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.