Binding Energy Curves from Nonempirical Density Functionals. I. Covalent Bonds in Closed-Shell and Radical Molecules

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Abstract
Binding or potential energy curves have been calculated for the ground-state diatomics H2+, He2+, LiH+, H2, N2, and C2, for the transition state H3, and for the triplet first excited state of H2 using the nonempirical density functionals from the first three rungs of a ladder of approximations: the local spin density (LSD) approximation, the Perdew−Burke−Ernzerhof (PBE) generalized gradient approximation (GGA), and the Tao−Perdew−Staroverov−Scuseria (TPSS) meta GGA. Good binding energy curves in agreement with coupled cluster or configuration interaction calculations are found from the PBE GGA and especially from the TPSS meta GGA. Expected exceptions are the symmetric radicals H2+ and He2+, where the functionals suffer from self-interaction error, and the exotically bonded C2. Although the energy barrier for the reaction H2 + H → H + H2 is better in PBE than in TPSS, the transition state H3 is a more properly positioned and curved saddle point of the energy surface in TPSS. The triplet first excited state of H2 obeys the Aufbau principle and thus is one of the exceptional excited states that are computable in principle from the ground-state functional. The PBE GGA and TPSS meta GGA are useful not only for chemical applications but also for the construction of higher-rung nonempirical functionals that can further improve the binding energy curves.