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

The radical cations He-2(+) (H2O)(2)(+), and (NH3)(2)(+) with two-center th ree-electron A-A bonds are investigated at the configuration interaction (C I), 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 functio nal theory (DFT). All methods tested consistently overestimate the stabilit y of A(2)(+): the corresponding D-e errors decrease for more diffuse valenc e densities in the series He-2(+) > (H2O)(2)(+) > (NH3)(2)(+). Upon compari son to the energy terms of the accurate Kohn-Sham solutions, the approximat e exchange functionals are found to be responsible for the errors of GGA-ty pe methods, which characteristically overestimate the exchange in A(2)(+). These so-called exchange functionals implicitly use localized holes. Such l ocalized holes do occur if there is left-right correlation, i.e., the excha nge functionals then also describe nondynamical correlation. However, in th e hemibonded A(2)(+) systems the typical molecular (left-right, nondynamica l) correlation of the two-electron pair bond is absent. The nondynamical co rrelation built into the exchange functionals is then spurious and yields t oo low energies.