  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 Angstrom. Density functional calculations using common
functionals such a LDA and B3LYP differ substantially from the QMC binding
curve. We show that use of full Hartree-Fock exchange and 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.
