Ground- and excited-state diatomic bond lengths, vibrational levels, and potential-energy curves are determined using conventional and localized Hartree–Fock (LHF)-based density-functional theory. Exchange only and hybrid functionals (with various fractions of exchange) are considered, together with a standard generalized gradient approximation (GGA). Ground-state bond lengths and vibrational wave numbers are relatively insensitive to whether orbital exchange is treated using the conventional or LHF approach. Excited-state calculations are much more sensitive. For a standard fraction of orbital exchange, N2 and CO vertical excitation energies at experimental bond lengths are accurately described by both conventional and LHF-based approaches, providing an asymptotic correction is present. Excited-state bond lengths and vibrational levels are more accurate with the conventional approach. The best quality, however, is obtained with an asymptotically corrected GGA functional. For the ground and lowest four singlet excited states, the GGA mean absolute errors in bond lengths are 0.006 Å (0.5%) and 0.011 Å (0.8%) for N2 and CO, respectively. Mean absolute errors in fundamental vibrational wavenumbers are 49 cm−1 (2.7%) and 68 cm−1 (5.0%), respectively. The GGA potential-energy curves are compared with near-exact Rydberg–Klein–Rees curves. Agreement is very good for the ground and first excited state, but deteriorates for the higher states.

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