly agrees with the present ab initio DMF but diverges significantly from the literature data. The potential-energy and dipole-moment functions for six electronic states are obtained both analytically, in the framework of long-range perturbation theory, and numerically, by using first-principles methods.