The failure of generalized gradient approximations (GGAs) and meta-GGAs for the two-center three-electron bonds in He2+, (H2O)2+, and (NH3)2+

The radical cations He(2)(+) (H(2)O)(2)(+), and (NH(3))(2)(+) with two-center three-electron A-A bonds are investigated at the configuration interaction (CI), accurate Kohn-Sham (KS), generalized gradient approximation (GGA), and meta-GGA levels. Assessment of seven different GGA and six meta-GGA methods shows that the A(2)(+) systems remain a difficult case for density functional theory (DFT). All methods tested consistently overestimate the stability of A(2)(+): the corresponding D(e) errors decrease for more diffuse valence densities in the series He(2)(+) > (H(2)O)(2)(+) > (NH(3))(2)(+). Upon comparison to the energy terms of the accurate Kohn-Sham solutions, the approximate exchange functionals are found to be responsible for the errors of GGA-type methods, which characteristically overestimate the exchange in A(2)(+). These so-called exchange functionals implicitly use localized holes. Such localized holes do occur if there is left-right correlation, i.e., the exchange functionals then also describe nondynamical correlation. However, in the hemibonded A(2)(+) systems the typical molecular (left-right, nondynamical) correlation of the two-electron pair bond is absent. The nondynamical correlation built into the exchange functionals is then spurious and yields too low energies.