Benchmark study of popular density functionals for calculating binding energies of three-center two-electron bonds

Density functional theory (DFT) can be used to study the three-center two-electron (3c2e) bonding mode, which is universal in catalysts containing alkaline-earth (Ae) and boron-group (Bg) elements. However, because of the delocalization pattern of the 3c2e bond, the wavefunction cannot be accurately described by DFT methods. The calculated energies of Ae and Bg catalysts therefore fluctuate greatly when different functionals are used, largely because of inconsistent DFT-calculated binding energies of 3c2e bonds. Nevertheless, with the development of supercomputers and theoretical calculation software, the DFT method is becoming increasingly popular for studying Ae and Bg catalysts. In this study, we compared the performances of 21 functionals with the high-level composite G3B3 method in calculations for the binding energies of 3c2e bonds. Several frequently used post-Hartree-Fock methods were also tested. The calculation results indicate that the M06-2X, MN12-L, and MN15 functionals give consistent and reliable binding energies for common 3c2e bonds. © 2018 Wiley Periodicals, Inc.