Possible calcium centers for hydrogen storage applications: An accurate many-body study by AFQMC calculations with large basis sets

Weak H$_2$ physisorption energies present a significant challenge to first-principle theoretical modeling and prediction of materials for H storage. There has been controversy regarding the accuracy of DFT on systems involving Ca cations. We use the auxiliary-field quantum Monte Carlo (AFQMC) method\footnote{ S.~Zhang and H.~Krakauer, Phys.~Rev.~Lett.~\textbf{90}, 136401 (2003); W.~A.~Al-Saidi, S.~Zhang and H.~Krakauer, J.~Chem.~Phys.~\textbf{124}, 224101 (2006). } to accurately predict the binding energy of Ca$^+$\,-\,4{H}$_2$. AFQMC scales as $N_{\textrm{\small{basis}}}^3$ and has demonstrated accuracy similar to or better than the gold-standard coupled cluster CCSD(T) method. We apply a modified Cholesky decomposition to achieve efficient Hubbard-Stratonovich transformation in AFQMC at large basis sizes. We employ the largest correlation consistent basis sets available, up to Ca/cc-pCV5Z, to extrapolate to the complete basis limit. The calculated potential energy curve exhibits binding with a double-well structure.