Quantum Monte Carlo calculations of dihydrogen binding energetics on Ca cations: An assessment of errors in density functionals for weakly bonded systems

We investigate the binding of single and quadruple hydrogen molecules on a positively charged Ca ion. By comparing with benchmark quantum Monte Carlo (QMC) calculations we demonstrate wide variability in other more approximate electronic-structure methods including common density functionals. Single determinant QMC calculations find no binding at short range by approximately 0.1 eV for the quadruple hydrogen molecule case, for a fixed hydrogen bond length of 0.77 Å. Density-functional calculations using common functionals such a local density approximation and B3LYP differ substantially from the QMC binding curve. We show that use of full Hartree-Fock exchange and Perdew-Burke- Ernzerhof (PBE) correlation (HFX+PBEC) obtains close agreement with the QMC results, both qualitatively and quantitatively. These results both motivate the use and development of improved functionals and indicate that caution is required applying electronic-structure methods to weakly bound systems such as hydrogen-storage materials based on metal-ion-decorated nanostructures.